├── .gitignore ├── Chapter2_MorePyMC ├── sms_model.png ├── Screen Shot 2013-02-08 at 11.23.49 AM.png ├── data │ └── challenger_data.csv ├── daft_plot.py └── separation_plot.py ├── ExamplesFromChapters ├── README.md ├── Chapter2 │ ├── FreqOfCheaters.py │ └── ORingFailure.py ├── Chapter1 │ └── SMS_behaviour.py └── Chapter3 │ └── ClusteringWithGaussians.py ├── Chapter4_TheGreatestTheoremNeverTold ├── reddit_comments.png └── top_pic_comments.py ├── Chapter1_Introduction ├── Screen Shot 2013-02-06 at 5.52.18 PM.png └── data │ └── txtdata.csv ├── styles ├── bmh_matplotlibrc.json └── custom.css ├── sandbox ├── github_events.py └── Chapter10_ │ ├── data │ ├── gh_forks.csv │ ├── gh_stars.csv │ ├── gh_forks_02112013.csv │ └── gh_stars_02112013.csv │ └── github_datapull.py ├── Chapter3_MCMC ├── data │ ├── smoking_death.csv │ ├── github_data.csv │ └── mixture_data.csv └── github_pull.py ├── Chapter5_LossFunctions ├── draw_sky2.py └── data │ ├── Test_haloCounts.csv │ └── Train_Skies │ └── Train_Skies │ ├── Training_Sky200.csv │ ├── Training_Sky191.csv │ ├── Training_Sky24.csv │ ├── Training_Sky45.csv │ ├── Training_Sky216.csv │ ├── Training_Sky132.csv │ ├── Training_Sky79.csv │ ├── Training_Sky168.csv │ └── Training_Sky145.csv ├── LICENSE.txt ├── book_layout.txt ├── Chapter6_Priorities ├── BanditsD3.html ├── other_strats.py ├── ystockquote.py └── d3bandits.js ├── Chapter7_BayesianMachineLearning └── MachineLearning.ipynb └── README.md /.gitignore: -------------------------------------------------------------------------------- 1 | .DS_Store 2 | *.pyc 3 | *~ 4 | *.png 5 | -------------------------------------------------------------------------------- /Chapter2_MorePyMC/sms_model.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/teoliphant/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/HEAD/Chapter2_MorePyMC/sms_model.png -------------------------------------------------------------------------------- /ExamplesFromChapters/README.md: -------------------------------------------------------------------------------- 1 | ## Read Me 2 | 3 | 4 | Included is all PyMC examples and models *out of context*, this is for users to easily view the entire Python program. 5 | 6 | -------------------------------------------------------------------------------- /Chapter4_TheGreatestTheoremNeverTold/reddit_comments.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/teoliphant/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/HEAD/Chapter4_TheGreatestTheoremNeverTold/reddit_comments.png -------------------------------------------------------------------------------- /Chapter2_MorePyMC/Screen Shot 2013-02-08 at 11.23.49 AM.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/teoliphant/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/HEAD/Chapter2_MorePyMC/Screen Shot 2013-02-08 at 11.23.49 AM.png -------------------------------------------------------------------------------- /Chapter1_Introduction/Screen Shot 2013-02-06 at 5.52.18 PM.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/teoliphant/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/HEAD/Chapter1_Introduction/Screen Shot 2013-02-06 at 5.52.18 PM.png -------------------------------------------------------------------------------- /ExamplesFromChapters/Chapter2/FreqOfCheaters.py: -------------------------------------------------------------------------------- 1 | import pymc as mc 2 | 3 | p = mc.Uniform( "freq_cheating", 0, 1) 4 | 5 | @mc.deterministic 6 | def p_skewed( p = p ): 7 | return 0.5*p + 0.25 8 | 9 | yes_responses = mc.Binomial( "number_cheaters", 100, p_skewed, value = 35, observed = True ) 10 | 11 | model = mc.Model( [yes_responses, p_skewed, p ] ) 12 | 13 | ### To Be Explained in Chapter 3! 