├── COPYING ├── COPYING.LESSER ├── README ├── project.clj └── src └── probabilistic_clojure ├── embedded ├── api.clj ├── choice_points.clj ├── demos.clj ├── fit_poly.clj ├── lda_demo.clj ├── sampling.clj ├── test_deps.clj ├── test_sampling.clj └── tests.clj ├── monadic ├── api.clj └── demos.clj ├── original ├── constraint-propagation.clj ├── demos.clj ├── metropolis_hastings.clj └── scratch.clj └── utils ├── finite_distributions.clj ├── sampling.clj └── stuff.clj /COPYING: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 3, 29 June 2007 3 | 4 | Copyright (C) 2007 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU General Public License is a free, copyleft license for 11 | software and other kinds of works. 12 | 13 | The licenses for most software and other practical works are designed 14 | to take away your freedom to share and change the works. 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Inspired by the bher compiler of the MIT Scheme dialect Church (see http://projects.csail.mit.edu/church/wiki/Church) it uses Metropolis Hastings MCMC to sample from probabilistic programs. 2 | 3 | The file src/probabilistic_clojure/monadic/api.clj contains the basic API for using the library. In the same directory, the file demos.clj demonstrates how generative models can be implemented. It relies on incanter (available from incanter.org) for graphical output and probability distributions. 4 | 5 | For a quick start clone the repository, add the src directory (as well as incanter.jar) to your Java classpath and (use 'probabilistic-clojure.monadic.demos). Then run (test-mixture mixture-mem) to fit a Dirichlet mixture of Gaussian with three components to some test data. 6 | 7 | LICENSE 8 | 9 | This software is released under the LGPL. See COPYING.LESSER for details. -------------------------------------------------------------------------------- /project.clj: -------------------------------------------------------------------------------- 1 | (defproject probnice "0.7.5" 2 | :description "Embedded probabilistic programming in Clojure." 3 | :url "https://github.com/bertschi/ProbClojureNice" 4 | :dependencies [[org.clojure/clojure "1.4.0"] 5 | [org.clojure/algo.monads "0.1.0"] 6 | [incanter "1.3.0-SNAPSHOT"] 7 | [org.apache.commons/commons-math "2.2"]] 8 | :plugins [[codox "0.6.1"] 9 | ;; [lein-swank "1.4.4"]]) 10 | ;; [lein-ritz "0.5.0"]]) 11 | [org.clojure/tools.nrepl "0.2.0-beta10"]]) 12 | 13 | -------------------------------------------------------------------------------- /src/probabilistic_clojure/embedded/api.clj: -------------------------------------------------------------------------------- 1 | ;;; Copyright (C) 2011 Nils Bertschinger 2 | 3 | ;;; This file is part of Probabilistic-Clojure 4 | 5 | ;;; Probabilistic-Clojure is free software: you can redistribute it and/or modify 6 | ;;; it under the terms of the GNU Lesser General Public License as published by 7 | ;;; the Free Software Foundation, either version 3 of the License, or 8 | ;;; (at your option) any later version. 9 | 10 | ;;; Probabilistic-Clojure is distributed in the hope that it will be useful, 11 | ;;; but WITHOUT ANY WARRANTY; without even the implied warranty of 12 | ;;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 13 | ;;; GNU Lesser General Public License for more details. 14 | 15 | ;;; You should have received a copy of the GNU Lesser General Public License 16 | ;;; along with Probabilistic-Clojure. If not, see . 17 | 18 | (ns 19 | ^{:author "Nils Bertschinger" 20 | :doc "This library implements probabilistic programming for Clojure. 21 | The program is considered as a network of probabilistic (and deterministic) 22 | choice points as specified by the user. Metropolis Hastings sampling is then 23 | used to obtain samples from the probability distribution corresponding to 24 | the probabilistic program. 25 | The system allows to condition and memoize probabilistic choice points and 26 | can be extended by user defined distributions."} 27 | probabilistic-clojure.embedded.api 28 | (:use [clojure.set :only (union difference intersection)]) 29 | (:use [probabilistic-clojure.utils.sampling :only (sample-from normalize random-selection random-selection-alias)] 30 | [probabilistic-clojure.utils.stuff :only (ensure-list error)])) 31 | 32 | (in-ns 'probabilistic-clojure.embedded.api) 33 | 34 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 35 | ;;; 36 | ;;; Basic data structures for the global store and choice points 37 | ;;; 38 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 39 | 40 | (defrecord State 41 | [choice-points recomputed newly-created possibly-removed failed?]) 42 | 43 | (defn fresh-state 44 | "Returns a fresh global store containing the given choice points. 45 | The sets of recomputed, newly-created and possibly-removed choice points 46 | are all initially empty and failed? is false." 47 | [choice-points] 48 | (State. choice-points #{} #{} #{} false)) 49 | 50 | (def ^:dynamic *global-store* 51 | (atom (fresh-state {}))) 52 | 53 | (defmacro with-fresh-store 54 | "Creates a fresh binding for the global store and evaluates the body in this context." 55 | [choice-points & body] 56 | `(binding [*global-store* (atom (fresh-state ~choice-points))] 57 | ~@body)) 58 | 59 | (defn reset-store! [] 60 | (swap! *global-store* (constantly (fresh-state {})))) 61 | 62 | (defmacro update-in-store! 63 | "Syntax like update-in, but updates the global store as a side effect. 64 | The global store should not be accessed directly, but only through this and 65 | the related macros assoc-in-store! and fetch-store. This way the representation 66 | of the global store could be changed with minimum effort." 67 | [[& keys] update-fn & args] 68 | `(swap! ~'*global-store* 69 | update-in ~(vec keys) ~update-fn ~@args)) 70 | 71 | (defmacro assoc-in-store! 72 | "Assoc-in for the global store of choice points. See also update-in-store!." 73 | [[& keys] new-val] 74 | `(swap! ~'*global-store* 75 | assoc-in ~(vec keys) ~new-val)) 76 | 77 | (defmacro fetch-store 78 | "Macro for reading from the global store. The syntax resembles the chaining macro ->, i.e. 79 | each key-form gets an automatic first argument inserted." 80 | [& key-forms] 81 | `(-> (deref ~'*global-store*) ~@key-forms)) 82 | 83 | ;;; choice points are maps with the following keys: 84 | ;;; name type recomputed recreate body dependents depends-on 85 | ;;; 86 | ;;; probabilistic choice points have additional keys: 87 | ;;; value log-lik sampler calc-log-lik proposer conditioned? 88 | 89 | (def no-value ::unbound) 90 | 91 | (defn make-choice-point 92 | "Create a new choice point with an unbound value and no dependencies." 93 | [name type whole body] 94 | {:name name :type type :recomputed no-value 95 | :whole whole :body body 96 | :dependents #{} :depends-on #{}}) 97 | 98 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 99 | ;;; 100 | ;;; Stuff to name choice points 101 | ;;; 102 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 103 | 104 | (def ^:dynamic *call-stack* (list)) 105 | 106 | (defn current-caller 107 | "Returns the name of the choice point which is currently active or nil if no caller is active." 108 | [] 109 | (when (seq *call-stack*) 110 | (first *call-stack*))) 111 | 112 | ;;; TODO: change this s.t. addr can be generated automatically [(with-tag ...) for local name change] 113 | 114 | (def ^:dynamic *addr* (list)) 115 | 116 | (defn make-addr [tag] 117 | (cons tag *addr*)) 118 | 119 | (defmacro within [name & body] 120 | `(binding [*addr* ~name 121 | *call-stack* (cons ~name *call-stack*)] 122 | ~@body)) 123 | 124 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 125 | ;;; 126 | ;;; Tracking dependencies between choice points 127 | ;;; 128 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 129 | 130 | (defn update-dependencies 131 | "Registers a new dependency between the choice point with the given name and the current caller." 132 | [cp-name] 133 | (let [caller-name (current-caller)] 134 | (when caller-name 135 | (update-in-store! [:choice-points caller-name :depends-on] 136 | conj cp-name) 137 | (update-in-store! [:choice-points cp-name :dependents] 138 | conj caller-name)))) 139 | 140 | (defn retract-dependent 141 | "Register that the choice point cp-name no longer depends on dependent-name. 142 | If cp-name has no dependents left afterwards it is tagged for possible removal." 143 | [cp-name dependent-name] 144 | (assert (contains? (fetch-store :choice-points (get cp-name) :dependents) dependent-name)) 145 | (update-in-store! [:choice-points cp-name :dependents] 146 | disj dependent-name) 147 | (when (empty? (fetch-store :choice-points (get cp-name) :dependents)) 148 | (update-in-store! [:possibly-removed] 149 | conj cp-name))) 150 | 151 | (defn recompute-value 152 | "Recompute the value of the given choice point. Updates the dependencies for the new 153 | value and registers the choice point as recomputed." 154 | [cp] 155 | (let [name (:name cp)] 156 | (update-in-store! [:recomputed] conj name) 157 | (within name 158 | (let [depended-on (fetch-store :choice-points (get name) :depends-on)] 159 | (assoc-in-store! [:choice-points name :depends-on] #{}) 160 | (let [val ((:body cp))] 161 | (doseq [used (difference depended-on 162 | (fetch-store :choice-points (get name) :depends-on))] 163 | (retract-dependent used name)) 164 | (assoc-in-store! [:choice-points name :recomputed] val) 165 | val))))) 166 | 167 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 168 | ;;; 169 | ;;; Deterministic choice points 170 | ;;; 171 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 172 | 173 | (defn make-det-cp 174 | "Create a new determinstic choice point." 175 | [name whole body] 176 | (make-choice-point name ::deterministic whole body)) 177 | 178 | (defn det-cp-fn 179 | "This function gets called if a determinstic choice point is evaluated. 180 | When the choice point is not already in the global store it is initialized, 181 | its value is computed and the new choice point is returned. 182 | Otherwise it is simply fetched from the store. 183 | This function should not be called directly, but only in the context of det-cp." 184 | [name whole-fn body-fn] 185 | (if (contains? (fetch-store :choice-points) name) 186 | ((fetch-store :choice-points) name) 187 | (let [det-cp (make-det-cp name whole-fn body-fn)] 188 | (update-in-store! [:newly-created] 189 | conj name) 190 | (assoc-in-store! [:choice-points name] 191 | det-cp) 192 | (recompute-value det-cp) 193 | (fetch-store :choice-points (get name))))) 194 | 195 | (defmacro det-cp 196 | "Establishes a deterministic choice point with the given name tag for the code in the body." 197 | [tag & body] 198 | `(let [addr# *addr* 199 | name# (make-addr ~tag) 200 | body-fn# (fn [] ~@body) 201 | whole-fn# (atom nil)] 202 | (swap! whole-fn# 203 | (constantly 204 | (fn [] 205 | (det-cp-fn name# @whole-fn# body-fn#)))) 206 | (det-cp-fn name# @whole-fn# body-fn#))) 207 | 208 | (defmulti gv 209 | "Accesses the value of a choice point. When used in the body of another choice 210 | point this creates a dependency between those choice points." 211 | :type) 212 | 213 | (defmethod gv ::deterministic 214 | ;; Accesses the value of a deterministic choice point. 215 | ;; Takes care of dependencies and creates the choice point if necessary. 216 | [det-cp] 217 | (let [name (:name det-cp)] 218 | (if (contains? (fetch-store :choice-points) name) 219 | (let [val (fetch-store :choice-points (get name) :recomputed)] 220 | (update-dependencies name) 221 | val) 222 | ;; the choice point is not in the trace, thus we have to recreate it first 223 | (gv ((:whole det-cp)))))) 224 | 225 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 226 | ;;; 227 | ;;; Probabilistic choice points 228 | ;;; 229 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 230 | 231 | (defn sample 232 | "Sample a new value for prob-cp." 233 | [prob-cp] 234 | (apply (:sampler prob-cp) (:recomputed prob-cp))) 235 | 236 | (defn calc-log-lik 237 | "Calculate the probability of x given the current parameters of prob-cp." 238 | [prob-cp x] 239 | (apply (:calc-log-lik prob-cp) x (:recomputed prob-cp))) 240 | 241 | (defn propose 242 | "Propose a new value new-x for prob-cp given that the current value is old-x. 243 | Returns three values [new-x q(new-x | old-x) q(old-x | new-x)] where q(.|.) denotes the 244 | proposal distribution." 245 | [prob-cp old-x] 246 | (apply (:proposer prob-cp) old-x (:recomputed prob-cp))) 247 | 248 | (defn make-prob-cp 249 | "Creates a new probabilistic choice point." 250 | [name whole body sampler calc-log-lik proposer] 251 | (merge (make-choice-point name ::probabilistic whole body) 252 | {:value no-value :log-lik 0 :sampler sampler :calc-log-lik calc-log-lik 253 | :proposer proposer :conditioned? false})) 254 | 255 | (defn update-log-lik 256 | "Update the probability for the given probabilistic choice point." 257 | [prob-cp-name] 258 | (let [prob-cp (fetch-store :choice-points (get prob-cp-name))] 259 | (assoc-in-store! 260 | [:choice-points prob-cp-name :log-lik] 261 | (calc-log-lik prob-cp (:value prob-cp))))) 262 | 263 | (defn prob-cp-fn 264 | "As det-cp-fn, but for probabilistic choice points." 265 | [name whole-fn body-fn dist] 266 | (if (contains? (fetch-store :choice-points) name) 267 | ((fetch-store :choice-points) name) 268 | (let [prob-cp (make-prob-cp name whole-fn body-fn 269 | (:sampler dist) 270 | (:calc-log-lik dist) 271 | (:proposer dist))] 272 | (update-in-store! [:newly-created] 273 | conj name) 274 | (assoc-in-store! [:choice-points name] 275 | prob-cp) 276 | (recompute-value prob-cp) 277 | (let [params (fetch-store :choice-points (get name) :recomputed)] 278 | (assoc-in-store! [:choice-points name :value] 279 | (sample (fetch-store :choice-points (get name)))) 280 | (update-log-lik name) 281 | (fetch-store :choice-points (get name)))))) 282 | 283 | (defn create-dist-map 284 | "Helper functions for def-prob-cp." 285 | [params dist-spec] 286 | (when-not (vector? params) 287 | (error "Provided parameters " params " are not a vector.")) 288 | (let [keys #{:sampler :calc-log-lik :proposer} 289 | find-spec-for (fn [key] 290 | (let [spec-form (rest (drop-while #(not (= % key)) dist-spec))] 291 | (when (empty? spec-form) 292 | (error "You must provide an implementation for " key)) 293 | (take-while (complement keys) spec-form)))] 294 | (-> {} 295 | (assoc :sampler 296 | (let [[args & body] (find-spec-for :sampler)] 297 | (when-not (vector? args) 298 | (error args " is not a parameter vector as required by ::sampler option")) 299 | `(fn ~(vec (concat args params)) ~@body))) 300 | (assoc :calc-log-lik 301 | (let [[args & body] (find-spec-for :calc-log-lik)] 302 | (when-not (vector? args) 303 | (error args " is not a parameter vector as required by ::calc-log-lik option")) 304 | `(fn ~(vec (concat args params)) ~@body))) 305 | (assoc :proposer 306 | (let [[args & body] (find-spec-for :proposer)] 307 | (when-not (vector? args) 308 | (error args " is not a parameter vector as required by ::proposer option")) 309 | `(fn ~(vec (concat args params)) ~@body)))))) 310 | 311 | (defmacro def-prob-cp 312 | "Macro to define probabilistic choice points. 313 | Each choice point has a name and parameters. Furthermore, it must specify 314 | functions :sampler, :calc-log-lik and :proposer. See the source of flip-cp 315 | for an example." 316 | [name [& params] & dist-spec] 317 | (let [dist-map (create-dist-map (vec params) dist-spec) 318 | tag (gensym "tag")] 319 | `(defmacro ~name [~tag ~@params] 320 | `(let [~'addr# *addr* 321 | ~'tag-name# (make-addr ~~tag) 322 | ~'body-fn# (fn [] (list ~~@params)) 323 | ~'whole-fn# (atom nil)] 324 | (swap! ~'whole-fn# 325 | (constantly 326 | (fn [] 327 | (prob-cp-fn ~'tag-name# @~'whole-fn# ~'body-fn# ~'~dist-map)))) 328 | (prob-cp-fn ~'tag-name# @~'whole-fn# ~'body-fn# ~'~dist-map))))) 329 | 330 | (defmethod gv ::probabilistic 331 | ;; Accesses the value of a probabilistic choice point 332 | [prob-cp] 333 | (let [name (:name prob-cp)] 334 | (if (contains? (fetch-store :choice-points) name) 335 | (let [val (fetch-store :choice-points (get name) :value)] 336 | (update-dependencies name) 337 | val) 338 | ;; the choice point is not in the trace, thus we have to recreate it first 339 | (gv ((:whole prob-cp)))))) 340 | 341 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 342 | ;;; 343 | ;;; Metropolis Hastings sampling 344 | ;;; 345 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 346 | 347 | ;;; Traces failures 348 | 349 | (defn trace-failure 350 | "Tags the current trace as failed. Used to implement rejection sampling." 351 | [] 352 | (assoc-in-store! [:failed?] true)) 353 | 354 | (defn trace-failed? [] 355 | (fetch-store :failed?)) 356 | 357 | ;;; Sampling routines 358 | 359 | (defn find-valid-trace 360 | "Returns a valid trace for the probabilistic program given as a no-arg function prob-chunk." 361 | [prob-chunk] 362 | (let [result (with-fresh-store {} 363 | (let [cp (prob-chunk)] 364 | (when-not (trace-failed?) 365 | [cp (fetch-store :choice-points)])))] 366 | (if result 367 | result 368 | (recur prob-chunk)))) 369 | 370 | (defn cp-value 371 | "Returns the value of the choice point cp within the trace choice points." 372 | [cp choice-points] 373 | (if (= (:type cp) ::deterministic) 374 | (:recomputed (get choice-points (:name cp))) 375 | (:value (get choice-points (:name cp))))) 376 | 377 | (defn monte-carlo-sampling 378 | "Simple Monte-Carlo sampling scheme which runs the whole probabilistic program 379 | over and over again. Returns a lazy sequence of the obtained outcomes. 380 | Rejections are not included in the output, so it may take a long time if the 381 | rejection rate is high." 382 | [prob-chunk] 383 | (repeatedly (fn [] (let [[cp choice-points] (find-valid-trace prob-chunk)] 384 | (cp-value cp choice-points))))) 385 | 386 | ;;; utility functions for sampling 387 | 388 | (defn total-log-lik 389 | "Returns the total sum of the log. probabilities of all requested choice points 390 | in the given trace. 391 | Choice points not in the trace are allowed and contribute zero log. probability." 392 | [cp-names choice-points] 393 | (reduce + 0 (map (fn [cp-name] 394 | (let [cp (choice-points cp-name)] 395 | (case (:type cp) 396 | ::probabilistic (:log-lik cp) 397 | ::deterministic 0 398 | 0))) 399 | cp-names))) 400 | 401 | (defn remove-uncalled-choices 402 | "Remove all choice points from the global store which have not been called. 403 | Starts from the choice points registered for possible removal and recursively 404 | retracts further dependents. 405 | Returns a set of the names of the removed choice points." 406 | [] 407 | (loop [candidate-names (seq (fetch-store :possibly-removed)) 408 | result []] 409 | (if (empty? candidate-names) 410 | (set result) 411 | (let [candidate (fetch-store :choice-points (get (first candidate-names)))] 412 | (if (empty? (:dependents candidate)) 413 | (let [candidate-name (:name candidate)] 414 | (update-in-store! [:choice-points] 415 | dissoc candidate-name) 416 | (doseq [cp-name (:depends-on candidate)] 417 | (retract-dependent cp-name candidate-name)) 418 | (recur (concat (rest candidate-names) 419 | (:depends-on candidate)) 420 | (conj result candidate-name))) 421 | (recur (rest candidate-names) result)))))) 422 | 423 | ;; THIS DOES NOT WORK ... replaced by straight forward propagation 424 | ;; with potential duplicate recomputations! 425 | 426 | ;; ;; Version using depth-first traversal to obtain topological ordering 427 | ;; ;; of all choice points which have to updated if cp-name is changed 428 | ;; (defn ordered-dependencies 429 | ;; "Return all direct and indirect dependents of cp-name in an order suitable for updating, i.e. 430 | ;; each choice point occurs before any of its dependents in this sequence (topologically sorted)." 431 | ;; [cp-name choice-points] 432 | ;; (let [visited (atom #{}) 433 | ;; ordered-deps (atom []) 434 | ;; dfs-path (atom #{}) 435 | ;; back-edge? (fn [cp-name] (@dfs-path cp-name))] 436 | ;; (letfn [(dfs-traverse [current-cp-name propagate?] 437 | ;; (swap! visited conj current-cp-name) 438 | ;; (swap! dfs-path conj current-cp-name) 439 | ;; (let [current-cp (choice-points current-cp-name) 440 | ;; direct-deps (if (or propagate? (= (:type current-cp) ::deterministic)) 441 | ;; (:dependents current-cp) 442 | ;; #{})] 443 | ;; (doseq [dep-cp-name direct-deps] 444 | ;; (when (back-edge? dep-cp-name) 445 | ;; (error "Cyclic dependencies between " current-cp-name 446 | ;; " and " dep-cp-name " detected!")) 447 | ;; (when-not (@visited dep-cp-name) 448 | ;; (dfs-traverse dep-cp-name false))) 449 | ;; (swap! dfs-path disj current-cp-name) 450 | ;; (swap! ordered-deps (fn [deps] (cons current-cp-name deps)))))] 451 | ;; (dfs-traverse cp-name true) 452 | ;; @ordered-deps))) 453 | 454 | (defn propagate-change-to 455 | "Propagate a change, starting with the given choice points." 456 | [cp-names] 457 | (loop [cpns (into clojure.lang.PersistentQueue/EMPTY cp-names) ; (seq cp-names) 458 | update-count 0] 459 | (if-not (empty? cpns) 460 | (let [cp-name (peek cpns) ; (first cpns) 461 | more-cps (pop cpns) ; (rest cpns) ; 462 | cp (fetch-store :choice-points (get cp-name)) 463 | old-val (:recomputed cp)] 464 | ;; (println cp-name ": " (count cp-names)) (Thread/sleep 10) 465 | (recompute-value cp) 466 | (when (= (:type cp) ::probabilistic) 467 | (update-log-lik (:name cp))) 468 | (let [cp (fetch-store :choice-points (get cp-name)) ; re-read to see changes 469 | direct-deps (if (or (= (:type cp) ::probabilistic) 470 | (= old-val (:recomputed cp))) 471 | ;; no propagation beyond prob. and unchanged choice points 472 | [] 473 | (:dependents cp))] 474 | ;; this implements (depth-first) breadth-first (with PersistentQueue) 475 | ;; traversal and potentially re-registers cp for update ... 476 | ;; ensures valid data after the propagation completes 477 | ;; (recur (concat direct-deps more-cps) (inc update-count)))) 478 | (recur (into more-cps direct-deps) (inc update-count)))) 479 | update-count))) 480 | 481 | ;; (defn propagate-change-to 482 | ;; "Propagate a change by recomputing all the given choice points in order." 483 | ;; [cp-names] 484 | ;; (doseq [dep-cp-name cp-names] 485 | ;; (let [dep-cp (fetch-store :choice-points (get dep-cp-name))] 486 | ;; (recompute-value dep-cp) 487 | ;; (when (= (:type dep-cp) ::probabilistic) 488 | ;; (update-log-lik (:name dep-cp)))))) 489 | 490 | ;;; Conditioning and memoization 491 | 492 | (defn cond-data [prob-cp cond-val] 493 | (let [name (:name prob-cp) 494 | val (gv prob-cp)] 495 | (if (fetch-store :choice-points (get name) :conditioned?) 496 | (do (when-not (= cond-val val) 497 | (error name " is already conditioned on value " val 498 | " and cannot be changed to " cond-val)) 499 | cond-val) 500 | (do 501 | (assoc-in-store! [:choice-points name :value] 502 | cond-val) 503 | (assoc-in-store! [:choice-points name :conditioned?] 504 | true) 505 | (update-log-lik name) 506 | (propagate-change-to (:dependents prob-cp)) 507 | cond-val)))) 508 | 509 | (defmacro memo [tag cp-form & memo-args] 510 | `(det-cp ~tag 511 | (binding [*addr* (list ~@(rest cp-form) ~@memo-args)] 512 | (gv ~cp-form)))) 513 | 514 | ;;; Finally the Metropolis Hastings sampling 515 | ;;; This combines the previous attempts for changing and fixed topologies. 516 | ;;; In case the topology remains unchanged the more efficient method is used. 517 | 518 | ;; Does not work so easily since for log. lik. computations we still need to track which 519 | ;; choice points are active and which are not!!! 520 | ;; (def ^:dynamic *remove-uncalled* 521 | ;; "Should uncalled choices be removed?" 522 | ;; true) 523 | 524 | ;; Idea for speedup: Use un-normalized selection distribution and do not recompute it 525 | ;; completely, but just update the changed choice points 526 | 527 | (defrecord UDist [weights total]) 528 | 529 | (defn prob-choice? 530 | "Returns true if cp is an un-conditioned probabilistic choice point." 531 | [cp] 532 | (and (= (:type cp) ::probabilistic) 533 | (not (:conditioned? cp)))) 534 | 535 | (defn count-all-dependents 536 | "Returns the number of all direct and indirect dependents of the given choice point." 537 | [cp-name choice-points] 538 | (let [visited (atom #{}) 539 | counter (atom 0)] 540 | (letfn [(dfs-traverse [current-cp-name] 541 | (swap! visited conj current-cp-name) 542 | (swap! counter inc) 543 | (let [current-cp (choice-points current-cp-name) 544 | direct-deps (:dependents current-cp)] 545 | (doseq [dep-cp-name direct-deps] 546 | (when-not (@visited dep-cp-name) 547 | (dfs-traverse dep-cp-name)))))] 548 | (dfs-traverse cp-name) 549 | @counter))) 550 | 551 | (defn cp-weight [cp-name choice-points] 552 | (Math/sqrt (count-all-dependents cp-name choice-points))) 553 | 554 | (defn prob-choice-dist 555 | "Return an un-normalized distribution for randomly choosing a choice point from the given trace. 556 | Implements the heuristic to prefer choice points with many dependents." 557 | [choice-points] 558 | (let [weights (into {} 559 | (for [[name cp] choice-points 560 | :when (prob-choice? cp)] 561 | [name (cp-weight name choice-points)]))] 562 | (UDist. weights (reduce + (vals weights))))) 563 | 564 | (defn add-to-prob-choice-dist [dist cp-names choice-points] 565 | (let [[new-weights new-total] 566 | (reduce (fn [[weights total] cp-name] 567 | (let [cp (choice-points cp-name)] 568 | (if (prob-choice? cp) 569 | (let [w (cp-weight cp-name choice-points)] 570 | (assert (not (contains? cp-name weights))) 571 | [(merge weights {cp-name w}) (+ total w)]) 572 | [weights total]))) 573 | [(:weights dist) (:total dist)] 574 | cp-names)] 575 | (UDist. new-weights new-total))) 576 | 577 | (defn remove-from-prob-choice-dist [dist cp-names] 578 | (let [[new-weights new-total] 579 | (reduce (fn [[weights total] cp-name] 580 | (if (contains? weights cp-name) ;; fails for non prob-choices 581 | (let [w (weights cp-name)] 582 | [(dissoc weights cp-name) (- total w)]) 583 | [weights total])) 584 | [(:weights dist) (:total dist)] 585 | cp-names)] 586 | (UDist. new-weights new-total))) 587 | 588 | (defn prob [dist cp-name] 589 | (/ ((:weights dist) cp-name) (:total dist))) 590 | 591 | (defn set-proposed-val! [cp-name prop-val] 592 | (assoc-in-store! [:choice-points cp-name :value] 593 | prop-val) 594 | (update-in-store! [:recomputed] conj cp-name) 595 | (update-log-lik cp-name)) 596 | 597 | (defn metropolis-hastings-step [choice-points selected selection-dist] 598 | (with-fresh-store choice-points 599 | (let [selected-cp (choice-points selected) 600 | 601 | [prop-val fwd-log-lik bwd-log-lik] 602 | (propose selected-cp (:value selected-cp))] 603 | ;; Propose a new value for the selected choice point and propagate change to dependents 604 | (set-proposed-val! (:name selected-cp) prop-val) 605 | (let [updates (propagate-change-to (:dependents selected-cp))] 606 | ;; (println "Proposed " (:name selected-cp) " for " updates " updates (" 607 | ;; (count-all-dependents (:name selected-cp) choice-points) " dependents)")) 608 | ) 609 | 610 | (if (trace-failed?) 611 | [choice-points ::rejected true selection-dist] 612 | (let [removed-cps (remove-uncalled-choices) 613 | same-topology (and (empty? (fetch-store :newly-created)) 614 | (empty? removed-cps)) 615 | ;; Here we have the following invariants: 616 | ;; * (assert (empty? (clojure.set/intersection removed-cps (fetch-store :newly-created)))) 617 | ;; * (let [new (set (keys (fetch-store :choice-points))) 618 | ;; old (set (keys choice-points))] 619 | ;; (assert (and (= new (difference (union old (fetch-store :newly-created)) 620 | ;; removed-cps)) 621 | ;; (= old (difference (union new removed-cps) (fetch-store :newly-created)))))) 622 | 623 | ;; Overall the recomputed and removed-cps were touched during the update 624 | ;; Thus, we have to calculate the total probability contributed to the old 625 | ;; as well as the new traces. 626 | touched-cps (union (fetch-store :recomputed) removed-cps) 627 | trace-log-lik (total-log-lik touched-cps choice-points) 628 | prop-trace-log-lik (total-log-lik touched-cps (fetch-store :choice-points)) 629 | 630 | ;; The forward and backward probabilities now account for the newly-created 631 | ;; and removed choice points 632 | fwd-trace-log-lik (total-log-lik (fetch-store :newly-created) (fetch-store :choice-points)) 633 | bwd-trace-log-lik (total-log-lik removed-cps choice-points) 634 | 635 | prop-selection-dist (if same-topology 636 | selection-dist 637 | ;; (prob-choice-dist (fetch-store :choice-points)))] 638 | (-> selection-dist 639 | (add-to-prob-choice-dist (fetch-store :newly-created) 640 | (fetch-store :choice-points)) 641 | (remove-from-prob-choice-dist removed-cps)))] 642 | ;; Randomly accept the new proposal according to the Metropolis Hastings formula 643 | (if (< (Math/log (rand)) 644 | (+ (- prop-trace-log-lik trace-log-lik) 645 | (- (Math/log (prob prop-selection-dist (:name selected-cp))) 646 | (Math/log (prob selection-dist (:name selected-cp)))) 647 | (- bwd-trace-log-lik fwd-trace-log-lik) 648 | (- bwd-log-lik fwd-log-lik))) 649 | [(fetch-store :choice-points) ::accepted same-topology prop-selection-dist] 650 | [choice-points ::rejected true selection-dist])))))) 651 | 652 | (def ^:dynamic *info-steps* 653 | "Display some status information every *info-steps* many samples" 654 | 500) 655 | 656 | (def ^:dynamic *selection-dist-steps* 657 | "Force a refresh of the selection distribution after that many steps. 658 | Anytime the topology has changed it is recomputed anyways." 659 | 25000) 660 | 661 | (def ^:dynamic *alias-sampling* true) 662 | 663 | (defn new-update-sequence [dist] 664 | (let [total (:total dist) 665 | pdist (into {} (for [[name weight] (:weights dist)] 666 | [name (/ weight total)]))] 667 | (if *alias-sampling* 668 | (random-selection-alias *selection-dist-steps* pdist) 669 | (random-selection *selection-dist-steps* pdist)))) 670 | 671 | (defn metropolis-hastings-sampling [prob-chunk] 672 | (println "Trying to find a valid trace ...") 673 | (let [[cp choice-points] (find-valid-trace prob-chunk)] 674 | (println "Started sampling") 675 | (letfn [(samples [choice-points idx num-accepted num-top-changed update-seq selection-dist] 676 | (lazy-seq 677 | (let [update-seq (or (seq update-seq) 678 | (new-update-sequence (prob-choice-dist choice-points))) 679 | val (cp-value cp choice-points) 680 | 681 | [next-choice-points status same-topology next-selection-dist] 682 | (metropolis-hastings-step choice-points (first update-seq) selection-dist) 683 | 684 | output-info (= (mod idx *info-steps*) 0)] 685 | (when output-info 686 | (println idx ": " val) 687 | (println "Log. lik.: " (total-log-lik (keys choice-points) choice-points)) 688 | (println "Accepted " num-accepted " out of last " *info-steps* " samples.") 689 | (println "Topology changed on " num-top-changed " samples.")) 690 | (cons val 691 | (samples next-choice-points 692 | (inc idx) 693 | (cond output-info 0 694 | (= status ::accepted) (inc num-accepted) 695 | :else num-accepted) 696 | (cond output-info 0 697 | (not same-topology) (inc num-top-changed) 698 | :else num-top-changed) 699 | (if same-topology 700 | (rest update-seq) 701 | (new-update-sequence next-selection-dist)) 702 | next-selection-dist)))))] 703 | (let [selection-dist (prob-choice-dist choice-points)] 704 | (samples choice-points 0 0 0 (new-update-sequence selection-dist) selection-dist))))) 705 | -------------------------------------------------------------------------------- /src/probabilistic_clojure/embedded/choice_points.clj: -------------------------------------------------------------------------------- 1 | ;;; Copyright (C) 2011 Nils Bertschinger 2 | 3 | ;;; This file is part of Probabilistic-Clojure 4 | 5 | ;;; Probabilistic-Clojure is free software: you can redistribute it and/or modify 6 | ;;; it under the terms of the GNU Lesser General Public License as published by 7 | ;;; the Free Software Foundation, either version 3 of the License, or 8 | ;;; (at your option) any later version. 9 | 10 | ;;; Probabilistic-Clojure is distributed in the hope that it will be useful, 11 | ;;; but WITHOUT ANY WARRANTY; without even the implied warranty of 12 | ;;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 13 | ;;; GNU Lesser General Public License for more details. 14 | 15 | ;;; You should have received a copy of the GNU Lesser General Public License 16 | ;;; along with Probabilistic-Clojure. If not, see . 17 | 18 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 19 | ;;;; Probabilistic programming using constraint propagation 20 | ;;;; to efficiently track dependencies between choice points 21 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 22 | 23 | (ns 24 | ^{:author "Nils Bertschinger" 25 | :doc "Part of probabilistic-clojure.embedded which implements a couple 26 | of probabilistic choice points."} 27 | probabilistic-clojure.embedded.choice-points 28 | (:use [probabilistic-clojure.embedded.api :only (def-prob-cp det-cp gv memo)] 29 | [probabilistic-clojure.utils.stuff :only (ensure-list error)]) 30 | ;; (:require [incanter.stats :as stat]) ; This does not work inside macros!!! 31 | (:import org.apache.commons.math.special.Gamma)) 32 | ;; (:import cern.jet.stat.tdouble.Gamma)) 33 | 34 | (in-ns 'probabilistic-clojure.embedded.choice-points) 35 | 36 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 37 | ;;; 38 | ;;; Bernoulli distribution 39 | ;;; 40 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 41 | 42 | (def-prob-cp flip-cp [p] 43 | :sampler [] (< (rand) p) 44 | :calc-log-lik [bool] (Math/log (if bool p (- 1 p))) 45 | ;; proposer returns a vector of [new-value forward-log-prob backward-log-prob] 46 | :proposer [bool] [(not bool) 0 0]) 47 | 48 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 49 | ;;; 50 | ;;; Discrete distribution 51 | ;;; 52 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 53 | 54 | (defn log-pdf-discrete [x dist] 55 | (if (contains? dist x) 56 | (Math/log (dist x)) 57 | (Math/log 0))) 58 | 59 | (def-prob-cp discrete-cp [dist] 60 | :sampler [] (probabilistic-clojure.utils.sampling/sample-from dist) 61 | :calc-log-lik [x] (probabilistic-clojure.embedded.choice-points/log-pdf-discrete x dist) 62 | :proposer [old-x] (let [prop-dist (probabilistic-clojure.utils.sampling/normalize (assoc dist old-x 0)) 63 | new-x (probabilistic-clojure.utils.sampling/sample-from prop-dist)] 64 | [new-x 65 | (probabilistic-clojure.embedded.choice-points/log-pdf-discrete new-x prop-dist) 66 | (probabilistic-clojure.embedded.choice-points/log-pdf-discrete 67 | old-x (probabilistic-clojure.utils.sampling/normalize (assoc dist new-x 0)))])) 68 | 69 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 70 | ;;; 71 | ;;; Gaussian distribution 72 | ;;; 73 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 74 | 75 | (def ^:dynamic *gaussian-proposal-sdev* 0.7) 76 | 77 | (def-prob-cp gaussian-cp [mu sdev] 78 | :sampler [] (incanter.stats/sample-normal 1 :mean mu :sd sdev) 79 | :calc-log-lik [x] (Math/log (incanter.stats/pdf-normal x :mean mu :sd sdev)) 80 | :proposer [old-x] (let [proposal-sd probabilistic-clojure.embedded.choice-points/*gaussian-proposal-sdev* 81 | new-x (incanter.stats/sample-normal 1 :mean old-x :sd proposal-sd)] 82 | [new-x 83 | (Math/log (incanter.stats/pdf-normal new-x :mean old-x :sd proposal-sd)) 84 | (Math/log (incanter.stats/pdf-normal old-x :mean new-x :sd proposal-sd))])) 85 | 86 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 87 | ;;; 88 | ;;; Dirichlet distribution 89 | ;;; 90 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 91 | 92 | (defn log-pdf-dirichlet [ps alphas] 93 | (assert (= (count ps) (count alphas)) 94 | "Dimension mismatch in log-pdf-dirichlet!") 95 | (let [log-gamma (fn [x] (Gamma/logGamma x)) 96 | norm (- (reduce + (map log-gamma alphas)) 97 | (log-gamma (reduce + alphas)))] 98 | (- (reduce + (map (fn [p a] (* (- a 1) (Math/log p))) ps alphas)) 99 | norm))) 100 | 101 | (def ^:dynamic *dirichlet-proposal-factor* 42) 102 | (def ^:dynamic *dirichlet-proposal-shift* 0.001) ; found a paper claiming that this is good 103 | (def ^:dynamic *dirichlet-initial-factor* 1) 104 | 105 | (def-prob-cp dirichlet-cp [alphas] 106 | :sampler [] (first 107 | (incanter.stats/sample-dirichlet 108 | 2 109 | (map (partial * probabilistic-clojure.embedded.choice-points/*dirichlet-initial-factor*) 110 | alphas))) 111 | :calc-log-lik [ps] (probabilistic-clojure.embedded.choice-points/log-pdf-dirichlet ps alphas) 112 | :proposer [old-ps] (letfn [(proposal-alphas [alphas] 113 | (for [a alphas] 114 | (+ (* probabilistic-clojure.embedded.choice-points/*dirichlet-proposal-factor* a) 115 | probabilistic-clojure.embedded.choice-points/*dirichlet-proposal-shift*)))] 116 | (let [new-ps (first (incanter.stats/sample-dirichlet 2 (proposal-alphas old-ps)))] 117 | [new-ps 118 | (probabilistic-clojure.embedded.choice-points/log-pdf-dirichlet new-ps (proposal-alphas old-ps)) 119 | (probabilistic-clojure.embedded.choice-points/log-pdf-dirichlet old-ps (proposal-alphas new-ps))]))) 120 | 121 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 122 | ;;; 123 | ;;; Beta distribution 124 | ;;; 125 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 126 | 127 | (def-prob-cp beta-cp [alpha beta] 128 | :sampler [] (incanter.stats/sample-beta 1 :alpha alpha :beta beta) 129 | :calc-log-lik [x] (Math/log (incanter.stats/pdf-beta x :alpha alpha :beta beta)) 130 | :proposer [old-x] (let [new-x (incanter.stats/sample-beta 1 :alpha alpha :beta beta)] 131 | [new-x 132 | (Math/log (incanter.stats/pdf-beta new-x :alpha alpha :beta beta)) 133 | (Math/log (incanter.stats/pdf-beta old-x :alpha alpha :beta beta))])) 134 | 135 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 136 | ;;; 137 | ;;; Dirichlet process 138 | ;;; 139 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 140 | 141 | (defn pick-a-stick [alpha idx] 142 | (let [stick (beta-cp [:pick :stick idx] 1 alpha) 143 | stop (flip-cp [:pick :stop idx] (gv stick))] 144 | (det-cp [:pick idx] 145 | (if (gv stop) 146 | idx 147 | (gv (pick-a-stick alpha (inc idx))))))) 148 | 149 | (defmacro dirichlet-process [tag alpha base] 150 | `(memo [~tag ~alpha] 151 | ~base 152 | (gv (pick-a-stick ~alpha 1)))) 153 | -------------------------------------------------------------------------------- /src/probabilistic_clojure/embedded/demos.clj: -------------------------------------------------------------------------------- 1 | ;;; Copyright (C) 2011 Nils Bertschinger 2 | 3 | ;;; This file is part of Probabilistic-Clojure 4 | 5 | ;;; Probabilistic-Clojure is free software: you can redistribute it and/or modify 6 | ;;; it under the terms of the GNU Lesser General Public License as published by 7 | ;;; the Free Software Foundation, either version 3 of the License, or 8 | ;;; (at your option) any later version. 9 | 10 | ;;; Probabilistic-Clojure is distributed in the hope that it will be useful, 11 | ;;; but WITHOUT ANY WARRANTY; without even the implied warranty of 12 | ;;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 13 | ;;; GNU Lesser General Public License for more details. 14 | 15 | ;;; You should have received a copy of the GNU Lesser General Public License 16 | ;;; along with Probabilistic-Clojure. If not, see . 17 | 18 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 19 | ;;;; Probabilistic programming using constraint propagation 20 | ;;;; to efficiently track dependencies between choice points 21 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 22 | 23 | (ns 24 | ^{:author "Nils Bertschinger" 25 | :doc "Part of probabilistic-clojure.embedded. Collection of demo programs."} 26 | probabilistic-clojure.embedded.demos 27 | (:use [probabilistic-clojure.embedded.api :only (det-cp gv trace-failure cond-data memo metropolis-hastings-sampling def-prob-cp)] 28 | [probabilistic-clojure.utils.stuff :only (indexed)] 29 | [probabilistic-clojure.utils.sampling :only (sample-from density)] 30 | [probabilistic-clojure.embedded.choice-points 31 | :only (flip-cp gaussian-cp dirichlet-cp discrete-cp dirichlet-process)] 32 | 33 | [incanter.core :only (view)] 34 | [incanter.charts :only (histogram add-lines xy-plot)] 35 | [incanter.stats :only (mean sample-normal pdf-normal)])) 36 | 37 | (in-ns 'probabilistic-clojure.embedded.demos) 38 | 39 | ;;; Simple Bayes net as a first example 40 | 41 | (defn noisy-or [x y] 42 | (det-cp :noisy-or 43 | (or (and (gv x) (gv (flip-cp :flip9 0.9))) 44 | (and (gv y) (gv (flip-cp :flip8 0.8))) 45 | (gv (flip-cp :flip1 0.1))))) 46 | 47 | (defn grass-bayes-net [] 48 | (det-cp :grass-bayes-net 49 | (let [rain (flip-cp :rain 0.3) 50 | sprinkler (flip-cp :sprinkler 0.5) 51 | grass-is-wet (gv (noisy-or rain sprinkler))] 52 | (when-not grass-is-wet 53 | (trace-failure)) 54 | (gv rain)))) 55 | 56 | (defn grass-bayes-net-fixed [] 57 | (det-cp :grass-bayes-net-fixed 58 | (let [rain (gv (flip-cp :rain 0.3)) 59 | sprinkler (gv (flip-cp :sprinkler 0.5)) 60 | noise-x (gv (flip-cp :noise-x 0.9)) 61 | noise-y (gv (flip-cp :noise-y 0.8)) 62 | noise-z (gv (flip-cp :noise-z 0.1))] 63 | (if (or (and rain noise-x) 64 | (and sprinkler noise-y) 65 | noise-z) 66 | rain 67 | (trace-failure))))) 68 | 69 | (defn run-bayes-net [model] 70 | (density 71 | (take 7500 (drop 500 (metropolis-hastings-sampling model))))) 72 | 73 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 74 | ;;; 75 | ;;; Gaussian mixture models 76 | ;;; 77 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 78 | 79 | (defn generate-data [] 80 | (let [mu (fn [] (sample-from {-5 0.2, 0 0.7, 8 0.1}))] 81 | (lazy-seq (cons (sample-normal 1 :mean (mu)) 82 | (generate-data))))) 83 | 84 | (def data (take 42 (generate-data))) 85 | 86 | (defn mixture [comp-labels data] 87 | (let [comp-weights (dirichlet-cp :weights (for [_ comp-labels] 10.0)) 88 | comp-mus (zipmap comp-labels 89 | (for [label comp-labels] (gaussian-cp [:mu label] 0.0 10.0)))] 90 | (doseq [[idx point] (indexed data)] 91 | (let [comp (discrete-cp [:comp idx] (zipmap comp-labels (gv comp-weights)))] 92 | ;; mu-comp (det-cp [:mu-comp idx] (gv (get comp-mus (gv comp))))] 93 | ;; (cond-data (gaussian-cp [:obs idx] (gv mu-comp) 1.0) point) 94 | (cond-data (gaussian-cp [:obs idx] (gv (get comp-mus (gv comp))) 1.0) point))) 95 | (det-cp :mixture 96 | [(into {} (for [[comp mu] comp-mus] [comp (gv mu)])) 97 | (gv comp-weights)]))) 98 | 99 | (defn mixture-memo [comp-labels data] 100 | (let [comp-weights (dirichlet-cp :weights (for [_ comp-labels] 10.0))] 101 | (doseq [[idx point] (indexed data)] 102 | (let [comp (discrete-cp [:comp idx] (zipmap comp-labels (gv comp-weights))) 103 | comp-mu (memo [:mu idx] (gaussian-cp :mu 0.0 10.0) (gv comp))] 104 | (cond-data (gaussian-cp [:obs idx] (gv comp-mu) 1.0) point))) 105 | (det-cp :mixture 106 | [(into {} (for [comp comp-labels] 107 | [comp (gv (memo [:mu comp] (gaussian-cp :mu 0.0 10.0) comp))])) 108 | (gv comp-weights)]))) 109 | 110 | (defn test-mixture [comp-labels model] 111 | (let [data-plot (histogram data :title "Dataset" :nbins 50 :density true) 112 | num-comp (count comp-labels) 113 | [comp-mus weights] (last (take 7500 (metropolis-hastings-sampling (fn [] (model comp-labels data))))) 114 | mus (for [label comp-labels] (get comp-mus label)) 115 | 116 | xs (range -10 10 0.01) 117 | 118 | comp-pdf (fn [i x] 119 | (* (nth weights i) (pdf-normal x :mean (nth mus i) :sd 1))) 120 | mix-pdf (fn [x] (reduce + (for [i (range num-comp)] (comp-pdf i x))))] 121 | ;; add the pdf of the fitted mixture 122 | (add-lines data-plot xs (map mix-pdf xs)) 123 | ;; and all individual components to the plot 124 | (doseq [i (range num-comp)] 125 | (add-lines data-plot xs (map (partial comp-pdf i) xs))) 126 | (view data-plot) 127 | [weights mus])) 128 | 129 | ;;; now we collapse out the component assignments 130 | 131 | (def-prob-cp collapsed-mixture-cp [comp-probs comp-models] 132 | :sampler [] [] ; just a dummy initialization ... no data drawn from model 133 | :calc-log-lik [xs] 134 | (let [sum (partial reduce +)] 135 | (sum (for [x xs] 136 | (Math/log ; switch to log-probabilities 137 | (sum (for [[p cm] (zipmap comp-probs comp-models)] 138 | ;; component model is a function that calculates the 139 | ;; probability for a given datapoint 140 | (* p (cm x)))))))) 141 | :proposer [_] (probabilistic-clojure.utils.stuff/error 142 | "collapsed-mixture-cp does not implement a proposer!")) 143 | 144 | (defn gaussian-comp-model [mu sdev] 145 | (fn [x] (pdf-normal x :mean mu :sd sdev))) 146 | 147 | (defn mixture-collapsed [comp-labels data] 148 | (let [comp-weights (dirichlet-cp :weights (repeat (count comp-labels) 10.0)) 149 | comp-mus (for [label comp-labels] 150 | (gaussian-cp [:mu label] 0.0 10.0)) 151 | comp-models (det-cp :models 152 | (doall (for [mu-cp comp-mus] 153 | (gaussian-comp-model (gv mu-cp) 1.0))))] 154 | (cond-data (collapsed-mixture-cp :data (gv comp-weights) (gv comp-models)) 155 | data) 156 | (det-cp :mixture 157 | [(zipmap comp-labels (map gv comp-mus)) 158 | (gv comp-weights)]))) 159 | 160 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 161 | ;;; 162 | ;;; Dirichlet process mixture model 163 | ;;; 164 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 165 | 166 | (defn mixture-DP [alpha data] 167 | (loop [points data 168 | idx 0 169 | comps (det-cp [:res 0] [0 {}])] 170 | (if (seq points) 171 | (let [mu-comp (dirichlet-process [::DP idx] alpha (gaussian-cp ::DP 0 15))] 172 | (cond-data (gaussian-cp [:mu idx] (gv mu-comp) 1.0) (first points)) 173 | (recur (rest points) (inc idx) 174 | (det-cp [:res (inc idx)] 175 | (let [[num-comp comp-mus] (gv comps) 176 | mu (gv mu-comp) 177 | mu-count (get comp-mus mu 0) 178 | comp-mus (assoc comp-mus mu (inc mu-count))] 179 | [(count comp-mus) comp-mus])))) 180 | comps))) 181 | 182 | (defn test-DP [alpha n] 183 | (let [res (metropolis-hastings-sampling (fn [] (mixture-DP alpha data)))] 184 | (loop [x res, i 0] 185 | (when-not (> i n) 186 | (recur (rest x) (inc i)))))) 187 | 188 | -------------------------------------------------------------------------------- /src/probabilistic_clojure/embedded/fit_poly.clj: -------------------------------------------------------------------------------- 1 | ;;; Copyright (C) 2012 Nils Bertschinger 2 | 3 | ;;; This file is part of Probabilistic-Clojure 4 | 5 | ;;; Probabilistic-Clojure is free software: you can redistribute it and/or modify 6 | ;;; it under the terms of the GNU Lesser General Public License as published by 7 | ;;; the Free Software Foundation, either version 3 of the License, or 8 | ;;; (at your option) any later version. 9 | 10 | ;;; Probabilistic-Clojure is distributed in the hope that it will be useful, 11 | ;;; but WITHOUT ANY WARRANTY; without even the implied warranty of 12 | ;;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 13 | ;;; GNU Lesser General Public License for more details. 14 | 15 | ;;; You should have received a copy of the GNU Lesser General Public License 16 | ;;; along with Probabilistic-Clojure. If not, see . 17 | 18 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 19 | ;;;; Probabilistic programming using constraint propagation 20 | ;;;; to efficiently track dependencies between choice points 21 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 22 | 23 | (ns 24 | ^{:author "Nils Bertschinger" 25 | :doc "Part of probabilistic-clojure.embedded. Demo of fitting polynomials."} 26 | probabilistic-clojure.embedded.fit-poly 27 | (:use [probabilistic-clojure.embedded.api :only (det-cp gv cond-data metropolis-hastings-sampling def-prob-cp)] 28 | [probabilistic-clojure.utils.stuff :only (indexed)] 29 | [probabilistic-clojure.utils.sampling :only (density)] 30 | [probabilistic-clojure.embedded.choice-points 31 | :only (gaussian-cp discrete-cp *gaussian-proposal-sdev*)] 32 | 33 | [incanter.core :only (view)] 34 | [incanter.charts :only (histogram add-lines xy-plot scatter-plot)] 35 | [incanter.stats :only (sample-normal pdf-normal)])) 36 | 37 | (in-ns 'probabilistic-clojure.embedded.fit-poly) 38 | 39 | (defn poly-ranked 40 | "Evaluate the polynomial with the given coefficients at x: 41 | f(x) = coeffs[0] + coeffs[1]*x + ... + coeffs[k]*x^(k-1)" 42 | [x coeffs] 43 | 44 | (reduce + (map * coeffs (iterate (partial * x) 1)))) 45 | 46 | (defn poly-horner 47 | "Evaluate the polynomial with the given coefficients at x. 48 | Evaluation follows the Horner scheme: 49 | f(x) = coeffs[0] + x*(coeffs[1] + ... + x*(coeffs[k])...)" 50 | [x coeffs] 51 | 52 | (reduce (fn [y c] 53 | (+ c (* x y))) 54 | (reverse coeffs))) 55 | 56 | (defn poly-roots 57 | [x [scale & roots]] 58 | (* scale 59 | (reduce * (map #(- x %) roots)))) 60 | 61 | (defn ^:dynamic legendre-basis [n x] 62 | (cond (= n 0) 1 63 | (= n 1) x 64 | :else (let [n- (dec n)] 65 | (/ (- (* (+ (* 2 n-) 1) x (legendre-basis n- x)) 66 | (* n- (legendre-basis (dec n-) x))) 67 | n)))) 68 | 69 | (defn poly-legendre [x coeffs] 70 | (binding [legendre-basis (memoize legendre-basis)] 71 | (let [x (/ x 4)] 72 | (reduce + 73 | (for [[i c] (indexed coeffs)] 74 | (* c (legendre-basis i x))))))) 75 | 76 | (def poly poly-legendre) 77 | 78 | (def test-poly [-1 1 -0.7 0.3]) 79 | 80 | (defn uni-rand [low high] 81 | (+ low (rand (- high low)))) 82 | 83 | (def demo-data 84 | (repeatedly 17 85 | (fn [] 86 | (let [x (uni-rand -5 5) 87 | y (poly-ranked x test-poly)] 88 | [x (sample-normal 1 :mean y :sd 2)])))) 89 | 90 | ;; special gaussian-cp which initially returns mu 91 | (def-prob-cp gaussian0-cp [mu sdev] 92 | :sampler [] (sample-normal 1 :mean 0 :sd 0.1) ;; mu 93 | :calc-log-lik [x] (Math/log (pdf-normal x :mean mu :sd sdev)) 94 | :proposer [old-x] (let [proposal-sd *gaussian-proposal-sdev* 95 | new-x (sample-normal 1 :mean old-x :sd proposal-sd)] 96 | [new-x 97 | (Math/log (pdf-normal new-x :mean old-x :sd proposal-sd)) 98 | (Math/log (pdf-normal old-x :mean new-x :sd proposal-sd))])) 99 | 100 | (defn poly-fit-fixed 101 | [rank data] 102 | (let [coeffs (det-cp :coeffs 103 | (doall 104 | (for [r (range (inc rank))] 105 | (gv (gaussian-cp [:coeff r] 106 | 0.0 5.0)))))] 107 | (doseq [[i [x y]] (indexed data)] 108 | (let [mu (det-cp [:mu i] (poly x (gv coeffs)))] 109 | (cond-data (gaussian-cp [:obs i] 110 | (gv mu) 111 | 1.0) 112 | y))) 113 | (det-cp :fit 114 | (gv coeffs)))) 115 | 116 | (defn poly-fit 117 | ([data] (poly-fit [1] data)) 118 | ([rank-range data] 119 | (let [n (count rank-range) 120 | rank (if (= n 1) 121 | (det-cp :rank (first rank-range)) 122 | (discrete-cp :rank (zipmap rank-range (repeat (/ 1 n))))) 123 | coeffs (det-cp :coeffs 124 | (into {} 125 | (for [rank rank-range] 126 | [rank (doall 127 | (for [r (range (inc rank))] 128 | (gv (gaussian0-cp [:coeff rank r] 129 | 0.0 5.0))))]))) 130 | obs-noise (det-cp :noise 131 | (into {} (for [rank rank-range] 132 | [rank (Math/abs (gv (gaussian-cp [:noise rank] 133 | 0.0 5.0)))])))] 134 | (doseq [[i [x y]] (indexed data)] 135 | (cond-data (gaussian-cp [:obs i] 136 | (poly x (get (gv coeffs) (gv rank))) 137 | (get (gv obs-noise) (gv rank))) 138 | y)) 139 | (det-cp :fit 140 | [(gv rank) (gv coeffs) (gv obs-noise)])))) 141 | 142 | (defn poly-demo [ranks data] 143 | (let [xs (range -5 5 0.05) 144 | 145 | fitted (last (take 7500 (metropolis-hastings-sampling 146 | (fn [] (poly-fit ranks demo-data))))) 147 | graph (scatter-plot (map first demo-data) (map second demo-data))] 148 | (doseq [r ranks] 149 | (add-lines graph xs (map #(poly % (get (second fitted) r)) xs))) 150 | (view graph))) 151 | 152 | (defn poly-fit-shared 153 | ([data] (poly-fit-shared [1] data)) 154 | ([rank-range data] 155 | (let [n (count rank-range) 156 | rank (if (= n 1) 157 | (det-cp :rank (first rank-range)) 158 | (discrete-cp :rank (zipmap rank-range (repeat (/ 1 n))))) 159 | coeffs (det-cp :coeffs 160 | ;; one set of coeffs which are shared by all models 161 | ;; and removed if unused 162 | (doall 163 | (for [r (range (inc (gv rank)))] 164 | (gv (gaussian0-cp [:coeff r] 165 | 0.0 5.0))))) 166 | obs-noise (det-cp :noise 167 | (Math/abs (gv (gaussian-cp [:noise rank] 168 | 0.0 5.0))))] 169 | (doseq [[i [x y]] (indexed data)] 170 | (cond-data (gaussian-cp [:obs i] 171 | (poly x (gv coeffs)) 172 | (gv obs-noise)) 173 | y)) 174 | (det-cp :fit 175 | [(gv rank) (gv coeffs) (gv obs-noise)])))) 176 | 177 | (defn poly-demo-shared [ranks data] 178 | (let [xs (range -5 5 0.05) 179 | 180 | samples (take 75000 (metropolis-hastings-sampling 181 | (fn [] (poly-fit-shared ranks demo-data)))) 182 | fitted (last samples) 183 | graph (scatter-plot (map first demo-data) (map second demo-data))] 184 | (println (density (map first samples))) 185 | (doseq [r ranks] 186 | (add-lines graph xs (map #(poly % (take r (second fitted))) xs))) 187 | (view graph))) 188 | -------------------------------------------------------------------------------- /src/probabilistic_clojure/embedded/lda_demo.clj: -------------------------------------------------------------------------------- 1 | ;;; Copyright (C) 2012 Nils Bertschinger 2 | 3 | ;;; This file is part of Probabilistic-Clojure 4 | 5 | ;;; Probabilistic-Clojure is free software: you can redistribute it and/or modify 6 | ;;; it under the terms of the GNU Lesser General Public License as published by 7 | ;;; the Free Software Foundation, either version 3 of the License, or 8 | ;;; (at your option) any later version. 9 | 10 | ;;; Probabilistic-Clojure is distributed in the hope that it will be useful, 11 | ;;; but WITHOUT ANY WARRANTY; without even the implied warranty of 12 | ;;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 13 | ;;; GNU Lesser General Public License for more details. 14 | 15 | ;;; You should have received a copy of the GNU Lesser General Public License 16 | ;;; along with Probabilistic-Clojure. If not, see . 17 | 18 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 19 | ;;;; Probabilistic programming using constraint propagation 20 | ;;;; to efficiently track dependencies between choice points 21 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 22 | 23 | (ns 24 | ^{:author "Nils Bertschinger" 25 | :doc "Part of probabilistic-clojure.embedded. Demo of Latent Dirichlet Allocation."} 26 | probabilistic-clojure.embedded.lda-demo 27 | (:use [probabilistic-clojure.embedded.api :only (det-cp gv cond-data memo metropolis-hastings-sampling def-prob-cp trace-failure)] 28 | [probabilistic-clojure.utils.stuff :only (indexed)] 29 | [probabilistic-clojure.embedded.choice-points 30 | :only (dirichlet-cp log-pdf-dirichlet *dirichlet-initial-factor* discrete-cp)] 31 | 32 | [incanter.core :only (view sqrt)] 33 | [incanter.stats :only (sample-dirichlet sample-multinomial sample-uniform sample-gamma pdf-gamma sample-normal pdf-normal)]) 34 | (:import [java.awt Color Graphics Dimension] 35 | [java.awt.image BufferedImage] 36 | [javax.swing JPanel JFrame] 37 | [org.apache.commons.math.special Gamma])) 38 | 39 | (in-ns 'probabilistic-clojure.embedded.lda-demo) 40 | 41 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 42 | ;;; 43 | ;;; Here we want to show the picture example from the LDA paper 44 | ;;; "Finding scientific topics" by D. Blei et al. 45 | ;;; 46 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 47 | 48 | ;;; Basic definitions and the LDA model as a probabilistic program 49 | 50 | (def alpha 1) 51 | (def beta 1) 52 | 53 | (defn lda [topic-labels documents] 54 | (let [words (distinct (apply concat documents)) 55 | num-topics (count topic-labels) 56 | alphas (repeat (count words) alpha) 57 | betas (repeat num-topics beta)] 58 | (doseq [[i doc] (indexed documents)] 59 | (let [topic-weights (dirichlet-cp [:weights i] betas)] 60 | ;; now for each word draw a topic and condition on the observed word 61 | (doseq [[j word] (indexed doc)] 62 | (let [assigned (discrete-cp [:assign i j] 63 | (zipmap topic-labels (gv topic-weights))) 64 | topic-dist (memo [:topic i j] (dirichlet-cp :weights alphas) (gv assigned))] 65 | (cond-data (discrete-cp [:word i j] 66 | (zipmap words (gv topic-dist))) 67 | word))))) 68 | (det-cp :lda 69 | (doall 70 | (into {} 71 | (for [tl topic-labels] 72 | [tl 73 | (zipmap words 74 | (gv (memo [:topic tl] 75 | (dirichlet-cp :weights alphas) tl)))])))))) 76 | 77 | 78 | ;;; Collapsing out the topic assignments should be faster 79 | 80 | ;; A collapsed mixture choice point that takes contigency counts as 81 | ;; data (usually much faster than the one in demo.clj) 82 | (def-prob-cp collapsed-mixture-cp [comp-probs comp-models] 83 | :sampler [] [] ; just a dummy initialization ... no data drawn from model 84 | :calc-log-lik [counts] 85 | (let [sum (partial reduce +)] 86 | (sum (for [[x c] counts] 87 | (* c 88 | (Math/log ; switch to log-probabilities 89 | (sum (for [[p cm] (zipmap comp-probs comp-models)] 90 | ;; component model is a function that calculates the 91 | ;; probability for a given datapoint 92 | (* p (cm x))))))))) 93 | :proposer [_] (probabilistic-clojure.utils.stuff/error 94 | "collapsed-mixture-cp does not implement a proposer!")) 95 | 96 | (defn lda-collapsed [topic-labels documents] 97 | (let [words (distinct (apply concat documents)) 98 | num-topics (count topic-labels) 99 | alphas (repeat (count words) alpha) 100 | betas (repeat num-topics beta) 101 | 102 | topic-dists (for [tl topic-labels] 103 | (dirichlet-cp [:topic tl] alphas))] 104 | (doseq [[i doc] (indexed documents)] 105 | (let [topic-weights (dirichlet-cp [:weights i] betas) 106 | topic-models (det-cp [:models i] 107 | (doall (for [w-probs topic-dists] 108 | (let [w-dist (zipmap words (gv w-probs))] 109 | (fn [word] (get w-dist word))))))] 110 | (cond-data (collapsed-mixture-cp [:doc i] 111 | (gv topic-weights) (gv topic-models)) 112 | (frequencies doc)))) 113 | (det-cp :lda-collapsed 114 | (into {} 115 | (for [[tl top] (zipmap topic-labels topic-dists)] 116 | [tl (zipmap words (gv top))]))))) 117 | 118 | ;;; Now generate example documents with the bar-like topics from the paper 119 | 120 | (def xy-dim 3) 121 | 122 | (def num-topics (* 2 xy-dim)) 123 | (def num-words (* xy-dim xy-dim)) 124 | 125 | (defn row-or-col-topic [row-or-col] 126 | (let [row (:row row-or-col), col (:col row-or-col)] 127 | (for [x (range xy-dim), y (range xy-dim) 128 | :when (or (and row (= row x)) (and col (= col y)))] 129 | [x y]))) 130 | 131 | (defn topics [] 132 | "Create topics corresponding to horizontal and vertical images. 133 | Each topic is a sequence of words that can appear in this topic." 134 | (concat (for [row (range xy-dim)] (row-or-col-topic {:row row})) 135 | (for [col (range xy-dim)] (row-or-col-topic {:col col})))) 136 | 137 | (defn sample-document [nwords theta topics] 138 | (let [assigned (sample-multinomial nwords :probs theta) 139 | wprobs (for [_ (range xy-dim)] (/ 1 xy-dim))] 140 | (map (fn [z wi] (nth (nth topics z) wi)) 141 | assigned (sample-multinomial nwords :probs wprobs)))) 142 | 143 | (defn train-data [n topics] 144 | (for [theta (sample-dirichlet n (repeat (count topics) beta))] 145 | ;; (sample-document (sample-uniform 1 :min 33 :max 44 :integers true) theta topics))) 146 | (sample-document 250 theta topics))) 147 | 148 | ;; (def demo-docs (train-data 55 (topics))) 149 | (def demo-docs (train-data 120 (topics))) 150 | 151 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; UI ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 152 | 153 | ;pixels per world cell 154 | (def scale 25) 155 | 156 | (def topic-labels (doall (map (partial str "T") (range num-topics)))) 157 | (def topic-samples (into {} (for [tl topic-labels] [tl (ref {})]))) 158 | 159 | (defn fill-cell [#^Graphics g x y c] 160 | (doto g 161 | (.setColor c) 162 | (.fillRect (* x scale) (* y scale) scale scale))) 163 | 164 | (defn render [g] 165 | (let [v (dosync (doall 166 | (for [z topic-labels] 167 | (apply vector (for [x (range xy-dim) y (range xy-dim)] 168 | (get @(get topic-samples z) [x y] 0)))))) 169 | img (new BufferedImage (* (+ num-topics 2) scale xy-dim) (* scale xy-dim) 170 | (. BufferedImage TYPE_INT_ARGB)) 171 | bg (. img (getGraphics))] 172 | (doto bg 173 | (.setColor (. Color blue)) 174 | (.fillRect 0 0 (. img (getWidth)) (. img (getHeight)))) 175 | (dorun 176 | (for [z (range num-topics) x (range xy-dim) y (range xy-dim)] 177 | (let [rgb (max 0 (- 255 (int (* xy-dim 255 ((nth v z) (+ (* x xy-dim) y))))))] 178 | (fill-cell bg (+ x (* z (inc xy-dim))) y (Color. rgb rgb rgb))))) 179 | (. g (drawImage img 0 0 nil)) 180 | (. bg (dispose)))) 181 | 182 | (def panel (doto (proxy [JPanel] [] 183 | (paint [g] (render g))) 184 | (.setPreferredSize (new Dimension 185 | (* (+ num-topics 2) scale xy-dim) 186 | (* scale xy-dim))))) 187 | 188 | (def frame (doto (new JFrame) (.add panel) .pack .show)) 189 | 190 | (defn run [num skip lda-model] 191 | (binding [*dirichlet-initial-factor* 50] 192 | (doseq [[i tops] (indexed 193 | (take num 194 | (metropolis-hastings-sampling 195 | (fn [] 196 | (lda-model topic-labels demo-docs)))))] 197 | (when (= (mod i skip) 0) 198 | (dosync 199 | (doseq [tl topic-labels] 200 | (ref-set (get topic-samples tl) 201 | (get tops tl)))) 202 | (. panel (repaint)))))) 203 | 204 | ;;; Dirichlet choice point based on Gamma samples => more local 205 | ;;; proposal distribution 206 | 207 | (defn diri-probs [gammas] 208 | (let [total (reduce + gammas)] 209 | (vec (map #(/ % total) gammas)))) 210 | 211 | (defn propose-gamma-prior [old-x shape rate] 212 | ;; propose new value from Gamma prior 213 | (let [new-x (sample-gamma 1 :shape shape :rate rate)] 214 | [new-x 215 | (Math/log (pdf-gamma new-x :shape shape :rate rate)) 216 | (Math/log (pdf-gamma old-x :shape shape :rate rate))])) 217 | 218 | (defn propose-gamma-normal [old-x shape sdev-factor] 219 | (let [sdev (* shape sdev-factor) 220 | new-x (sample-normal 1 :mean old-x :sd sdev)] 221 | (when (< new-x 0) 222 | (trace-failure)) 223 | [new-x 224 | (Math/log (pdf-normal new-x :mean old-x :sd sdev)) 225 | (Math/log (pdf-normal old-x :mean new-x :sd sdev))])) 226 | 227 | (defn propose-gamma-log-normal [old-x sdev] 228 | (let [log-old-x (Math/log old-x) 229 | log-new-x (sample-normal 1 :mean log-old-x :sd sdev)] 230 | [(Math/exp log-new-x) 231 | (Math/log (pdf-normal log-new-x :mean log-old-x :sd sdev)) 232 | (Math/log (pdf-normal log-old-x :mean log-new-x :sd sdev))])) 233 | 234 | ;; un-normalized Dirichlet distribution 235 | (def-prob-cp dirichlet-cp-gamma [alphas] 236 | :sampler [] (vec (for [a alphas] (sample-gamma 1 :shape a :rate 1))) 237 | :calc-log-lik [gs] (log-pdf-dirichlet (diri-probs gs) alphas) 238 | :proposer [old-gs] (let [idx (rand-int (count old-gs)) 239 | [new-g fwd bwd] 240 | ;; (propose-gamma-prior (nth old-gs idx) (nth alphas idx) 1)] 241 | (propose-gamma-normal (nth old-gs idx) (nth alphas idx) 1)] 242 | ;; (propose-gamma-log-normal (nth old-gs idx) 1)] 243 | [(assoc old-gs idx new-g) fwd bwd])) 244 | 245 | (defn lda-collapsed-gamma [topic-labels documents] 246 | (let [words (distinct (apply concat documents)) 247 | num-topics (count topic-labels) 248 | alphas (repeat (count words) alpha) 249 | betas (repeat num-topics beta) 250 | 251 | topic-dists (for [tl topic-labels] 252 | (dirichlet-cp-gamma [:topic tl] alphas))] 253 | (doseq [[i doc] (indexed documents)] 254 | (let [topic-weights (dirichlet-cp-gamma [:weights i] betas) 255 | topic-models (det-cp [:models i] 256 | (doall (for [w-probs topic-dists] 257 | (let [w-dist (zipmap words (diri-probs (gv w-probs)))] 258 | (fn [word] (get w-dist word))))))] 259 | (cond-data (collapsed-mixture-cp [:doc i] 260 | (diri-probs (gv topic-weights)) (gv topic-models)) 261 | (frequencies doc)))) 262 | (det-cp :lda-collapsed 263 | (into {} 264 | (for [[tl top] (zipmap topic-labels topic-dists)] 265 | [tl (zipmap words (diri-probs (gv top)))]))))) 266 | 267 | (def-prob-cp gamma-cp [shape rate] 268 | :sampler [] (sample-gamma 1 :shape shape :rate rate) 269 | :calc-log-lik [x] 270 | (Math/log (pdf-gamma x :shape shape :rate rate)) 271 | :proposer [old-x] 272 | (propose-gamma-log-normal old-x 1)) -------------------------------------------------------------------------------- /src/probabilistic_clojure/embedded/sampling.clj: -------------------------------------------------------------------------------- 1 | ;;; Copyright (C) 2012 Nils Bertschinger 2 | 3 | ;;; This file is part of Probabilistic-Clojure 4 | 5 | ;;; Probabilistic-Clojure is free software: you can redistribute it and/or modify 6 | ;;; it under the terms of the GNU Lesser General Public License as published by 7 | ;;; the Free Software Foundation, either version 3 of the License, or 8 | ;;; (at your option) any later version. 9 | 10 | ;;; Probabilistic-Clojure is distributed in the hope that it will be useful, 11 | ;;; but WITHOUT ANY WARRANTY; without even the implied warranty of 12 | ;;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 13 | ;;; GNU Lesser General Public License for more details. 14 | 15 | ;;; You should have received a copy of the GNU Lesser General Public License 16 | ;;; along with Probabilistic-Clojure. If not, see . 17 | 18 | (ns 19 | ^{:author "Nils Bertschinger" 20 | :doc "Part of probabilistic programming for Clojure. 21 | 22 | Experimental support for simulated annealing as well as annealed 23 | importance sampling. Basically, refactors the core sampling routine to 24 | get a handle on the acceptance condition and allow for interrupting 25 | and restarting sampling."} 26 | probabilistic-clojure.embedded.sampling 27 | (:use [clojure.set :only (union)]) 28 | (:use probabilistic-clojure.embedded.api)) 29 | 30 | (in-ns 'probabilistic-clojure.embedded.sampling) 31 | 32 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 33 | ;;; 34 | ;;; New interface to the sampler 35 | ;;; 36 | ;;; More flexible, easy to support different sampling strategies 37 | ;;; 38 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 39 | 40 | (defn split-log-lik 41 | "Like total-log-lik, but returns two separate sums for the unconditioned 42 | and conditioned choice points. This allows to distinguish the prior (unconditioned) 43 | and likelihood contributions (conditioned) to the total log-likelihood 44 | of the trace. 45 | Choice points not in the trace are allowed and don't effect the result." 46 | 47 | [cp-names choice-points] 48 | (reduce (fn [[uncond-sum cond-sum :as sums] cp-name] 49 | (let [cp (choice-points cp-name)] 50 | (case (:type cp) 51 | :probabilistic-clojure.embedded.api/probabilistic 52 | (if (:conditioned? cp) 53 | [uncond-sum (+ cond-sum (:log-lik cp))] 54 | [(+ uncond-sum (:log-lik cp)) cond-sum]) 55 | :probabilistic-clojure.embedded.api/deterministic 56 | sums 57 | ;; else 58 | sums))) 59 | [0 0] cp-names)) 60 | 61 | (defn metropolis-hastings-stepper [choice-points selected selection-dist acceptor] 62 | (with-fresh-store choice-points 63 | (let [selected-cp (choice-points selected) 64 | 65 | [prop-val fwd-log-lik bwd-log-lik] 66 | (propose selected-cp (:value selected-cp))] 67 | ;; Propose a new value for the selected choice point and propagate change to dependents 68 | (set-proposed-val! (:name selected-cp) prop-val) 69 | (let [updates (propagate-change-to (:dependents selected-cp))] 70 | ;; (println "Proposed " (:name selected-cp) " for " updates " updates (" 71 | ;; (count-all-dependents (:name selected-cp) choice-points) " dependents)")) 72 | ) 73 | 74 | (if (trace-failed?) 75 | [choice-points ::rejected true selection-dist] 76 | (let [removed-cps (remove-uncalled-choices) 77 | same-topology (and (empty? (fetch-store :newly-created)) 78 | (empty? removed-cps)) 79 | ;; Here we have the following invariants: 80 | ;; * (assert (empty? (clojure.set/intersection removed-cps (fetch-store :newly-created)))) 81 | ;; * (let [new (set (keys (fetch-store :choice-points))) 82 | ;; old (set (keys choice-points))] 83 | ;; (assert (and (= new (difference (union old (fetch-store :newly-created)) 84 | ;; removed-cps)) 85 | ;; (= old (difference (union new removed-cps) (fetch-store :newly-created)))))) 86 | 87 | ;; Overall the recomputed and removed-cps were touched during the update 88 | ;; Thus, we have to calculate the total probability contributed to the old 89 | ;; as well as the new traces. 90 | touched-cps (union (fetch-store :recomputed) removed-cps) 91 | [uncond-trace-log-lik cond-trace-log-lik] (split-log-lik touched-cps choice-points) 92 | [uncond-prop-trace-log-lik cond-prop-trace-log-lik] (split-log-lik touched-cps (fetch-store :choice-points)) 93 | 94 | ;; The forward and backward probabilities now account for the newly-created 95 | ;; and removed choice points 96 | fwd-trace-log-lik (total-log-lik (fetch-store :newly-created) (fetch-store :choice-points)) 97 | bwd-trace-log-lik (total-log-lik removed-cps choice-points) 98 | 99 | prop-selection-dist (if same-topology 100 | selection-dist 101 | ;; (prob-choice-dist (fetch-store :choice-points)))] 102 | (-> selection-dist 103 | (add-to-prob-choice-dist (fetch-store :newly-created) 104 | (fetch-store :choice-points)) 105 | (remove-from-prob-choice-dist removed-cps)))] 106 | ;; Randomly accept the new proposal according to the Metropolis Hastings formula 107 | (if (acceptor uncond-prop-trace-log-lik cond-prop-trace-log-lik 108 | uncond-trace-log-lik cond-trace-log-lik 109 | ;; the total forward proposal probability 110 | (+ (Math/log (prob selection-dist (:name selected-cp))) 111 | fwd-trace-log-lik 112 | fwd-log-lik) 113 | ;; and the backward probability 114 | (+ (Math/log (prob prop-selection-dist (:name selected-cp))) 115 | bwd-trace-log-lik 116 | bwd-log-lik)) 117 | ;; (< (Math/log (rand)) 118 | ;; (+ (- prop-trace-log-lik trace-log-lik) 119 | ;; (- (Math/log (prob prop-selection-dist (:name selected-cp))) 120 | ;; (Math/log (prob selection-dist (:name selected-cp)))) 121 | ;; (- bwd-trace-log-lik fwd-trace-log-lik) 122 | ;; (- bwd-log-lik fwd-log-lik))) 123 | [(fetch-store :choice-points) ::accepted same-topology prop-selection-dist] 124 | [choice-points ::rejected true selection-dist])))))) 125 | 126 | ;; The sampler core has to change as well: 127 | ;; * The acceptor can be specified from the outside 128 | 129 | ;; * To allow for interrupting and restarting of sampling the 130 | ;; choice-points are passed in from the outside and returned 131 | ;; alongside each sample which is now of the form 132 | ;; {:value val :choice-points choice-points} 133 | (defn metropolis-hastings-sampling-core [[cp choice-points] acceptor] 134 | (letfn [(samples [choice-points idx num-accepted num-top-changed update-seq selection-dist] 135 | (lazy-seq 136 | (let [update-seq (or (seq update-seq) 137 | (new-update-sequence (prob-choice-dist choice-points))) 138 | val (cp-value cp choice-points) 139 | 140 | [next-choice-points status same-topology next-selection-dist] 141 | (metropolis-hastings-stepper choice-points (first update-seq) selection-dist acceptor) 142 | 143 | output-info (and *info-steps* (= (mod idx *info-steps*) 0)) 144 | num-accepted (if (= status ::accepted) 145 | (inc num-accepted) num-accepted) 146 | num-top-changed (if same-topology 147 | num-top-changed (inc num-top-changed))] 148 | (when output-info 149 | (println idx ": " val) 150 | (println "Log. lik.: " (total-log-lik (keys choice-points) choice-points)) 151 | (println "Accepted " num-accepted " out of last " *info-steps* " samples.") 152 | (println "Topology changed on " num-top-changed " samples.")) 153 | (cons {:value val :choice-points choice-points} 154 | (samples next-choice-points 155 | (inc idx) 156 | (if output-info 0 num-accepted) 157 | (if output-info 0 num-top-changed) 158 | (if same-topology 159 | (rest update-seq) 160 | (new-update-sequence next-selection-dist)) 161 | next-selection-dist)))))] 162 | (let [selection-dist (prob-choice-dist choice-points)] 163 | (samples choice-points 0 0 0 (new-update-sequence selection-dist) selection-dist)))) 164 | 165 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 166 | ;;; 167 | ;;; This shows how the standard sampling procedure can be obtained 168 | ;;; using the new interface to the sampler 169 | ;;; 170 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 171 | 172 | (defn metropolis-hastings-acceptor 173 | [uncond-prop-trace-log-lik cond-prop-trace-log-lik 174 | uncond-trace-log-lik cond-trace-log-lik 175 | total-fwd-log-lik total-bwd-log-lik] 176 | (< (Math/log (rand)) 177 | (+ (- (+ uncond-prop-trace-log-lik cond-prop-trace-log-lik) 178 | (+ uncond-trace-log-lik cond-trace-log-lik)) 179 | (- total-bwd-log-lik 180 | total-fwd-log-lik)))) 181 | 182 | (defn standard-metropolis-hastings-sampling 183 | ([prob-thunk] 184 | (standard-metropolis-hastings-sampling prob-thunk 185 | metropolis-hastings-acceptor)) 186 | ([prob-thunk acceptor] 187 | (println "Trying to find a valid trace ...") 188 | (let [cp-and-choice-points (find-valid-trace prob-thunk)] 189 | (println "Started sampling") 190 | (map :value 191 | (metropolis-hastings-sampling-core cp-and-choice-points 192 | acceptor))))) 193 | 194 | ;; test this on the demo code 195 | 196 | (comment 197 | (probabilistic-clojure.utils.sampling/density 198 | (take 7500 199 | (drop 500 200 | (standard-metropolis-hastings-sampling 201 | probabilistic-clojure.embedded.demos/grass-bayes-net)))) 202 | 203 | (last 204 | (take 7500 205 | (standard-metropolis-hastings-sampling 206 | (fn [] (probabilistic-clojure.embedded.demos/mixture-memo 207 | [:a :b :c] 208 | probabilistic-clojure.embedded.demos/data)))))) 209 | 210 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 211 | ;;; 212 | ;;; Simulated annealing ... simple plug in a different acceptor 213 | ;;; 214 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 215 | 216 | (defn simulated-annealing-acceptor [inv-temperature] 217 | (fn [uncond-prop-trace-log-lik cond-prop-trace-log-lik 218 | uncond-trace-log-lik cond-trace-log-lik 219 | total-fwd-log-lik total-bwd-log-lik] 220 | ;; ignores the forward-backward probability and accepts according 221 | ;; to the scaled (with the inverse temperature) total log-probability 222 | ;; difference 223 | (< (Math/log (rand)) 224 | (* inv-temperature 225 | (- (+ uncond-prop-trace-log-lik cond-prop-trace-log-lik) 226 | (+ uncond-trace-log-lik cond-trace-log-lik)))))) 227 | 228 | (defn simulated-annealing-acceptor-prior [inv-temperature] 229 | (fn [uncond-prop-trace-log-lik cond-prop-trace-log-lik 230 | uncond-trace-log-lik cond-trace-log-lik 231 | total-fwd-log-lik total-bwd-log-lik] 232 | ;; ignores the forward-backward probability and accepts according 233 | ;; to the (unscaled) prior and scaled (with the inverse temperature) 234 | ;; log-likelihood difference 235 | (< (Math/log (rand)) 236 | (+ (- uncond-prop-trace-log-lik uncond-trace-log-lik) 237 | (* inv-temperature 238 | (- cond-prop-trace-log-lik cond-trace-log-lik)))))) 239 | 240 | (defn simulated-annealing 241 | "Implements simulated annealing. The temperature schedule is a 242 | sequence containing [inv-temperature number-of-steps] pairs. 243 | 244 | Usually one wants to start with a rather low inverse temperature and 245 | increase it over time." 246 | ([prob-thunk inv-temperature-schedule] 247 | (simulated-annealing prob-thunk inv-temperature-schedule simulated-annealing-acceptor)) 248 | ([prob-thunk inv-temperature-schedule acceptor] 249 | (println "Trying to find a valid trace ...") 250 | (let [[cp choice-points] (find-valid-trace prob-thunk)] 251 | (println "Started sampling") 252 | (reduce concat 253 | (first 254 | (reduce (fn [[samples choice-points] [inv-temperature steps]] 255 | (let [more-samples 256 | (take steps (metropolis-hastings-sampling-core 257 | [cp choice-points] 258 | (acceptor inv-temperature)))] 259 | [(conj samples (map :value more-samples)) 260 | (:choice-points (last more-samples))])) 261 | [[] choice-points] 262 | inv-temperature-schedule)))))) 263 | 264 | ;; This nicely optimizes the Gaussian mixture model 265 | (comment 266 | (last 267 | (simulated-annealing 268 | (fn [] (probabilistic-clojure.embedded.demos/mixture-memo 269 | [:a :b :c] probabilistic-clojure.embedded.demos/data)) 270 | [[0.01 2500] [0.1 2500] [1 2500] [10 2500] [100 2500]]))) 271 | 272 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 273 | ;;; 274 | ;;; Annealed importance sampling 275 | ;;; 276 | ;;; TODO: Distinguish between conditioned and unconditioned choice 277 | ;;; points to handle prior and likelihood weights differently! 278 | ;;; 279 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 280 | 281 | (defn annealed-importance-acceptor 282 | "One way to obtain a sequence of chains for annealed importance 283 | sampling. Uses the Metropolis-Hastings acceptance condition, but 284 | mixes for the distribution p(x) p(y|x)^beta instead of p(x,y)." 285 | [beta] 286 | (fn 287 | [uncond-prop-trace-log-lik cond-prop-trace-log-lik 288 | uncond-trace-log-lik cond-trace-log-lik 289 | total-fwd-log-lik total-bwd-log-lik] 290 | (< (Math/log (rand)) 291 | (+ (- uncond-prop-trace-log-lik uncond-trace-log-lik) 292 | (* beta (- cond-prop-trace-log-lik cond-trace-log-lik)) 293 | (- total-bwd-log-lik total-fwd-log-lik))))) 294 | 295 | (defn annealed-importance-sample 296 | "Implements annealed importance sampling to draw ONE sample with its 297 | corresponding importance weight. For the sample a sequence of 298 | Markov-chains according to the given annealing schedule (sequence of 299 | [beta num-steps] pairs) is run and used to calculate its importance 300 | weight. Beta should start close to zero and then slowly increase 301 | towards 1. 302 | 303 | Running this function repeatedly produces independent, weighted 304 | samples from the distribution specified by the probabilistic 305 | function prob-thunk. The variance of the importance weights can be 306 | used as diagnostic for the quality of the obtained samples which 307 | depends on how well the Markov chains are mixing." 308 | [prob-thunk annealing-schedule] 309 | 310 | (let [[cp choice-points] (find-valid-trace prob-thunk)] 311 | (print "Sampling ... ") 312 | (let [chain-log-lik (fn [beta choice-points] 313 | (let [[uncond-log-lik cond-log-lik] 314 | (split-log-lik (keys choice-points) choice-points)] 315 | (+ uncond-log-lik (* beta cond-log-lik)))) 316 | 317 | [x-0 log-weights choice-points] 318 | (reduce (fn [[x-n-1 log-ws choice-points] [beta-n-1 steps-T-n-1]] 319 | (let [prob-x-n-1 (chain-log-lik beta-n-1 choice-points) 320 | {x-n-2 :value new-choice-points :choice-points} 321 | (last (take steps-T-n-1 322 | (metropolis-hastings-sampling-core 323 | [cp choice-points] 324 | (annealed-importance-acceptor beta-n-1)))) 325 | prob-x-n-2 (chain-log-lik beta-n-1 new-choice-points)] 326 | ;; (println "Chain moved " x-n-1 " to " x-n-2) 327 | ;; (println "Log. weight difference: " (- prob-x-n-1 prob-x-n-2)) 328 | [x-n-2 329 | (conj log-ws (- prob-x-n-1 prob-x-n-2)) 330 | new-choice-points])) 331 | [(cp-value cp choice-points) 332 | (let [[prior-log-lik _] (split-log-lik (keys choice-points) choice-points)] 333 | [(- prior-log-lik)]) 334 | choice-points] 335 | annealing-schedule) 336 | prob-x-0 (total-log-lik (keys choice-points) choice-points)] 337 | (println "value: " x-0 " with weight: " (+ prob-x-0 (reduce + log-weights))) 338 | {:value x-0 339 | :log-importance-weight (+ prob-x-0 (reduce + log-weights)) 340 | :debug (conj log-weights prob-x-0)}))) 341 | 342 | ;; Try this on a very simple model, i.e. fitting the mean of a 343 | ;; standard Gaussian with a Gaussian prior 344 | 345 | (use '[probabilistic-clojure.embedded.choice-points :only (gaussian-cp)]) 346 | (use '[probabilistic-clojure.utils.stuff :only (indexed)]) 347 | (use '[incanter.stats :only (sample-normal pdf-normal)]) 348 | 349 | (defn gauss-fit [mu-prior sd-prior sd-likelihood data] 350 | (let [mu (gaussian-cp :mu mu-prior sd-prior)] 351 | (doseq [[i x] (indexed data)] 352 | (cond-data (gaussian-cp [:obs i] (gv mu) sd-likelihood) 353 | x)) 354 | (det-cp :fit (gv mu)))) 355 | 356 | (def xs (sample-normal 10 :mean 2.5 :sd 1)) 357 | 358 | ;; The theoretical posterior and marginal likelihood for the Gaussian 359 | ;; mean fit Formulas are from notes by Kevin Murphy ... simplify by 360 | ;; using precision (lambda) instead of variance 361 | 362 | (defn posterior [mu-0 lambda-0 lambda xs] 363 | (let [lambda-n (+ lambda-0 (* (count xs) lambda)) 364 | mu-n (/ (+ (* lambda (reduce + xs)) 365 | (* lambda-0 mu-0)) 366 | lambda-n)] 367 | {:mu mu-n :sdev (Math/sqrt (/ 1 lambda-n))})) 368 | 369 | (defn log-marginal-likelihood [mu-0 lambda-0 lambda xs] 370 | ;; formula (42) from the notes 371 | (let [sig (Math/sqrt (/ 1 lambda)) 372 | n-*-x-mean (reduce + xs) 373 | n (count xs)] 374 | (+ (Math/log (/ sig (* (Math/pow (* (Math/sqrt (* 2 Math/PI)) sig) n) 375 | (Math/sqrt (+ (* n (/ 1 lambda-0)) (/ 1 lambda)))))) 376 | (- (+ (/ (reduce + (map * xs xs)) (* 2 (/ 1 lambda))) 377 | (/ (* mu-0 mu-0) (* 2 (/ 1 lambda-0))))) 378 | (/ (+ (/ (* (/ 1 lambda-0) n-*-x-mean n-*-x-mean) 379 | (/ 1 lambda)) 380 | (/ (* (/ 1 lambda) mu-0 mu-0) 381 | (/ 1 lambda-0)) 382 | (* 2 n-*-x-mean mu-0)) 383 | (* 2 (+ (* n (/ 1 lambda-0)) (/ 1 lambda))))))) 384 | 385 | ;; TODO: check this formula ... seems to use improper flat prior!!! 386 | 387 | ;; The empirical average of the importance weights should be close to that! 388 | 389 | (use '[incanter.core :only (view)]) 390 | (use '[incanter.charts :only (histogram add-lines)]) 391 | 392 | (use '[probabilistic-clojure.utils.sampling :only (sample-from normalize density)]) 393 | 394 | (defn resampling-distribution [importance-samples] 395 | (let [max-log-weight (reduce max (map :log-importance-weight importance-samples))] 396 | (normalize 397 | (into {} (for [sample importance-samples] 398 | [(:value sample) 399 | (Math/exp (- (:log-importance-weight sample) max-log-weight))]))))) 400 | 401 | (defn log-sum-exp 402 | "Evaluates \\log \\sum_i e^{x_i}." 403 | [xs] 404 | (let [x-max (apply max xs)] 405 | (+ x-max 406 | (Math/log (reduce + (map #(Math/exp (- % x-max)) xs)))))) 407 | 408 | (defn effective-size 409 | "Calculates the effective sample size for the given importance weights: 410 | N_{eff} = \\frac{(\\sum_i w_i)^2}{\\sum w_i^2} 411 | " 412 | [importance-weights] 413 | (Math/exp (- (* 2 (log-sum-exp importance-weights)) 414 | (log-sum-exp (map (partial * 2) importance-weights))))) 415 | 416 | (defn test-ais [xs num-samples] 417 | (let [mu-prior 0 418 | sd-prior 10 419 | sd-likelihood 1 420 | lambda-0 (/ 1 (* sd-prior sd-prior)) 421 | lambda (/ 1 (* sd-likelihood sd-likelihood)) 422 | 423 | {mu-n :mu sd-n :sdev} (posterior mu-prior lambda-0 lambda xs) 424 | 425 | ;; a-schedule (for [beta (range 0.05 0.95 0.05)] 426 | ;; [beta 100]) 427 | a-schedule (for [beta (range 0.01 1 0.01)] 428 | [beta 10]) 429 | samples 430 | (repeatedly num-samples 431 | (fn [] (annealed-importance-sample (fn [] (gauss-fit mu-prior sd-prior sd-likelihood xs)) a-schedule)))] 432 | (println "Posterior: mu = " mu-n ", sdev = " sd-n) 433 | (println "Log. marginal likelihood of data: " (log-marginal-likelihood mu-prior lambda-0 lambda xs)) 434 | (println "Log. average importance weights: " 435 | (- (log-sum-exp (map :log-importance-weight samples)) 436 | (Math/log (count samples)))) 437 | ;; How to calculate the variance of those weights to access sample quality???? 438 | ;; (let [N-eff (effective-size (map :log-importance-weight samples))] 439 | ;; (println (map :log-importance-weight samples)) 440 | ;; (println "Variance of importance weights: " 441 | ;; (- (/ (count samples) N-eff) 442 | ;; 1) 443 | ;; " " 444 | ;; (reduce + (map #(* % %) (vals (resampling-distribution samples)))))) 445 | (println "Effective sample size: " (effective-size (map :log-importance-weight samples))) 446 | (let [dist (resampling-distribution samples) 447 | hist (histogram (repeatedly 250 (fn [] (sample-from dist))) 448 | :nbins 50 :density true) 449 | x-range (range -5 5 0.01)] 450 | (doto hist 451 | (add-lines x-range (map (fn [x] (pdf-normal x :mean mu-n :sd sd-n)) x-range)) 452 | view)))) 453 | 454 | (defn test-MH [xs num-samples] 455 | (let [mu-prior 0 456 | sd-prior 10 457 | sd-likelihood 1 458 | lambda-0 (/ 1 (* sd-prior sd-prior)) 459 | lambda (/ 1 (* sd-likelihood sd-likelihood)) 460 | 461 | {mu-n :mu sd-n :sdev} (posterior mu-prior lambda-0 lambda xs) 462 | 463 | samples (take num-samples 464 | (drop 2500 465 | (standard-metropolis-hastings-sampling 466 | (fn [] (gauss-fit mu-prior sd-prior sd-likelihood xs))))) 467 | 468 | hist (histogram (repeatedly 250 (fn [] (sample-from (density samples)))) 469 | :nbins 50 :density true) 470 | x-range (range -5 5 0.01)] 471 | (doto hist 472 | (add-lines x-range (map (fn [x] (pdf-normal x :mean mu-n :sd sd-n)) x-range)) 473 | view))) 474 | -------------------------------------------------------------------------------- /src/probabilistic_clojure/embedded/test_deps.clj: -------------------------------------------------------------------------------- 1 | ;;; Copyright (C) 2011 Nils Bertschinger 2 | 3 | ;;; This file is part of Probabilistic-Clojure 4 | 5 | ;;; Probabilistic-Clojure is free software: you can redistribute it and/or modify 6 | ;;; it under the terms of the GNU Lesser General Public License as published by 7 | ;;; the Free Software Foundation, either version 3 of the License, or 8 | ;;; (at your option) any later version. 9 | 10 | ;;; Probabilistic-Clojure is distributed in the hope that it will be useful, 11 | ;;; but WITHOUT ANY WARRANTY; without even the implied warranty of 12 | ;;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 13 | ;;; GNU Lesser General Public License for more details. 14 | 15 | ;;; You should have received a copy of the GNU Lesser General Public License 16 | ;;; along with Probabilistic-Clojure. If not, see . 17 | 18 | (ns 19 | ^{:author "Nils Bertschinger" 20 | :doc "Tests for probabilistic-clojure.embedded. 21 | Checks dependency tracking between choice points"} 22 | probabilistic-clojure.embedded.test-deps 23 | (:use clojure.test) 24 | (:use probabilistic-clojure.embedded.api 25 | [probabilistic-clojure.embedded.choice-points :only (flip-cp)])) 26 | 27 | (in-ns 'probabilistic-clojure.embedded.test-deps) 28 | 29 | ;;; TODO: use testing framework and write real unit tests!!! 30 | 31 | (defn deps-fixture [dep-test-func] 32 | (with-fresh-store {} 33 | (dep-test-func))) 34 | 35 | (use-fixtures :each deps-fixture) 36 | 37 | (defn check-store 38 | "Pass sets of cp-names for the corresponding entries in the global-store. 39 | Those are then tested against the current store, i.e. (is (= ))." 40 | [{:keys [recomputed newly-created possibly-removed]}] 41 | (are [store-key val] (= (fetch-store store-key) val) 42 | :recomputed recomputed 43 | :newly-created newly-created 44 | :possibly-removed possibly-removed)) 45 | 46 | (defn check-cps [tag & cp-data] 47 | (doseq [[cp-name v dependents depends-on] cp-data] 48 | (let [cp (fetch-store :choice-points (get cp-name)) 49 | msg (str tag ": checking choice point " cp-name)] 50 | (is (= (:recomputed cp) v) msg) 51 | (is (= (:dependents cp) dependents) msg) 52 | (is (= (:depends-on cp) depends-on) msg)))) 53 | 54 | (defn set-value! [cp val] 55 | (assoc-in-store! [:choice-points (:name cp) :recomputed] val)) 56 | 57 | (defn refresh [] 58 | (reset! *global-store* 59 | (fresh-state (fetch-store :choice-points)))) 60 | 61 | (deftest dynamic-dependencies 62 | (let [a (det-cp :a true) 63 | b (det-cp :b (list :hello (gv a))) 64 | c (det-cp :c (if (gv a) 65 | (list (gv b) :c) 66 | :nope)) 67 | 68 | [na nb nc] (map :name [a b c])] 69 | ;; check initial values 70 | (check-cps :initial 71 | [na true #{nb nc} #{}] 72 | [nb (list :hello true) #{nc} #{na}] 73 | [nc (list (list :hello true) :c) #{} #{na nb}]) 74 | (check-store {:recomputed #{na nb nc} 75 | :newly-created #{na nb nc} 76 | :possibly-removed #{}}) 77 | ;; now update b and recompute 78 | (refresh) 79 | (set-value! b :huhu) 80 | (recompute-value c) 81 | (check-cps :huhu 82 | [na true #{nb nc} #{}] 83 | [nb :huhu #{nc} #{na}] 84 | [nc (list :huhu :c) #{} #{na nb}]) 85 | (check-store {:recomputed #{nc} 86 | :newly-created #{} 87 | :possibly-removed #{}}) 88 | ;; setting a to false changes dependencies 89 | (refresh) 90 | (set-value! a false) 91 | (recompute-value c) 92 | (check-cps :a-false 93 | [na false #{nb nc} #{}] 94 | [nb :huhu #{} #{na}] 95 | [nc :nope #{} #{na}]) 96 | (check-store {:recomputed #{nc} 97 | :newly-created #{} 98 | :possibly-removed #{nb}}) 99 | ;; now changing b has not much effect 100 | (refresh) 101 | (set-value! b :nowhere) 102 | (recompute-value c) 103 | (check-cps :nowhere 104 | [na false #{nb nc} #{}] 105 | [nb :nowhere #{} #{na}] 106 | [nc :nope #{} #{na}]) 107 | (check-store {:recomputed #{nc} 108 | :newly-created #{} 109 | :possibly-removed #{}}) 110 | ;; now remove b from the store and set a back to true 111 | ;; dependencies change again and b is re-created 112 | (refresh) 113 | (update-in-store! [:choice-points] dissoc nb) 114 | (set-value! a true) 115 | (recompute-value c) 116 | (check-cps :init-again 117 | [na true #{nb nc} #{}] 118 | [nb (list :hello true) #{nc} #{na}] 119 | [nc (list (list :hello true) :c) #{} #{na nb}]) 120 | (check-store {:recomputed #{nb nc} 121 | :newly-created #{nb} 122 | :possibly-removed #{}}))) 123 | 124 | (deftest propagation-consistency-1 125 | (let [a (det-cp :a :a) 126 | b (det-cp :b (list :b (gv a))) 127 | c (det-cp :c (list :c (gv b) (gv a))) 128 | p (flip-cp :p (if (gv a) 0.0 1.0)) 129 | d (det-cp :d (list :d (gv p) (gv c))) 130 | e (det-cp :e (list :e (gv p))) 131 | 132 | [na nb nc np nd ne] (map :name [a b c p d e])] 133 | (check-cps :initial 134 | [na :a #{nb nc np} #{}] 135 | [nb '(:b :a) #{nc} #{na}] 136 | [nc '(:c (:b :a) :a) #{nd} #{na nb}] 137 | [np '(0.0) #{nd ne} #{na}] 138 | [nd '(:d false (:c (:b :a) :a)) #{} #{nc np}] 139 | [ne '(:e false) #{} #{np}]) 140 | (set-value! a nil) 141 | (propagate-change-to 142 | (fetch-store :choice-points (get na) :dependents)) 143 | (check-cps :initial 144 | [na nil #{nb nc np} #{}] 145 | [nb '(:b nil) #{nc} #{na}] 146 | [nc '(:c (:b nil) nil) #{nd} #{na nb}] 147 | [np '(1.0) #{nd ne} #{na}] ;; the value false is not changed, even though it has prob. zero now! 148 | [nd '(:d false (:c (:b nil) nil)) #{} #{nc np}] 149 | [ne '(:e false) #{} #{np}]))) 150 | 151 | (deftest propagation-consistency-2 152 | (let [c (atom 0) 153 | a (det-cp :a true) 154 | b (det-cp :b (if (gv a) 155 | :b-true 156 | (list :a-false (gv @c))))] 157 | (reset! c (det-cp :c (if (gv a) 158 | (list :a-true (gv b)) 159 | :c-false))) 160 | (let [[na nb nc] (map :name [a b @c])] 161 | (check-cps :initial 162 | [na true #{nb nc} #{}] 163 | [nb :b-true #{nc} #{na}] 164 | [nc '(:a-true :b-true) #{} #{na nb}]) 165 | (refresh) 166 | (set-value! a false) 167 | (propagate-change-to 168 | (fetch-store :choice-points (get na) :dependents)) 169 | (check-cps :flip 170 | [na false #{nb nc} #{}] 171 | [nb '(:a-false :c-false) #{} #{na nc}] 172 | [nc :c-false #{nb} #{na}]) 173 | (refresh) 174 | (set-value! a true) 175 | (propagate-change-to 176 | (fetch-store :choice-points (get na) :dependents)) 177 | (check-cps :flip-flip 178 | [na true #{nb nc} #{}] 179 | [nb :b-true #{nc} #{na}] 180 | [nc '(:a-true :b-true) #{} #{na nb}])))) -------------------------------------------------------------------------------- /src/probabilistic_clojure/embedded/test_sampling.clj: -------------------------------------------------------------------------------- 1 | (ns 2 | ^{:author "Nils Bertschinger" 3 | :doc "Tests for probabilistic-clojure.embedded. 4 | Approximate tests for the sampling related stuff"} 5 | probabilistic-clojure.embedded.test-sampling 6 | (:use clojure.test) 7 | (:use probabilistic-clojure.embedded.api 8 | probabilistic-clojure.embedded.choice-points 9 | probabilistic-clojure.embedded.demos 10 | probabilistic-clojure.utils.sampling)) 11 | 12 | (in-ns 'probabilistic-clojure.embedded.test-sampling) 13 | 14 | (defn info-fixture [tests] 15 | (binding [*info-steps* 2500] 16 | (tests))) 17 | 18 | (use-fixtures :once info-fixture) 19 | 20 | (defn sample-bayes-net [steps bayes-net sampler] 21 | (->> (sampler bayes-net) 22 | (drop (/ steps 4)) 23 | (take steps) 24 | density)) 25 | 26 | (defn retracts-net 27 | "Example of a changing topology -- choice points are removed and re-created -- 28 | to test dependency tracking and sampling." 29 | [] 30 | (let [root (flip-cp :root 0.5) 31 | path-left (flip-cp :left (do (gv root) 0.5)) 32 | path-right (flip-cp :right (do (gv root) 0.5))] 33 | (det-cp :result 34 | (if (gv root) 35 | [:left (gv path-left)] 36 | [:right (gv path-right)])))) 37 | 38 | (defn prob= [x y] 39 | (let [eps 0.01 40 | diff (- x y)] 41 | (< (- eps) diff eps))) 42 | 43 | (deftest retracts-sampling 44 | (is (prob= (get (sample-bayes-net 10000 retracts-net monte-carlo-sampling) 45 | [:left false]) 46 | 0.25)) 47 | (is (prob= (get (sample-bayes-net 10000 retracts-net metropolis-hastings-sampling) 48 | [:left false]) 49 | 0.25))) 50 | 51 | (deftest grass-demos 52 | (let [true-prob (float 1419/3029)] 53 | ;; The exact prob. of the grass net being true was calculated with the prob. monad 54 | (are [sampler bayes-net] 55 | (prob= (get (sample-bayes-net 10000 bayes-net sampler) true) true-prob) 56 | 57 | monte-carlo-sampling grass-bayes-net 58 | metropolis-hastings-sampling grass-bayes-net 59 | monte-carlo-sampling grass-bayes-net-fixed 60 | metropolis-hastings-sampling grass-bayes-net-fixed))) -------------------------------------------------------------------------------- /src/probabilistic_clojure/embedded/tests.clj: -------------------------------------------------------------------------------- 1 | ;;; Copyright (C) 2011 Nils Bertschinger 2 | 3 | ;;; This file is part of Probabilistic-Clojure 4 | 5 | ;;; Probabilistic-Clojure is free software: you can redistribute it and/or modify 6 | ;;; it under the terms of the GNU Lesser General Public License as published by 7 | ;;; the Free Software Foundation, either version 3 of the License, or 8 | ;;; (at your option) any later version. 9 | 10 | ;;; Probabilistic-Clojure is distributed in the hope that it will be useful, 11 | ;;; but WITHOUT ANY WARRANTY; without even the implied warranty of 12 | ;;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 13 | ;;; GNU Lesser General Public License for more details. 14 | 15 | ;;; You should have received a copy of the GNU Lesser General Public License 16 | ;;; along with Probabilistic-Clojure. If not, see . 17 | 18 | (ns 19 | ^{:author "Nils Bertschinger" 20 | :doc "Tests for probabilistic-clojure.embedded"} 21 | probabilistic-clojure.embedded.tests 22 | (:use probabilistic-clojure.embedded.api 23 | probabilistic-clojure.embedded.choice-points 24 | probabilistic-clojure.utils.sampling 25 | probabilistic-clojure.embedded.demos)) 26 | 27 | (in-ns 'probabilistic-clojure.embedded.tests) 28 | 29 | ;;; TODO: use testing framework and write real unit tests!!! 30 | 31 | (defn cp-str [cp] 32 | (str (:name cp) ": " 33 | (:recomputed cp) 34 | " dependents " (:dependents cp) 35 | " depends on " (:depends-on cp))) 36 | 37 | (defn test-dynamic-dependencies [] 38 | (with-fresh-store {} 39 | (let [a (det-cp :a true) 40 | b (det-cp :b (list :hello (gv a))) 41 | c (det-cp :c 42 | (do (println "Here") 43 | (if (gv a) (list (gv b) :c) :nope))) 44 | show-cps (fn [] 45 | (println "Recomputed: " (:recomputed @*global-store*)) 46 | (println "Newly created: " (:newly-created @*global-store*)) 47 | (println "Possibly removed: " (:possibly-removed @*global-store*)) 48 | (doseq [[name cp] (:choice-points @*global-store*)] 49 | (println (cp-str cp)))) 50 | set-value! (fn [cp val] 51 | (assoc-in-store! [:choice-points (:name cp) :recomputed] val)) 52 | refresh (fn [] (swap! *global-store* (constantly 53 | (fresh-state (:choice-points @*global-store*)))))] 54 | (show-cps) 55 | (refresh) 56 | (set-value! b :huhu) 57 | (recompute-value c) 58 | (show-cps) 59 | (refresh) 60 | (set-value! a false) 61 | (recompute-value c) 62 | (show-cps) 63 | (refresh) 64 | (set-value! b :nowhere) 65 | (recompute-value c) 66 | (show-cps) 67 | (refresh) 68 | (swap! *global-store* update-in [:choice-points] dissoc (:name b)) 69 | (set-value! a true) 70 | (recompute-value c) 71 | (show-cps)))) 72 | 73 | (defn test-bayes-net [bayes-net] 74 | (density (take 25000 (monte-carlo-sampling bayes-net)))) 75 | 76 | (defn test-topsort [] 77 | (with-fresh-store {} 78 | (let [a (det-cp :a :a) 79 | b (det-cp :b (list :b (gv a))) 80 | c (det-cp :c (list :c (gv b) (gv a))) 81 | p (flip-cp :p (if (gv a) 0.2 0.8)) 82 | d (det-cp :d (list :d (gv p) (gv c))) 83 | e (det-cp :e (list :e (gv p))) 84 | 85 | show-cps (fn [] 86 | (doseq [[name cp] (fetch-store :choice-points)] 87 | (println (cp-str cp))))] 88 | ;; Not using topological sort any more, but all choice points up-to data after propagation 89 | (show-cps) 90 | (assoc-in-store! [:choice-points (:name a) :recomputed] :aa) 91 | (println "Updated " 92 | (propagate-change-to 93 | (fetch-store :choice-points (get (:name a)) :dependents)) 94 | " choice points") 95 | (show-cps)))) 96 | 97 | 98 | (defn topsort-bug [] 99 | ;; Illustrates a bug resulting from update in topological order if order changes 100 | ;; during the re-evaluation!!! 101 | ;; DONE: Should be fixed now ... but unnecessary recomputations triggered 102 | (with-fresh-store {} 103 | (let [c (atom 0) 104 | a (det-cp :a true) 105 | b (det-cp :b (if (gv a) 106 | :b-true 107 | (list :a-false (gv @c)))) 108 | show-cps (fn [] 109 | (doseq [[name cp] (:choice-points @*global-store*)] 110 | (println (cp-str cp)))) 111 | set-value! (fn [cp val] 112 | (assoc-in-store! [:choice-points (:name cp) :recomputed] val)) 113 | refresh (fn [] (swap! *global-store* (constantly 114 | (fresh-state (:choice-points @*global-store*)))))] 115 | ;; examples requires cyclic dependency ... so maybe cannot arise otherwise??? 116 | (swap! c (fn [_] (det-cp :c (if (gv a) 117 | (list :a-true (gv b)) 118 | :c-false)))) 119 | 120 | (show-cps) 121 | (refresh) 122 | (set-value! a false) 123 | (println "Updated " 124 | (propagate-change-to 125 | (fetch-store :choice-points (get (:name a)) :dependents)) 126 | " choice points") 127 | ;; this works nicely now 128 | (show-cps) 129 | ;; so flip a back again 130 | (set-value! a true) 131 | (println "Updated " 132 | (propagate-change-to 133 | (fetch-store :choice-points (get (:name a)) :dependents)) 134 | " choice points") 135 | (show-cps)))) 136 | 137 | (defn test-retracts-net 138 | "Somewhat involved example of a changing topology, to test dependency tracking and sampling." 139 | [] 140 | (let [root (flip-cp :root 0.5) 141 | path-left (flip-cp :left (do (gv root) 0.5)) 142 | path-right (flip-cp :right (do (gv root) 0.5))] 143 | (det-cp :result 144 | (if (gv root) 145 | [:left (gv path-left)] 146 | [:right (gv path-right)])))) 147 | -------------------------------------------------------------------------------- /src/probabilistic_clojure/monadic/api.clj: -------------------------------------------------------------------------------- 1 | ;;; Copyright (C) 2011 Nils Bertschinger 2 | 3 | ;;; This file is part of Probabilistic-Clojure 4 | 5 | ;;; Probabilistic-Clojure is free software: you can redistribute it and/or modify 6 | ;;; it under the terms of the GNU Lesser General Public License as published by 7 | ;;; the Free Software Foundation, either version 3 of the License, or 8 | ;;; (at your option) any later version. 9 | 10 | ;;; Probabilistic-Clojure is distributed in the hope that it will be useful, 11 | ;;; but WITHOUT ANY WARRANTY; without even the implied warranty of 12 | ;;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 13 | ;;; GNU Lesser General Public License for more details. 14 | 15 | ;;; You should have received a copy of the GNU Lesser General Public License 16 | ;;; along with Probabilistic-Clojure. If not, see . 17 | 18 | (ns 19 | ^{:author "Nils Bertschinger" 20 | :doc "This library implements a version of the probability monad 21 | which uses Metropolis Hastings sampling. 22 | The system allows to condition and memoize probabilistic choice points and 23 | can be extended by user defined distributions."} 24 | probabilistic-clojure.monadic.api 25 | (:use [clojure.algo.monads :only (defmonad)] 26 | [probabilistic-clojure.utils.sampling :only (sample-from normalize)] 27 | [probabilistic-clojure.utils.stuff :only (ensure-list error)])) 28 | 29 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 30 | ;;; 31 | ;;; Basic data structures 32 | ;;; 33 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 34 | 35 | (defrecord ^{:doc "Basic data structure for random choice points"} 36 | ChoicePoint 37 | [sampler get-log-prob proposer get-log-proposal-prob]) 38 | 39 | (defrecord ^{:doc "Entry holding information about random choices encountered 40 | during a run of probabilistic programs"} 41 | DBentry 42 | [value log-lik status type params choice-point]) 43 | 44 | (defn- activate [database addr] 45 | (assoc-in database [addr :status] :active)) 46 | 47 | (defn- inactivate-all [database] 48 | (into {} (for [[addr entry] database] 49 | [addr (assoc entry :status :inactive)]))) 50 | 51 | (defn- clean-db-back 52 | "Runs through the database to remove all inactive choice points. Returns the cleaned 53 | database as well as the log-likelihood of the removed choice points which is needed to 54 | calculate the backward probability" 55 | [database] 56 | (reduce (fn [[db log-bwd-prob] [addr entry]] 57 | (if (= (:status entry) :active) 58 | [(assoc db addr entry) log-bwd-prob] 59 | [db (+ log-bwd-prob (apply (:get-log-prob (:choice-point entry)) 60 | (:value entry) (:params entry)))])) 61 | [{} 0] (seq database))) 62 | 63 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 64 | ;;; 65 | ;;; The monadic interface 66 | ;;; 67 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 68 | 69 | (def log-prob-zero (Math/log 0)) 70 | 71 | (defn- m-result-MH [v] 72 | (fn [addr database log-fwd-prob log-lik mems] 73 | ;; there is no choice here, so just return everything directly 74 | [v log-lik database log-fwd-prob mems])) 75 | 76 | (def m-zero-MH 77 | (fn [addr database log-fwd-prob log-lik mems] 78 | ;; invalidate this trace 79 | [::invalid log-prob-zero database log-fwd-prob mems])) 80 | 81 | (defn invalid? [v] 82 | (= v ::invalid)) 83 | 84 | (defn- m-bind-MH [m f] 85 | (fn [addr database log-fwd-prob log-lik mems] 86 | ;; here we first run the monad m and then 87 | ;; plug the values into the continuation f 88 | ;; (compare the state monad) 89 | (let [[v log-lik database log-fwd-prob mems] 90 | (m (cons "BIND-M" addr) database log-fwd-prob log-lik mems)] 91 | (if (invalid? v) 92 | (m-zero-MH (cons "BIND-F" addr) database log-fwd-prob log-lik mems) 93 | ((f v) (cons "BIND-F" addr) database log-fwd-prob log-lik mems))))) 94 | 95 | ;; Definition of our monad (note that no implementation of m-plus is provided!) 96 | (defmonad probabilistic-sampling-m 97 | [m-result m-result-MH 98 | m-bind m-bind-MH 99 | m-zero m-zero-MH]) 100 | 101 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 102 | ;;; 103 | ;;; User functions for defining choice points and running probabilistic programs 104 | ;;; 105 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 106 | 107 | (defn make-choice-point 108 | "Allows to define a new probabilistic choice point by providing a function 109 | for sampling and calculating the log-likelihood. 110 | See the source code of flip for an example." 111 | ([name params sampler get-log-prob] 112 | (make-choice-point name params 113 | sampler get-log-prob 114 | ;; provide a default proposer that simply samples from the distribution 115 | (fn [val & args] (apply sampler args)) 116 | (fn [new-val old-val & args] (apply get-log-prob new-val args)))) 117 | ([name params sampler get-log-prob proposer get-log-proposal-prob] 118 | (fn [addr database log-fwd-prob log-lik mems] 119 | ;; this function runs the choice-point with entries from the database and updates the trace 120 | (let [addr (cons name addr) 121 | create-new-randomness 122 | (fn [] 123 | (let [val (apply sampler params) 124 | ll (apply get-log-prob val params)] 125 | [val 126 | (+ log-lik ll) 127 | (assoc database addr 128 | (DBentry. val ll :active name params 129 | (ChoicePoint. sampler get-log-prob proposer get-log-proposal-prob))) 130 | (+ log-fwd-prob ll) mems]))] 131 | (if (contains? database addr) 132 | (let [entry (database addr)] 133 | (if (= (:params entry) params) 134 | ;; we found an exact match, so just lookup the value 135 | (let [val (:value entry) 136 | ll (apply (:get-log-prob (:choice-point entry)) val params)] 137 | [val (+ log-lik ll) (activate database addr) log-fwd-prob mems]) 138 | ;; no exact match, we have to reweight the trace 139 | (let [val (:value entry) 140 | ll (apply (:get-log-prob (:choice-point entry)) val params)] 141 | (if (= ll log-prob-zero) 142 | (create-new-randomness) 143 | [val (+ log-lik ll) 144 | (-> database 145 | (activate addr) 146 | (assoc-in [addr :log-lik] ll) 147 | (assoc-in [addr :params] params)) 148 | log-fwd-prob mems])))) 149 | ;; not in database, create new randomness 150 | (create-new-randomness)))))) 151 | 152 | (defn- get-trace [m-MH database] 153 | (m-MH (list "TOP") database 0 0 {})) 154 | 155 | (defn cond-data 156 | "Condition a choice point on the specified value. 157 | This function must be applied to an elementary random choice point, e.g. (flip 0.6). 158 | A trace running through this value is then weighted according to the likelihood of the data value." 159 | [choice val] 160 | (fn [addr database log-fwd-prob log-lik mems] 161 | (let [[[_ choice-entry] & more] (seq (get (get-trace choice {}) 2)) 162 | choice-point (:choice-point choice-entry) 163 | ll (apply (:get-log-prob choice-point) val (:params choice-entry))] 164 | (when more ; ensure that its was called on an elementary choice point 165 | (error "Cond-data can only be called on an elementary choice point!")) 166 | [val (+ log-lik ll) database log-fwd-prob mems]))) 167 | 168 | (defmacro mem 169 | "Memoize a MH monadic value on some given arguments, i.e. if the same arguments 170 | are encountered again it refers back to the original choice 171 | point which was established for these arguments in the trace, i.e. 172 | no new randomness is created in this case." 173 | [m-MH-form & add-args] 174 | `(fn [addr# database# log-fwd-prob# log-lik# mems#] 175 | (let [mem-addr# (list "MEMO" (str '~(first (ensure-list m-MH-form))) ~@(rest (ensure-list m-MH-form)) ~@add-args) 176 | ;; now just redirect the choice point to the new address 177 | ;; which identifies it according to its arguments 178 | [val# ll# db# lfp# ms#] (~m-MH-form mem-addr# database# log-fwd-prob# log-lik# mems#)] 179 | (if (contains? mems# mem-addr#) 180 | [val# log-lik# database# log-fwd-prob# (update-in ms# [mem-addr#] inc)] 181 | [val# ll# db# lfp# (assoc ms# mem-addr# 1)])))) 182 | 183 | ;; These two functions are used to select the next choice point to be proposed 184 | ;; They implement the heuristics that memoized choices should be tried more often 185 | ;; since they got reused several times 186 | (defn- select-prob-choice-dist [database mems] 187 | (normalize 188 | (into {} (for [[addr entry] database] 189 | [[addr entry] (if (contains? mems (rest addr)) 190 | (mems (rest addr)) 191 | 1)])))) 192 | 193 | (defn- calc-select-prob [addr database mems] 194 | (let [total (+ (count database) ; each entry gets weight one 195 | (reduce + (vals mems)) ; weight of mem-entries 196 | (- (count mems)))] ; but got double counted 197 | (if (contains? mems (rest addr)) 198 | (/ (mems (rest addr)) total) 199 | (/ 1 total)))) 200 | 201 | (def ^{:doc "Every *trace-verbose* steps sample-traces ouputs some status information. 202 | Can be set to false for no output." 203 | :dynamic true} 204 | *trace-verbose* 205 | 500) 206 | 207 | (defn- output? [idx] 208 | (and (number? *trace-verbose*) 209 | (= (mod idx *trace-verbose*) 0))) 210 | 211 | (defn sample-traces 212 | "The main routine implementing Metropolis Hastings sampling. Returns a lazy 213 | sequence of samples when called on a monadic value from this library. 214 | Burn-in and thinning can be obtained using for example drop and keep-indexed respectively." 215 | ([m-MH] 216 | (println "Trying to find valid trace ...") 217 | (loop [[val log-lik database _fwd-ll_ mems] (get-trace m-MH {})] 218 | (if (or (invalid? val) (= log-lik log-prob-zero)) 219 | (recur (get-trace m-MH {})) 220 | (do (println "Starting MH-sampling.") 221 | (sample-traces m-MH database mems log-lik val 1 1))))) 222 | ([m-MH database mems log-lik val idx num-acc] 223 | (when (output? idx) 224 | (println (str idx ": value " val " with log. likelihood " log-lik)) 225 | (println (str "Accepted " num-acc " out of last " *trace-verbose* " proposals"))) 226 | (let [num-acc (if (output? idx) 0 num-acc) 227 | [addr entry] (sample-from (select-prob-choice-dist database mems)) 228 | prop-val (apply (:proposer (:choice-point entry)) (:value entry) (:params entry)) 229 | ll-prop-val (apply (:get-log-proposal-prob (:choice-point entry)) 230 | prop-val (:value entry) (:params entry)) 231 | ll-val (apply (:get-log-proposal-prob (:choice-point entry)) 232 | (:value entry) prop-val (:params entry)) 233 | [next-val next-log-lik next-database log-fwd-prob next-mems] 234 | (get-trace m-MH 235 | (-> (inactivate-all database) 236 | (assoc-in [addr :value] prop-val) 237 | (assoc-in [addr :log-lik] 238 | (apply (:get-log-prob (:choice-point entry)) 239 | prop-val (:params entry)))))] 240 | (if (invalid? next-val) ; trace was rejected => retry 241 | (lazy-seq (cons val (sample-traces m-MH database mems log-lik val (inc idx) num-acc))) 242 | (let [[next-database log-bwd-prob] (clean-db-back next-database)] 243 | (if (< (Math/log (rand)) 244 | (+ (- next-log-lik log-lik) 245 | (- (Math/log (calc-select-prob addr next-database next-mems)) 246 | (Math/log (calc-select-prob addr database mems))) 247 | (- ll-val ll-prop-val) 248 | (- log-bwd-prob log-fwd-prob))) 249 | (lazy-seq (cons next-val (sample-traces m-MH next-database next-mems 250 | next-log-lik next-val 251 | (inc idx) (inc num-acc)))) 252 | (lazy-seq (cons val (sample-traces m-MH database mems log-lik val (inc idx) num-acc))))))))) 253 | 254 | (defn monte-carlo-samples 255 | "Run the probabilistic program repeatedly to obtain samples. Note that this is more like 256 | rejection sampling and usually less efficient than sample-traces." 257 | [m-MH] 258 | (lazy-seq 259 | (cons (first (get-trace m-MH {})) 260 | (monte-carlo-samples m-MH)))) 261 | 262 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 263 | ;;; 264 | ;;; Basic example of how to define a probabilistic choice point 265 | ;;; 266 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 267 | 268 | (defn flip 269 | "A binary random choice which is true with probability p. 270 | Provides a good example of how user-defined choice points look like." 271 | [p] 272 | (make-choice-point "FLIP" [p] 273 | (fn [p] (< (rand) p)) ; the sampling function 274 | (fn [b p] (Math/log (if b p (- 1 p)))) ; calculates the log-likelihood of outcome b 275 | ;; The proposer (consisting of theses two functions) is optional 276 | (fn [b p] (not b)) 277 | (fn [new-b old-b p] (Math/log 1)))) 278 | -------------------------------------------------------------------------------- /src/probabilistic_clojure/monadic/demos.clj: -------------------------------------------------------------------------------- 1 | ;;; Copyright (C) 2011 Nils Bertschinger 2 | 3 | ;;; This file is part of Probabilistic-Clojure 4 | 5 | ;;; Probabilistic-Clojure is free software: you can redistribute it and/or modify 6 | ;;; it under the terms of the GNU Lesser General Public License as published by 7 | ;;; the Free Software Foundation, either version 3 of the License, or 8 | ;;; (at your option) any later version. 9 | 10 | ;;; Probabilistic-Clojure is distributed in the hope that it will be useful, 11 | ;;; but WITHOUT ANY WARRANTY; without even the implied warranty of 12 | ;;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 13 | ;;; GNU Lesser General Public License for more details. 14 | 15 | ;;; You should have received a copy of the GNU Lesser General Public License 16 | ;;; along with Probabilistic-Clojure. If not, see . 17 | 18 | (ns 19 | ^{:author "Nils Bertschinger" 20 | :doc "Demo of how the probability monad can be used. 21 | Also defines several useful probabilistic choice points and 22 | requires incanter for different distributions as well as the 23 | graphical output."} 24 | probabilistic-clojure.monadic.demos 25 | (:use [probabilistic-clojure.monadic.api 26 | :only (probabilistic-sampling-m make-choice-point cond-data mem sample-traces flip log-prob-zero)] 27 | [probabilistic-clojure.utils.sampling :only (density sample-from)] 28 | [probabilistic-clojure.utils.stuff :only (transpose)] 29 | [probabilistic-clojure.utils.finite-distributions :only (cond-dist-m normalize-cond choose)]) 30 | (:use [clojure.algo.monads :only (domonad defmonadfn m-bind m-result with-monad)]) 31 | (:use [incanter.core :only (gamma view)] 32 | [incanter.stats :only (sample-normal pdf-normal sample-dirichlet sample-beta pdf-beta mean)] 33 | [incanter.charts :only (histogram xy-plot add-lines)])) 34 | 35 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 36 | ;;; 37 | ;;; First a simple Bayes net as found in many introductory texts 38 | ;;; 39 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 40 | 41 | (defmonadfn noisy-or [x y] 42 | (domonad 43 | [noise-x (flip 0.9) 44 | noise-y (flip 0.8) 45 | noise-z (flip 0.1)] 46 | (or (and x noise-x) 47 | (and y noise-y) 48 | noise-z))) 49 | 50 | (defmonadfn grass-bayes-net [] 51 | (domonad 52 | [rain (flip 0.3) 53 | sprinkler (flip 0.5) 54 | grass-is-wet (noisy-or rain sprinkler) 55 | :when grass-is-wet] 56 | rain)) 57 | 58 | (defn run-grass-example [num-samples] 59 | (with-monad probabilistic-sampling-m 60 | (let [rain (density (take num-samples (sample-traces (grass-bayes-net))))] 61 | (println "Given grass-is-wet the probability for rain is " (get rain true)) 62 | rain))) 63 | 64 | (defn solve-grass-example [] 65 | (with-redefs [flip (fn [p] (choose p true (- 1 p) false))] 66 | (with-monad cond-dist-m 67 | (normalize-cond (grass-bayes-net))))) 68 | 69 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 70 | ;;; 71 | ;;; Some more probabilistic choice points as required by the mixture example 72 | ;;; 73 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 74 | 75 | (defn discrete [dist] 76 | (make-choice-point "DISCRETE" [dist] 77 | (fn [dist] (sample-from dist)) 78 | (fn [x dist] 79 | (if (contains? dist x) 80 | (Math/log (dist x)) 81 | log-prob-zero)))) 82 | 83 | (defn gaussian [mu sdev] 84 | (let [proposal-sd 0.7] 85 | (make-choice-point "GAUSSIAN" [mu sdev] 86 | (fn [mu sdev] (sample-normal 1 :mean mu :sd sdev)) 87 | (fn [x mu sdev] (Math/log (pdf-normal x :mean mu :sd sdev))) 88 | (fn [x mu sdev] (sample-normal 1 :mean x :sd proposal-sd)) 89 | (fn [new-x old-x mu sdev] 90 | (Math/log (pdf-normal new-x :mean old-x :sd proposal-sd)))))) 91 | 92 | (defn pdf-dirichlet [ps alphas] 93 | (let [norm (/ (reduce * (map gamma alphas)) 94 | (gamma (reduce + alphas)))] 95 | (/ (reduce * (map (fn [p a] (Math/pow p (- a 1))) ps alphas)) 96 | norm))) 97 | 98 | (defn dirichlet [alphas] 99 | (let [proposal-alphas (fn [alphas] 100 | (for [a alphas] (* 18 a)))] 101 | (make-choice-point "DIRICHLET" [alphas] 102 | (fn [alphas] (first (sample-dirichlet 2 alphas))) 103 | (fn [ps alphas] (Math/log (pdf-dirichlet ps alphas))) 104 | (fn [ps alphas] (first (sample-dirichlet 2 (proposal-alphas ps)))) 105 | (fn [new-ps old-ps alphas] 106 | (Math/log (pdf-dirichlet new-ps (proposal-alphas old-ps))))))) 107 | 108 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 109 | ;;; 110 | ;;; Fitting of a mixture model to illustrate how mem can be used to share randomness 111 | ;;; 112 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 113 | 114 | (defn generate-data [] 115 | (let [mu (fn [] (sample-from {-5 0.2, 0 0.7, 8 0.1}))] 116 | (lazy-seq (cons (sample-normal 1 :mean (mu)) 117 | (generate-data))))) 118 | 119 | (def data (take 42 (generate-data))) 120 | 121 | (defn fit-components [data comp-weights mu-comps] 122 | (with-monad probabilistic-sampling-m 123 | (if (empty? data) ; are we done yet? 124 | (m-result ()) 125 | (domonad 126 | [comp (discrete {:a (nth comp-weights 0), :b (nth comp-weights 1), :c (nth comp-weights 2)}) 127 | ;; first draw a component for this data point 128 | :let [mu-comp (mu-comps comp)] 129 | ;; then condition a Gaussian for this component on the observed data point 130 | obs (cond-data (gaussian mu-comp 1) (first data)) 131 | assignment (fit-components (rest data) comp-weights mu-comps)] 132 | (cons comp assignment))))) 133 | 134 | (defn mixture 135 | "Basic example of a mixture model." 136 | [data] 137 | (domonad probabilistic-sampling-m 138 | [ca (gaussian 0 15) ; draw means of three components from a Gaussian prior 139 | cb (gaussian 0 15) 140 | cc (gaussian 0 15) 141 | comp-weights (dirichlet [1 1 1]) ; draw component proportions from a Dirichlet prior 142 | :let [mu-comps {:a ca :b cb :c cc}] 143 | assignment (fit-components data comp-weights mu-comps)] ; assign each data point to these components 144 | [mu-comps comp-weights assignment])) 145 | 146 | (defn mixture-mem 147 | "The same model as in mixture, but simplified using mem to reuse random choices." 148 | [data] 149 | (with-monad probabilistic-sampling-m 150 | (if (empty? data) 151 | (m-result [{} [] ()]) 152 | (domonad 153 | [comp-weights (mem (dirichlet [10 10 10])) ; mem ensures that the component proportions 154 | ; are the same for each data point 155 | comp (discrete {:a (nth comp-weights 0), :b (nth comp-weights 1), :c (nth comp-weights 2)}) 156 | mu-comp (mem (gaussian 0 15) comp) ; similarly the means of the same component are shared 157 | obs (cond-data (gaussian mu-comp 1) (first data)) ; condition on the observed data 158 | [other-mus cws assignment] (mixture-mem (rest data))] 159 | [(assoc other-mus comp mu-comp) comp-weights (cons comp assignment)])))) 160 | 161 | (defn test-mixture [model] 162 | (let [data-plot (histogram data :title "Dataset" :nbins 50 :density true) 163 | samples (take 200 (drop 8000 (sample-traces (model data)))) ; burn-in of 8000 samples 164 | comp-mus (map first samples) 165 | comp-weights (map second samples)] 166 | (let [xs (range -10 10 0.01) 167 | ;; average over the last samples ... even though this should not be done!!! 168 | weights (map mean (transpose comp-weights)) 169 | mus (map mean (transpose (for [mus comp-mus] [(:a mus) (:b mus) (:c mus)])))] 170 | (doto data-plot 171 | (add-lines xs (map (fn [x] (* (nth weights 0) (pdf-normal x :mean (nth mus 0)))) xs)) 172 | (add-lines xs (map (fn [x] (* (nth weights 1) (pdf-normal x :mean (nth mus 1)))) xs)) 173 | (add-lines xs (map (fn [x] (* (nth weights 2) (pdf-normal x :mean (nth mus 2)))) xs)) 174 | view) 175 | [weights mus]))) 176 | 177 | (comment 178 | (test-mixture mixture) 179 | (test-mixture mixture-mem)) 180 | 181 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 182 | ;;; 183 | ;;; Finally, extend this to a Dirichlet process such that also the number of 184 | ;;; components is learned 185 | ;;; 186 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 187 | 188 | ;; first a Beta distributed choice point is needed 189 | (defn beta [alpha beta] 190 | (make-choice-point "BETA" [alpha beta] 191 | (fn [alpha beta] (sample-beta 1 :alpha alpha :beta beta)) 192 | (fn [x alpha beta] (Math/log (pdf-beta x :alpha alpha :beta beta))))) 193 | 194 | ;; this implements the stick breaking construction 195 | ;; note the use of mem to reuse randomness 196 | (defn pick-a-stick [alpha idx] 197 | (domonad probabilistic-sampling-m 198 | [stick (mem (beta 1 alpha) idx) 199 | stop (flip stick) 200 | num (if stop 201 | (m-result idx) 202 | (pick-a-stick alpha (inc idx)))] 203 | num)) 204 | 205 | (defn dirichlet-process 206 | "A Dirichlet process with parameter alpha and base measure base." 207 | [alpha base] 208 | (domonad probabilistic-sampling-m 209 | [idx (pick-a-stick alpha 1) 210 | val (mem base idx)] 211 | val)) 212 | 213 | (defn mixture-DP 214 | "A Gaussian Dirichlet process mixture model." 215 | [alpha data] 216 | (with-monad probabilistic-sampling-m 217 | (if (empty? data) 218 | (m-result [0 {} ()]) 219 | (domonad 220 | [mu-comp (dirichlet-process alpha (gaussian 0 15)) 221 | obs (cond-data (gaussian mu-comp 1) (first data)) 222 | [num-comp comp-mus assignment] (mixture-DP alpha (rest data))] 223 | (let [comp-idx (if (contains? comp-mus mu-comp) 224 | (comp-mus mu-comp) 225 | (inc num-comp)) 226 | comp-mus (assoc comp-mus mu-comp comp-idx)] 227 | [(count comp-mus) comp-mus (cons comp-idx assignment)]))))) 228 | 229 | (defn plot-DP-fit [data res] 230 | (let [data-plot (histogram data :nbins 50 :density true) 231 | [num-comp mus assignment] res 232 | weights (density assignment) 233 | xs (range -15 15 0.01)] 234 | (doseq [[mu idx] (seq mus)] 235 | (add-lines data-plot xs (map (fn [x] (* (weights idx) (pdf-normal x :mean mu))) xs))) 236 | (add-lines data-plot xs (map (fn [x] (reduce + (for [[mu idx] (seq mus)] 237 | (* (weights idx) (pdf-normal x :mean mu))))) 238 | xs)) 239 | (view data-plot))) 240 | 241 | (defn test-DP [alpha n] 242 | (let [res (sample-traces (mixture-DP alpha data))] 243 | (loop [x res, i 0] 244 | (when (not (> i n)) 245 | (when (= (mod i 2500) 0) 246 | (plot-DP-fit data (first x))) 247 | (recur (rest x) (inc i)))))) 248 | 249 | (comment 250 | (test-DP 1.0 7500)) 251 | -------------------------------------------------------------------------------- /src/probabilistic_clojure/original/demos.clj: -------------------------------------------------------------------------------- 1 | ;;; Copyright (C) 2011 Nils Bertschinger 2 | 3 | ;;; This file is part of Probabilistic-Clojure 4 | 5 | ;;; Probabilistic-Clojure is free software: you can redistribute it and/or modify 6 | ;;; it under the terms of the GNU Lesser General Public License as published by 7 | ;;; the Free Software Foundation, either version 3 of the License, or 8 | ;;; (at your option) any later version. 9 | 10 | ;;; Probabilistic-Clojure is distributed in the hope that it will be useful, 11 | ;;; but WITHOUT ANY WARRANTY; without even the implied warranty of 12 | ;;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 13 | ;;; GNU Lesser General Public License for more details. 14 | 15 | ;;; You should have received a copy of the GNU Lesser General Public License 16 | ;;; along with Probabilistic-Clojure. If not, see . 17 | 18 | (ns probabilistic.demos 19 | (:use probabilistic.metropolis-hastings) 20 | (:use [clojure.contrib.monads :only (domonad m-bind m-result with-monad)]) 21 | (:use [incanter.core :only (view)] 22 | [incanter.stats :only (sample-normal pdf-normal mean sample-beta pdf-beta)] 23 | [incanter.charts :only (histogram xy-plot add-lines)])) 24 | 25 | (in-ns 'probabilistic.demos) 26 | 27 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 28 | ;;; 29 | ;;; First a simple Bayes net as found in many introductory texts 30 | ;;; 31 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 32 | 33 | (defn noisy-or [x y] 34 | (domonad probabilistic-sampling-m 35 | [noise-x (flip 0.9) 36 | noise-y (flip 0.8) 37 | noise-z (flip 0.1)] 38 | (or (and x noise-x) 39 | (and y noise-y) 40 | noise-z))) 41 | 42 | (defn grass-bayes-net [] 43 | (domonad probabilistic-sampling-m 44 | [rain (flip 0.3) 45 | sprinkler (flip 0.5) 46 | grass-is-wet (noisy-or rain sprinkler) 47 | :when grass-is-wet] 48 | rain)) 49 | 50 | (defn density [samples] 51 | (let [freqs (frequencies samples) 52 | total (reduce + (vals freqs))] 53 | (into {} (for [[k v] freqs] [k (float (/ v total))])))) 54 | 55 | (density (take 10000 (sample-traces (grass-bayes-net)))) 56 | 57 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 58 | ;;; 59 | ;;; Fitting of a mixture model to illustrate how mem can be used to share randomness 60 | ;;; 61 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 62 | 63 | (defn generate-data [] 64 | (let [mu (fn [] (sample-from {-5 0.2, 0 0.7, 8 0.1}))] 65 | (lazy-seq (cons (sample-normal 1 :mean (mu)) 66 | (generate-data))))) 67 | 68 | (def data (take 42 (generate-data))) 69 | 70 | (defn fit-components [data comp-weights mu-comps] 71 | (with-monad probabilistic-sampling-m 72 | (if (empty? data) 73 | (m-result ()) 74 | (domonad 75 | [comp (discrete {:a (nth comp-weights 0), :b (nth comp-weights 1), :c (nth comp-weights 2)}) 76 | :let [mu-comp (mu-comps comp)] 77 | obs (cond-data (gaussian mu-comp 1) (first data)) 78 | assignment (fit-components (rest data) comp-weights mu-comps)] 79 | (cons comp assignment))))) 80 | 81 | (defn mixture [data] 82 | (domonad probabilistic-sampling-m 83 | [ca (gaussian 0 15) 84 | cb (gaussian 0 15) 85 | cc (gaussian 0 15) 86 | comp-weights (dirichlet [1 1 1]) 87 | :let [mu-comps {:a ca :b cb :c cc}] 88 | assignment (fit-components data comp-weights mu-comps)] 89 | [mu-comps comp-weights assignment])) 90 | 91 | (defn mixture-mem [data] 92 | (with-monad probabilistic-sampling-m 93 | (if (empty? data) 94 | (m-result [{} [] ()]) 95 | (domonad 96 | [comp-weights (mem (dirichlet [10 10 10])) 97 | comp (discrete {:a (nth comp-weights 0), :b (nth comp-weights 1), :c (nth comp-weights 2)}) 98 | mu-comp (mem (gaussian 0 15) comp) 99 | obs (cond-data (gaussian mu-comp 1) (first data)) 100 | [other-mus cws assignment] (mixture-mem (rest data))] 101 | [(assoc other-mus comp mu-comp) comp-weights (cons comp assignment)])))) 102 | 103 | (defn transpose 104 | "Transpose a list of lists, i.e. (transpose [[1 2] [3 4] [5 6]]) = ((1 3 5) (2 4 6))" 105 | [lls] 106 | (apply map list lls)) 107 | 108 | (defn test-mixture [model] 109 | (let [data-plot (histogram data :title "Dataset" :nbins 50 :density true) 110 | samples (take 2000 (drop 8000 (sample-traces (model data)))) 111 | comp-mus (map first samples) 112 | comp-weights (map second samples)] 113 | (let [xs (range -10 10 0.01) 114 | weights (map mean (transpose comp-weights)) 115 | mus (map mean (transpose (for [mus comp-mus] [(:a mus) (:b mus) (:c mus)])))] 116 | (doto data-plot 117 | (add-lines xs (map (fn [x] (* (nth weights 0) (pdf-normal x :mean (nth mus 0)))) xs)) 118 | (add-lines xs (map (fn [x] (* (nth weights 1) (pdf-normal x :mean (nth mus 1)))) xs)) 119 | (add-lines xs (map (fn [x] (* (nth weights 2) (pdf-normal x :mean (nth mus 2)))) xs)) 120 | view) 121 | [weights mus]))) 122 | 123 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 124 | ;;; 125 | ;;; Finally, extend this to a Dirichlet process such that also the number of 126 | ;;; components is learned 127 | ;;; 128 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 129 | 130 | (defn beta [alpha beta] 131 | (make-choice-point "BETA" [alpha beta] 132 | (fn [alpha beta] (sample-beta 1 :alpha alpha :beta beta)) 133 | (fn [x alpha beta] (Math/log (pdf-beta x :alpha alpha :beta beta))))) 134 | 135 | (defn pick-a-stick [alpha idx] 136 | (domonad probabilistic-sampling-m 137 | [stick (mem (beta 1 alpha) idx) 138 | stop (flip stick) 139 | num (if stop 140 | (m-result idx) 141 | (pick-a-stick alpha (inc idx)))] 142 | num)) 143 | 144 | (defn dirichlet-process [alpha base] 145 | (domonad probabilistic-sampling-m 146 | [idx (pick-a-stick alpha 1) 147 | val (mem base idx)] 148 | val)) 149 | 150 | (defn mixture-DP [alpha data] 151 | (with-monad probabilistic-sampling-m 152 | (if (empty? data) 153 | (m-result [0 {} ()]) 154 | (domonad 155 | [mu-comp (dirichlet-process alpha (gaussian 0 15)) 156 | obs (cond-data (gaussian mu-comp 1) (first data)) 157 | [num-comp comp-mus assignment] (mixture-DP alpha (rest data))] 158 | (let [comp-idx (if (contains? comp-mus mu-comp) 159 | (comp-mus mu-comp) 160 | (inc num-comp)) 161 | comp-mus (assoc comp-mus mu-comp comp-idx)] 162 | [(count comp-mus) comp-mus (cons comp-idx assignment)]))))) 163 | 164 | (defn plot-DP-fit [data res] 165 | (let [data-plot (histogram data :nbins 50 :density true) 166 | [num-comp mus assignment] res 167 | weights (density assignment) 168 | xs (range -15 15 0.01)] 169 | (doseq [[mu idx] (seq mus)] 170 | (add-lines data-plot xs (map (fn [x] (* (weights idx) (pdf-normal x :mean mu))) xs))) 171 | (add-lines data-plot xs (map (fn [x] (reduce + (for [[mu idx] (seq mus)] 172 | (* (weights idx) (pdf-normal x :mean mu))))) 173 | xs)) 174 | (view data-plot))) 175 | 176 | (defn test-DP [alpha n] 177 | (let [res (sample-traces (mixture-DP alpha data))] 178 | (loop [x res, i 0] 179 | (when (not (> i n)) 180 | (when (= (mod i 2500) 0) 181 | (plot-DP-fit data (first x))) 182 | (recur (rest x) (inc i)))))) -------------------------------------------------------------------------------- /src/probabilistic_clojure/original/metropolis_hastings.clj: -------------------------------------------------------------------------------- 1 | ;;; Copyright (C) 2011 Nils Bertschinger 2 | 3 | ;;; This file is part of Probabilistic-Clojure 4 | 5 | ;;; Probabilistic-Clojure is free software: you can redistribute it and/or modify 6 | ;;; it under the terms of the GNU Lesser General Public License as published by 7 | ;;; the Free Software Foundation, either version 3 of the License, or 8 | ;;; (at your option) any later version. 9 | 10 | ;;; Probabilistic-Clojure is distributed in the hope that it will be useful, 11 | ;;; but WITHOUT ANY WARRANTY; without even the implied warranty of 12 | ;;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 13 | ;;; GNU Lesser General Public License for more details. 14 | 15 | ;;; You should have received a copy of the GNU Lesser General Public License 16 | ;;; along with Probabilistic-Clojure. If not, see . 17 | 18 | (ns 19 | ^{:author "Nils Bertschinger" 20 | :doc "This library implements Metropolis-Hastings sampling for 21 | the probability monad. The system allows to condition and memoize 22 | choice points and can be extended by user defined probabilistic choices."} 23 | probabilistic.metropolis-hastings 24 | (:use [clojure.contrib.monads :only (defmonad)]) 25 | (:use [incanter.core :only (gamma)] 26 | [incanter.stats :only (sample-normal pdf-normal sample-dirichlet sample-beta pdf-beta)])) 27 | 28 | (in-ns 'probabilistic.metropolis-hastings) 29 | 30 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 31 | ;;; 32 | ;;; Basic data structures and utilities 33 | ;;; 34 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 35 | 36 | (defrecord ChoicePoint 37 | [sampler get-log-prob proposer get-log-proposal-prob]) 38 | 39 | (defrecord DBentry 40 | [value log-lik status type params choice-point]) 41 | 42 | (defn- activate [database addr] 43 | (assoc-in database [addr :status] :active)) 44 | 45 | (defn- inactivate-all [database] 46 | (into {} (for [[addr entry] database] 47 | [addr (assoc entry :status :inactive)]))) 48 | 49 | (defn- clean-db-back [database] 50 | (reduce (fn [[db log-bwd-prob] [addr entry]] 51 | (if (= (:status entry) :active) 52 | [(assoc db addr entry) log-bwd-prob] 53 | [db (+ log-bwd-prob (apply (:get-log-prob (:choice-point entry)) 54 | (:value entry) (:params entry)))])) 55 | [{} 0] (seq database))) 56 | 57 | (defn- ensure-list [x] 58 | (if (seq? x) x (list x))) 59 | 60 | (defn sample-from 61 | "Sample from a discrete distribution implemented as a hash-map from 62 | values to probabilities." 63 | [dist] 64 | (when (seq dist) 65 | (let [total (reduce + (vals dist)) 66 | threshold (rand)] 67 | (loop [cum-p 0 68 | [[v p] & more] (seq dist)] 69 | (if (< threshold (+ cum-p p)) 70 | v 71 | (recur (+ cum-p p) more)))))) 72 | 73 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 74 | ;;; 75 | ;;; The monadic interface 76 | ;;; 77 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 78 | 79 | (def log-prob-zero (Math/log 0)) 80 | 81 | (defn- m-result-MH [v] 82 | (fn [addr database log-fwd-prob log-lik mems] 83 | ;; there is no choice here, so just return everything directly 84 | [v log-lik database log-fwd-prob mems])) 85 | 86 | (def m-zero-MH 87 | (fn [addr database log-fwd-prob log-lik mems] 88 | ;; invalidate this trace 89 | [:invalid log-prob-zero database log-fwd-prob mems])) 90 | 91 | (defn- m-bind-MH [m f] 92 | (fn [addr database log-fwd-prob log-lik mems] 93 | ;; here we first run the monad m and then 94 | ;; plug the values into the continuation f 95 | (let [[v log-lik database log-fwd-prob mems] 96 | (m (cons "BIND-M" addr) database log-fwd-prob log-lik mems)] 97 | (if (= v :invalid) 98 | (m-zero-MH (cons "BIND-F" addr) database log-fwd-prob log-lik mems) 99 | ((f v) (cons "BIND-F" addr) database log-fwd-prob log-lik mems))))) 100 | 101 | ;; Definition of our monad (note that no implementation of m-plus is provided!) 102 | (defmonad probabilistic-sampling-m 103 | [m-result m-result-MH 104 | m-bind m-bind-MH 105 | m-zero m-zero-MH]) 106 | 107 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 108 | ;;; 109 | ;;; User functions for defining choice points and running probabilistic programs 110 | ;;; 111 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 112 | 113 | (defn make-choice-point 114 | "Allows to define a new probabilistic choice point by providing a function 115 | for sampling and calculating the log-likelihood. 116 | See the source code of flip for an example." 117 | ([name params sampler get-log-prob] 118 | (make-choice-point name params 119 | sampler get-log-prob 120 | (fn [val & args] (apply sampler args)) 121 | (fn [new-val old-val & args] (apply get-log-prob new-val args)))) 122 | ([name params sampler get-log-prob proposer get-log-proposal-prob] 123 | (fn [addr database log-fwd-prob log-lik mems] 124 | ;; this function runs the choice-point with entries from the database and updates the trace 125 | (let [addr (cons name addr) 126 | create-new-randomness 127 | (fn [] 128 | (let [val (apply sampler params) 129 | ll (apply get-log-prob val params)] 130 | [val 131 | (+ log-lik ll) 132 | (assoc database addr 133 | (DBentry. val ll :active name params 134 | (ChoicePoint. sampler get-log-prob proposer get-log-proposal-prob))) 135 | (+ log-fwd-prob ll) mems]))] 136 | (if (contains? database addr) 137 | (let [entry (database addr)] 138 | (if (= (:params entry) params) 139 | ;; we found an exact match, so just lookup the value 140 | (let [val (:value entry) 141 | ll (apply (:get-log-prob (:choice-point entry)) val params)] 142 | [val (+ log-lik ll) (activate database addr) log-fwd-prob mems]) 143 | ;; no exact match, we have to reweight the trace 144 | (let [val (:value entry) 145 | ll (apply (:get-log-prob (:choice-point entry)) val params)] 146 | (if (= ll log-prob-zero) 147 | (create-new-randomness) 148 | [val (+ log-lik ll) 149 | (-> database 150 | (activate addr) 151 | (assoc-in [addr :log-lik] ll) 152 | (assoc-in [addr :params] params)) 153 | log-fwd-prob mems])))) 154 | ;; not in database, create new randomness 155 | (create-new-randomness)))))) 156 | 157 | (defn- get-trace [m-MH database] 158 | (m-MH (list "TOP") database 0 0 {})) 159 | 160 | (defn cond-data 161 | "Condition on a specific value of data. 162 | This function must be applied to an elementary random choice point, e.g. (flip 0.6). 163 | A trace running through this value is then weighted according to the likelihood of the data value." 164 | [choice val] 165 | (fn [addr database log-fwd-prob log-lik mems] 166 | (let [[[_ choice-entry] & more] (seq (get (get-trace choice {}) 2)) 167 | choice-point (:choice-point choice-entry) 168 | ll (apply (:get-log-prob choice-point) val (:params choice-entry))] 169 | (assert (nil? more)) ; ensure that its was called on an elementary choice point 170 | [val (+ log-lik ll) database log-fwd-prob mems]))) 171 | 172 | (defmacro mem 173 | "Memoize a MH monadic value on some given arguments, i.e. if the same arguments 174 | are encountered again it refers back to the original choice 175 | point which was established for these arguments in the trace." 176 | [m-MH-form & add-args] 177 | `(fn [addr# database# log-fwd-prob# log-lik# mems#] 178 | (let [mem-addr# (list "MEMO" (str '~(first (ensure-list m-MH-form))) ~@(rest (ensure-list m-MH-form)) ~@add-args) 179 | ;; now just redirect the choice point to the new address 180 | ;; which identifies it according to its arguments 181 | [val# ll# db# lfp# ms#] (~m-MH-form mem-addr# database# log-fwd-prob# log-lik# mems#)] 182 | (if (contains? mems# mem-addr#) 183 | (do ;; (assert (= database# db#)) 184 | [val# log-lik# database# log-fwd-prob# (update-in ms# [mem-addr#] inc)]) 185 | [val# ll# db# lfp# (assoc ms# mem-addr# 1)])))) 186 | 187 | (defn sample-traces 188 | ([m-MH] 189 | (println "Trying to find valid trace ...") 190 | (loop [[val log-lik database mems] (get-trace m-MH {})] 191 | (if (or (= val :invalid) (= log-lik log-prob-zero)) 192 | (recur (get-trace m-MH {})) 193 | (do (println "Starting MH-sampling.") 194 | (sample-traces m-MH database mems log-lik val 1 1))))) 195 | ([m-MH database mems log-lik val idx num-acc] 196 | (when (= (mod idx 500) 0) 197 | (println (str idx ": value " val " with log. likelihood " log-lik)) 198 | (println (str "Accepted " num-acc " out of last 500 proposals"))) 199 | (let [num-acc (if (= (mod idx 500) 0) 0 num-acc) 200 | [addr entry] (rand-nth (for [[addr entry] database, 201 | en (repeat (if (contains? mems (rest addr)) 202 | (mems (rest addr)) 203 | 1) 204 | entry)] 205 | [addr en])) 206 | prop-val (apply (:proposer (:choice-point entry)) (:value entry) (:params entry)) 207 | ll-prop-val (apply (:get-log-proposal-prob (:choice-point entry)) 208 | prop-val (:value entry) (:params entry)) 209 | ll-val (apply (:get-log-proposal-prob (:choice-point entry)) 210 | (:value entry) prop-val (:params entry)) 211 | [next-val next-log-lik next-database log-fwd-prob next-mems] 212 | (get-trace m-MH 213 | (-> (inactivate-all database) 214 | (assoc-in [addr :value] prop-val) 215 | (assoc-in [addr :log-lik] 216 | (apply (:get-log-prob (:choice-point entry)) prop-val (:params entry)))))] 217 | (if (= next-val :invalid) ; trace was rejected => retry 218 | (lazy-seq (cons val (sample-traces m-MH database mems log-lik val (inc idx) num-acc))) 219 | ; (recur m-MH database log-lik val) 220 | (let [[next-database log-bwd-prob] (clean-db-back next-database)] 221 | (if (< (Math/log (rand)) 222 | (+ (- next-log-lik log-lik) 223 | (Math/log (/ (count database) (count next-database))) 224 | (- ll-val ll-prop-val) 225 | (- log-bwd-prob log-fwd-prob))) 226 | (lazy-seq (cons next-val (sample-traces m-MH next-database next-mems 227 | next-log-lik next-val 228 | (inc idx) (inc num-acc)))) 229 | (lazy-seq (cons val (sample-traces m-MH database mems log-lik val (inc idx) num-acc))))))))) 230 | 231 | (defn monte-carlo-sample [m-MH] 232 | (first (get-trace m-MH {}))) 233 | 234 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 235 | ;;; 236 | ;;; Definitions of useful basic choice points 237 | ;;; 238 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 239 | 240 | (defn flip [p] 241 | (make-choice-point "FLIP" [p] 242 | (fn [p] (< (rand) p)) 243 | (fn [b p] (Math/log (if b p (- 1 p)))) 244 | (fn [b p] (not b)) 245 | (fn [new-b old-b p] (Math/log 1)))) 246 | 247 | (defn discrete [dist] 248 | (make-choice-point "DISCRETE" [dist] 249 | (fn [dist] (sample-from dist)) 250 | (fn [x dist] 251 | (if (contains? dist x) 252 | (Math/log (dist x)) 253 | log-prob-zero)))) 254 | 255 | (defn gaussian [mu sdev] 256 | (let [proposal-sd 0.7] 257 | (make-choice-point "GAUSSIAN" [mu sdev] 258 | (fn [mu sdev] (sample-normal 1 :mean mu :sd sdev)) 259 | (fn [x mu sdev] (Math/log (pdf-normal x :mean mu :sd sdev))) 260 | (fn [x mu sdev] (sample-normal 1 :mean x :sd proposal-sd)) 261 | (fn [new-x old-x mu sdev] 262 | (Math/log (pdf-normal new-x :mean old-x :sd proposal-sd 0.7)))))) 263 | 264 | (defn pdf-dirichlet [ps alphas] 265 | (let [norm (/ (reduce * (map gamma alphas)) 266 | (gamma (reduce + alphas)))] 267 | (/ (reduce * (map (fn [p a] (Math/pow p (- a 1))) ps alphas)) 268 | norm))) 269 | 270 | (defn dirichlet [alphas] 271 | (let [proposal-alphas (fn [alphas] 272 | (for [a alphas] (* 18 a)))] 273 | (make-choice-point "DIRICHLET" [alphas] 274 | (fn [alphas] (first (sample-dirichlet 2 alphas))) 275 | (fn [ps alphas] (pdf-dirichlet ps alphas)) 276 | (fn [ps alphas] (first (sample-dirichlet 2 (proposal-alphas ps)))) 277 | (fn [new-ps old-ps alphas] 278 | (Math/log (pdf-dirichlet new-ps (proposal-alphas old-ps))))))) 279 | -------------------------------------------------------------------------------- /src/probabilistic_clojure/original/scratch.clj: -------------------------------------------------------------------------------- 1 | ;;; These old sampling routines are now replaced by metropolis-hastings-sampling 2 | 3 | ;;; The actual Metropolis Hastings sampling 4 | 5 | (defn sampling-step [choice-points] 6 | (with-fresh-store choice-points 7 | (let [prob-choices (prob-choice-dist choice-points) 8 | selected-cp (choice-points (sample-from prob-choices)) 9 | change-set (ordered-dependencies (:name selected-cp) choice-points) 10 | trace-log-lik (total-log-lik change-set choice-points) 11 | 12 | [prop-val fwd-log-lik bwd-log-lik] 13 | (propose selected-cp (:value selected-cp))] 14 | ;; (println "Proposing: " (:name selected-cp) ": " change-set) 15 | ;; (do (println :OLD) (doseq [cp (vals choice-points)] (println (probabilistic-clojure.embedded.tests/cp-str cp)))) 16 | (assoc-in-store! [:choice-points (:name selected-cp) :value] 17 | prop-val) 18 | (propagate-change-to change-set) 19 | (if (trace-failed?) 20 | choice-points 21 | (let [;; _ (do (println :NEW) (doseq [cp (vals (fetch-store :choice-points))] (println (probabilistic-clojure.embedded.tests/cp-str cp)))) 22 | _ (assert (clojure.set/subset? (set change-set) (fetch-store :recomputed))) 23 | _ (assert (= (fetch-store :recomputed) (union (set change-set) (fetch-store :newly-created))) 24 | (println "Aha " (str [(fetch-store :recomputed) (set change-set) (fetch-store :newly-created)]))) 25 | removed-cps (remove-uncalled-choices) 26 | ;; _ (do (println :CLEAN) (doseq [cp (vals (fetch-store :choice-points))] (println (probabilistic-clojure.embedded.tests/cp-str cp)))) 27 | _ (assert (empty? (clojure.set/intersection removed-cps (fetch-store :newly-created)))) 28 | _ (let [new (set (keys (fetch-store :choice-points))) 29 | old (set (keys choice-points))] 30 | (assert (and (= new (difference (union old (fetch-store :newly-created)) 31 | removed-cps)) 32 | (= old (difference (union new removed-cps) (fetch-store :newly-created)))) 33 | [old (fetch-store :newly-created) removed-cps new])) 34 | 35 | trace-log-lik (total-log-lik (union (set change-set) removed-cps) 36 | ;; (keys choice-points) 37 | ;; (difference (fetch-store :recomputed) (fetch-store :newly-created)) 38 | choice-points) 39 | prop-trace-log-lik (total-log-lik ;; (keys (fetch-store :choice-points)) 40 | (difference (fetch-store :recomputed) removed-cps) 41 | (fetch-store :choice-points)) 42 | 43 | fwd-trace-log-lik (total-log-lik (fetch-store :newly-created) (fetch-store :choice-points)) 44 | bwd-trace-log-lik (total-log-lik removed-cps choice-points) 45 | ;; prop-trace-log-lik (total-log-lik (difference 46 | ;; ;; TODO: What about reweighting of reused choice-points??? 47 | ;; ;; (union (set change-set) (-> @*global-store* :newly-created)) 48 | ;; (fetch-store :recomputed)) 49 | ;; ;; removed-cps 50 | ;; (fetch-store :choice-points)) 51 | prop-prob-choices (prob-choice-dist (fetch-store :choice-points))] 52 | ;; (when-not (empty? (clojure.set/intersection (fetch-store :recomputed) removed-cps)) 53 | ;; (print ".")) 54 | ;; (when-let [it (seq removed-cps)] (println "Removed: " (pr-str (map :name it)) " (" (count it) ")")) 55 | ;; (when-let [it (seq (fetch-store :newly-created))] (println "Created: " it " (" (count it) ")")) 56 | (if (< (Math/log (rand)) 57 | (+ (- prop-trace-log-lik trace-log-lik) 58 | (- (Math/log (prop-prob-choices (:name selected-cp))) 59 | (Math/log (prob-choices (:name selected-cp)))) 60 | (- bwd-trace-log-lik fwd-trace-log-lik) 61 | (- bwd-log-lik fwd-log-lik))) 62 | (fetch-store :choice-points) 63 | choice-points)))))) 64 | 65 | (defn sample-traces [prob-chunk] 66 | (println "Trying to find a valid trace ...") 67 | (let [[cp choice-points] (find-valid-trace prob-chunk)] 68 | (println "Started sampling") 69 | (letfn [(samples [choice-points idx accepted] 70 | (lazy-seq 71 | (let [val (cp-value cp choice-points) 72 | next-choices (sampling-step choice-points) 73 | output? (= (mod idx 500) 0) 74 | accepted (if (= choice-points next-choices) 75 | accepted 76 | (inc accepted))] 77 | (when output? 78 | (println idx ": " val) 79 | (println "Log. lik.: " (total-log-lik (keys choice-points) choice-points)) 80 | (println "Accepted " accepted " out of last 500 samples")) 81 | (cons val 82 | (samples next-choices (inc idx) 83 | (if output? 0 accepted))))))] 84 | (samples choice-points 0 0)))) 85 | 86 | ;;; faster sampling for fixed topology ==> TODO: combine for general sampling routine!!! 87 | 88 | (defn sampling-step-fixed [choice-points selected all-dependencies] 89 | (with-fresh-store choice-points 90 | (let [selected-cp (choice-points selected) 91 | change-set (ordered-dependencies (:name selected-cp) choice-points) 92 | trace-log-lik (total-log-lik change-set choice-points) 93 | 94 | [prop-val fwd-log-lik bwd-log-lik] 95 | (propose selected-cp (:value selected-cp))] 96 | (assoc-in-store! [:choice-points (:name selected-cp) :value] 97 | prop-val) 98 | (propagate-change-to change-set) 99 | 100 | (if (trace-failed?) 101 | [choice-points false] 102 | (do (let [removed-cps (remove-uncalled-choices)] 103 | (when-not (empty? (fetch-store :newly-created)) 104 | (error "New choice points created during fixed sampling: " 105 | (pr-str (fetch-store :newly-created)))) 106 | (when-not (empty? removed-cps) 107 | (error "Choice points deleted during fixed sampling: " 108 | (pr-str removed-cps)))) 109 | (let [prop-trace-log-lik (total-log-lik (fetch-store :recomputed) 110 | (fetch-store :choice-points))] 111 | (if (< (Math/log (rand)) 112 | (+ (- prop-trace-log-lik trace-log-lik) 113 | (- bwd-log-lik fwd-log-lik))) 114 | [(fetch-store :choice-points) true] 115 | [choice-points false]))))))) 116 | 117 | (defn sample-traces-fixed [prob-chunk select-update] 118 | (println "Trying to find a valid trace ...") 119 | (let [[cp choice-points] (find-valid-trace prob-chunk)] 120 | (println "Generating update sequence ...") 121 | (let [update-seq (select-update (prob-choice-dist choice-points))] 122 | (println "Started sampling") 123 | (letfn [(samples [choice-points idx accepted update-seq all-dependencies] 124 | (if (seq update-seq) 125 | (lazy-seq 126 | (let [val (cp-value cp choice-points) 127 | [next-choices accepted?] 128 | (sampling-step-fixed choice-points 129 | (first update-seq) 130 | all-dependencies) 131 | output? (= (mod idx 500) 0) 132 | accepted (if accepted? (inc accepted) accepted)] 133 | (when output? 134 | (println idx ": " val) 135 | (println "Log. lik.: " (total-log-lik (keys choice-points) choice-points)) 136 | (println "Accepted " accepted " out of last 500 samples")) 137 | (cons val 138 | (samples next-choices (inc idx) 139 | (if output? 0 accepted) 140 | (rest update-seq) 141 | all-dependencies)))) 142 | ()))] 143 | (samples choice-points 0 0 update-seq 144 | (do (println "Caching dependencies ...") 145 | (time 146 | (into {} (for [cp-name (keys choice-points)] 147 | [cp-name (ordered-dependencies cp-name choice-points)]))))))))) 148 | 149 | -------------------------------------------------------------------------------- /src/probabilistic_clojure/utils/finite_distributions.clj: -------------------------------------------------------------------------------- 1 | ;; Finite probability distributions 2 | 3 | ;; by Konrad Hinsen 4 | ;; last updated January 8, 2010 5 | 6 | ;; Copyright (c) Konrad Hinsen, 2009-2010. All rights reserved. The use 7 | ;; and distribution terms for this software are covered by the Eclipse 8 | ;; Public License 1.0 (http://opensource.org/licenses/eclipse-1.0.php) 9 | ;; which can be found in the file epl-v10.html at the root of this 10 | ;; distribution. By using this software in any fashion, you are 11 | ;; agreeing to be bound by the terms of this license. You must not 12 | ;; remove this notice, or any other, from this software. 13 | 14 | ;; Modified to work with Clojure 1.3 15 | 16 | (ns 17 | ^{:author "Konrad Hinsen" 18 | :doc "Finite probability distributions 19 | This library defines a monad for combining finite probability 20 | distributions."} 21 | probabilistic-clojure.utils.finite-distributions 22 | (:use [clojure.algo.monads 23 | :only (defmonad domonad with-monad maybe-t m-lift m-chain)])) 24 | 25 | (in-ns 'probabilistic-clojure.utils.finite-distributions) 26 | 27 | ; The probability distribution monad. It is limited to finite probability 28 | ; distributions (e.g. there is a finite number of possible value), which 29 | ; are represented as maps from values to probabilities. 30 | 31 | (defmonad dist-m 32 | "Monad describing computations on fuzzy quantities, represented by a finite 33 | probability distribution for the possible values. A distribution is 34 | represented by a map from values to probabilities." 35 | [m-result (fn m-result-dist [v] 36 | {v 1}) 37 | m-bind (fn m-bind-dist [mv f] 38 | (reduce (partial merge-with +) 39 | (for [[x p] mv [y q] (f x)] 40 | {y (* q p)}))) 41 | ]) 42 | 43 | ; Applying the monad transformer maybe-t to the basic dist monad results 44 | ; in the cond-dist monad that can handle invalid values. The total probability 45 | ; for invalid values ends up as the probability of m-zero (which is nil). 46 | ; The function normalize takes this probability out of the distribution and 47 | ; re-distributes its weight over the valid values. 48 | 49 | (def cond-dist-m 50 | "Variant of the dist monad that can handle undefined values." 51 | (maybe-t dist-m)) 52 | 53 | ; Normalization 54 | 55 | (defn- scale-by 56 | "Multiply each entry in dist by the scale factor s and remove zero entries." 57 | [dist s] 58 | (into {} 59 | (for [[val p] dist :when (> p 0)] 60 | [val (* p s)]))) 61 | 62 | (defn normalize-cond [cdist] 63 | "Normalize a probability distribution resulting from a computation in 64 | the cond-dist monad by re-distributing the weight of the invalid values 65 | over the valid ones." 66 | (let [missing (get cdist nil 0) 67 | dist (dissoc cdist nil)] 68 | (cond (zero? missing) dist 69 | (= 1 missing) {} 70 | :else (let [scale (/ 1 (- 1 missing))] 71 | (scale-by dist scale))))) 72 | 73 | (defn normalize 74 | "Convert a weight map (e.g. a map of counter values) to a distribution 75 | by multiplying with a normalization factor. If the map has a key 76 | :total, its value is assumed to be the sum over all the other values and 77 | it is used for normalization. Otherwise, the sum is calculated 78 | explicitly. The :total key is removed from the resulting distribution." 79 | [weights] 80 | (let [total (:total weights) 81 | w (dissoc weights :total) 82 | s (/ 1 (if (nil? total) (reduce + (vals w)) total))] 83 | (scale-by w s))) 84 | 85 | ; Functions that construct distributions 86 | 87 | (defn uniform 88 | "Return a distribution in which each of the elements of coll 89 | has the same probability." 90 | [coll] 91 | (let [n (count coll) 92 | p (/ 1 n)] 93 | (into {} (for [x (seq coll)] [x p])))) 94 | 95 | (defn choose 96 | "Construct a distribution from an explicit list of probabilities 97 | and values. They are given in the form of a vector of probability-value 98 | pairs. In the last pair, the probability can be given by the keyword 99 | :else, which stands for 1 minus the total of the other probabilities." 100 | [& choices] 101 | (letfn [(add-choice [dist [p v]] 102 | (cond (nil? p) dist 103 | (= p :else) 104 | (let [total-p (reduce + (vals dist))] 105 | (assoc dist v (- 1 total-p))) 106 | :else (assoc dist v p)))] 107 | (reduce add-choice {} (partition 2 choices)))) 108 | 109 | (defn bernoulli 110 | [p] 111 | "Returns the Bernoulli distribution for probability p." 112 | (choose p 1 :else 0)) 113 | 114 | (defn- bc 115 | [n] 116 | "Returns the binomial coefficients for a given n." 117 | (let [r (inc n)] 118 | (loop [c 1 119 | f (list 1)] 120 | (if (> c n) 121 | f 122 | (recur (inc c) (cons (* (/ (- r c) c) (first f)) f)))))) 123 | 124 | (defn binomial 125 | [n p] 126 | "Returns the binomial distribution, which is the distribution of the 127 | number of successes in a series of n experiments whose individual 128 | success probability is p." 129 | (let [q (- 1 p) 130 | n1 (inc n) 131 | k (range n1) 132 | pk (take n1 (iterate #(* p %) 1)) 133 | ql (reverse (take n1 (iterate #(* q %) 1))) 134 | f (bc n)] 135 | (into {} (map vector k (map * f pk ql))))) 136 | 137 | (defn make-distribution 138 | "Returns the distribution in which each element x of the collection 139 | has a probability proportional to (f x)" 140 | [coll f] 141 | (normalize (into {} (for [k coll] [k (f k)])))) 142 | 143 | (defn zipf 144 | "Returns the Zipf distribution in which the numbers k=1..n have 145 | probabilities proportional to 1/k^s." 146 | [s n] 147 | (make-distribution (range 1 (inc n)) #(/ (java.lang.Math/pow % s)))) 148 | 149 | (defn certainly 150 | "Returns a distribution in which the single value v has probability 1." 151 | [v] 152 | {v 1}) 153 | 154 | (with-monad dist-m 155 | 156 | (defn join-with 157 | "Returns the distribution of (f x y) with x from dist1 and y from dist2." 158 | [f dist1 dist2] 159 | ((m-lift 2 f) dist1 dist2)) 160 | 161 | ) 162 | 163 | (with-monad cond-dist-m 164 | (defn cond-prob 165 | "Returns the conditional probability for the values in dist that satisfy 166 | the predicate pred." 167 | [pred dist] 168 | (normalize-cond 169 | (domonad 170 | [v dist 171 | :when (pred v)] 172 | v)))) 173 | 174 | ; Select (with equal probability) N items from a sequence 175 | 176 | (defn- nth-and-rest [n xs] 177 | "Return a list containing the n-th value of xs and the sequence 178 | obtained by removing the n-th value from xs." 179 | (let [[h t] (split-at n xs)] 180 | (list (first t) (concat h (rest t))))) 181 | 182 | (with-monad dist-m 183 | 184 | (defn- select-n [n xs] 185 | (letfn [(select-1 [[s xs]] 186 | (uniform (for [i (range (count xs))] 187 | (let [[nth rest] (nth-and-rest i xs)] 188 | (list (cons nth s) rest)))))] 189 | ((m-chain (replicate n select-1)) (list '() xs)))) 190 | 191 | (defn select [n xs] 192 | "Return the distribution for all possible ordered selections of n elements 193 | out of xs." 194 | ((m-lift 1 first) (select-n n xs))) 195 | 196 | ) 197 | 198 | ; Find the probability that a given predicate is satisfied 199 | 200 | (defn prob 201 | "Return the probability that the predicate pred is satisfied in the 202 | distribution dist, i.e. the sum of the probabilities of the values 203 | that satisfy pred." 204 | [pred dist] 205 | (apply + (for [[x p] dist :when (pred x)] p))) 206 | 207 | -------------------------------------------------------------------------------- /src/probabilistic_clojure/utils/sampling.clj: -------------------------------------------------------------------------------- 1 | ;;; Copyright (C) 2011 Nils Bertschinger 2 | 3 | ;;; This file is part of Probabilistic-Clojure 4 | 5 | ;;; Probabilistic-Clojure is free software: you can redistribute it and/or modify 6 | ;;; it under the terms of the GNU Lesser General Public License as published by 7 | ;;; the Free Software Foundation, either version 3 of the License, or 8 | ;;; (at your option) any later version. 9 | 10 | ;;; Probabilistic-Clojure is distributed in the hope that it will be useful, 11 | ;;; but WITHOUT ANY WARRANTY; without even the implied warranty of 12 | ;;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 13 | ;;; GNU Lesser General Public License for more details. 14 | 15 | ;;; You should have received a copy of the GNU Lesser General Public License 16 | ;;; along with Probabilistic-Clojure. If not, see . 17 | 18 | (ns 19 | ^{:author "Nils Bertschinger" 20 | :doc "Utility functions for discrete probability distributions."} 21 | probabilistic-clojure.utils.sampling) 22 | 23 | 24 | (defn sample-from 25 | "Sample from a discrete distribution implemented as a hash-map from 26 | values to probabilities." 27 | [dist] 28 | (when (seq dist) 29 | (let [total (reduce + (vals dist)) 30 | threshold (rand)] 31 | (loop [cum-p 0 32 | [[v p] & more] (seq dist)] 33 | (if (< threshold (+ cum-p p)) 34 | v 35 | (recur (+ cum-p p) more)))))) 36 | 37 | ;;; fast sampling using the alias method 38 | 39 | (defn init-alias 40 | "Takes a vector of probabilities and initializes the \"magic\" arrays 41 | prob and alias used by the alias method." 42 | [p] 43 | (let [n (count p) 44 | {large :large, small :small} 45 | (group-by (fn [i] (if (> (p i) (/ 1 n)) 46 | :large 47 | :small)) 48 | (range n)) 49 | 50 | prob (make-array Double n) 51 | alias (make-array Long n)] 52 | 53 | (loop [p p 54 | small small 55 | large large] 56 | (if (and (seq small) (seq large)) 57 | (let [[j & small] small 58 | [k & large] large] 59 | (aset prob j (double (* n (p j)))) 60 | (aset alias j k) 61 | 62 | (let [p (assoc p k 63 | (+ (p k) (- (p j) (/ 1 n)))) 64 | push-large? (> (p k) (/ 1 n))] 65 | (recur p 66 | (if push-large? small (cons k small)) 67 | (if push-large? (cons k large) large)))) 68 | (do (loop [small small] 69 | (when (seq small) 70 | (aset prob (first small) (double 1)) 71 | (recur (rest small)))) 72 | (loop [large large] 73 | (when (seq large) 74 | (aset prob (first large) (double 1)) 75 | (recur (rest large))))))) 76 | 77 | [n (vec (seq prob)) (vec (seq alias))])) 78 | 79 | (defn sample-alias 80 | "Draws one sample using the alias method. n denotes the length of the vectors prob and alias." 81 | [n prob alias] 82 | (let [u (* n (rand)) 83 | j (int u)] 84 | (if (<= (- u j) (prob j)) 85 | j 86 | (alias j)))) 87 | 88 | ;;; Lazy streams of random draws 89 | 90 | (defn random-selection 91 | "Returns a lazy sequence of random draws from dist. Optionally the requested 92 | number of samples can be specified." 93 | ([dist] 94 | (repeatedly (fn [] (sample-from dist)))) 95 | ([n dist] 96 | (repeatedly n (fn [] (sample-from dist))))) 97 | 98 | (defn random-selection-alias 99 | "Returns a lazy sequence of random draws from dist using the alias method (very fast if a large 100 | number of samples is required). Optionally the requested number of samples can be specified." 101 | ([dist] 102 | (repeatedly (let [vs (vec (keys dist)) 103 | [n prob alias] (init-alias (vec (vals dist)))] 104 | (fn [] (vs (sample-alias n prob alias)))))) 105 | ([n dist] 106 | (take n (random-selection-alias dist)))) 107 | 108 | ;;; Distribution utilities 109 | 110 | (defn normalize 111 | "Normalize the distribution given by the hash-map dist" 112 | [dist] 113 | (let [total (reduce + (vals dist))] 114 | (if (= total 1) 115 | dist 116 | (into {} (for [[x p] dist] [x (/ p total)]))))) 117 | 118 | (defn density 119 | "Like frequencies, but normalizes the counts." 120 | [vs] 121 | (let [freqs (frequencies vs) 122 | total (reduce + (vals freqs))] 123 | (into {} (for [[v c] freqs] [v (double (/ c total))])))) 124 | 125 | 126 | -------------------------------------------------------------------------------- /src/probabilistic_clojure/utils/stuff.clj: -------------------------------------------------------------------------------- 1 | ;;; Copyright (C) 2011 Nils Bertschinger 2 | 3 | ;;; This file is part of Probabilistic-Clojure 4 | 5 | ;;; Probabilistic-Clojure is free software: you can redistribute it and/or modify 6 | ;;; it under the terms of the GNU Lesser General Public License as published by 7 | ;;; the Free Software Foundation, either version 3 of the License, or 8 | ;;; (at your option) any later version. 9 | 10 | ;;; Probabilistic-Clojure is distributed in the hope that it will be useful, 11 | ;;; but WITHOUT ANY WARRANTY; without even the implied warranty of 12 | ;;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 13 | ;;; GNU Lesser General Public License for more details. 14 | 15 | ;;; You should have received a copy of the GNU Lesser General Public License 16 | ;;; along with Probabilistic-Clojure. If not, see . 17 | 18 | (ns 19 | ^{:author "Nils Bertschinger" 20 | :doc "Small collections of little helpers"} 21 | probabilistic-clojure.utils.stuff) 22 | 23 | (defn ensure-list [x] 24 | (if (seq? x) x (list x))) 25 | 26 | (defn error [& args] 27 | (throw (Error. (apply str args)))) 28 | 29 | (defn transpose 30 | "Transpose a list of lists, i.e. (transpose [[1 2] [3 4] [5 6]]) = [[1 3 5] [2 4 6]]" 31 | [lls] 32 | (apply map list lls)) 33 | 34 | (defn indexed 35 | "Returns a new collection containing index-value pairs for each value 36 | in the given collection." 37 | [coll] 38 | (map vector (iterate inc 0) coll)) 39 | --------------------------------------------------------------------------------