14 | mcmc = mc.MCMC(model) 15 | mcmc.sample( 50000, 25000 ) 16 | -------------------------------------------------------------------------------- /Chapter2_MorePyMC/data/challenger_data.csv: -------------------------------------------------------------------------------- 1 | Date,Temperature,Damage Incident 2 | 04/12/1981,66,0 3 | 11/12/1981,70,1 4 | 3/22/82,69,0 5 | 6/27/82,80,NA 6 | 01/11/1982,68,0 7 | 04/04/1983,67,0 8 | 6/18/83,72,0 9 | 8/30/83,73,0 10 | 11/28/83,70,0 11 | 02/03/1984,57,1 12 | 04/06/1984,63,1 13 | 8/30/84,70,1 14 | 10/05/1984,78,0 15 | 11/08/1984,67,0 16 | 1/24/85,53,1 17 | 04/12/1985,67,0 18 | 4/29/85,75,0 19 | 6/17/85,70,0 20 | 7/29/85,81,0 21 | 8/27/85,76,0 22 | 10/03/1985,79,0 23 | 10/30/85,75,1 24 | 11/26/85,76,0 25 | 01/12/1986,58,1 26 | 1/28/86,31,Challenger Accident 27 | -------------------------------------------------------------------------------- /styles/bmh_matplotlibrc.json: -------------------------------------------------------------------------------- 1 | { 2 | "lines.linewidth": 2.0, 3 | "examples.download": true, 4 | "axes.edgecolor": "#bcbcbc", 5 | "patch.linewidth": 0.5, 6 | "legend.fancybox": true, 7 | "axes.color_cycle": [ 8 | "#348ABD", 9 | "#A60628", 10 | "#7A68A6", 11 | "#467821", 12 | "#CF4457", 13 | "#188487", 14 | "#E24A33" 15 | ], 16 | "axes.facecolor": "#eeeeee", 17 | "axes.labelsize": "large", 18 | "axes.grid": true, 19 | "patch.edgecolor": "#eeeeee", 20 | "axes.titlesize": "x-large", 21 | "svg.embed_char_paths": "path", 22 | "examples.directory": "" 23 | } 24 | -------------------------------------------------------------------------------- /sandbox/github_events.py: -------------------------------------------------------------------------------- 1 | #github_events.py 2 | 3 | try: 4 | from json import loads 5 | 6 | import numpy as np 7 | from requests import get 8 | 9 | except ImportError as e: 10 | raise e 11 | 12 | 13 | URL = "https://api.github.com/events" 14 | 15 | #github allows up to 10 pages of 30 events, but we will only keep the unique ones. 16 | ids = np.empty(300, dtype=int) 17 | 18 | k = 0 19 | for page in range(10,0, -1): 20 | 21 | r = get( URL, params = {"page":page} ) 22 | data = loads(r.text) 23 | for event in data: 24 | ids[k] = ( event["actor"]["id"] ) 25 | k+=1 26 | 27 | ids = np.unique( ids.astype(int) ) -------------------------------------------------------------------------------- /Chapter3_MCMC/data/smoking_death.csv: -------------------------------------------------------------------------------- 1 | age,smoke_cigars_pipe,smoke_both, smoke_cigarettes, population, deaths 2 | 1,0,0,0,656,18 3 | 2,0,0,0,359,22 4 | 3,0,0,0,249,19 5 | 4,0,0,0,632,55 6 | 5,0,0,0,1067,117 7 | 6,0,0,0,897,170 8 | 7,0,0,0,668,179 9 | 8,0,0,0,361,120 10 | 9,0,0,0,274,120 11 | 1,1,0,0,145,2 12 | 2,1,0,0,104,4 13 | 3,1,0,0,98,3 14 | 4,1,0,0,372,38 15 | 5,1,0,0,846,113 16 | 6,1,0,0,949,173 17 | 7,1,0,0,824,212 18 | 8,1,0,0,667,243 19 | 9,1,0,0,537,253 20 | 1,0,1,0,4531,149 21 | 2,0,1,0,3030,169 22 | 3,0,1,0,2267,193 23 | 4,0,1,0,4682,576 24 | 5,0,1,0,6052,1001 25 | 6,0,1,0,3880,901 26 | 7,0,1,0,2033,613 27 | 8,0,1,0,871,337 28 | 9,0,1,0,345,189 29 | 1,0,0,1,3410,124 30 | 2,0,0,1,2239,140 31 | 3,0,0,1,1851,187 32 | 4,0,0,1,3270,514 33 | 5,0,0,1,3791,778 34 | 6,0,0,1,2421,689 35 | 7,0,0,1,1195,432 36 | 8,0,0,1,436,214 37 | 9,0,0,1,113,63 38 | -------------------------------------------------------------------------------- /Chapter5_LossFunctions/draw_sky2.py: -------------------------------------------------------------------------------- 1 | import matplotlib.pyplot as plt 2 | from matplotlib.patches import Ellipse 3 | import numpy as np 4 | 5 | def draw_sky( galaxies ): 6 | """adapted from Vishal Goklani""" 7 | size_multiplier = 45 8 | fig = plt.figure(figsize=(10,10)) 9 | fig.patch.set_facecolor("blue") 10 | ax = fig.add_subplot(111, aspect='equal') 11 | n = galaxies.shape[0] 12 | for i in xrange(n): 13 | _g = galaxies[i,:] 14 | x,y = _g[0], _g[1] 15 | d = np.sqrt( _g[2]**2 + _g[3]**2 ) 16 | a = 1.0/ ( 1 - d ) 17 | b = 1.0/( 1 + d) 18 | theta = np.degrees( np.arctan2( _g[3], _g[2])*0.5 ) 19 | 20 | ax.add_patch( Ellipse(xy=(x, y), width=size_multiplier*a, height=size_multiplier*b, angle=theta) ) 21 | ax.autoscale_view(tight=True) 22 | 23 | return fig -------------------------------------------------------------------------------- /Chapter2_MorePyMC/daft_plot.py: -------------------------------------------------------------------------------- 1 | #daft drawing for SMS example 2 | import matplotlib.pyplot as plt 3 | 4 | 5 | 6 | try: 7 | import daft 8 | except ImportError: 9 | print "python library Daft required." 10 | 11 | 12 | pgm = daft.PGM([9, 4], origin=[.5,.5]) 13 | pgm.add_node(daft.Node("tau", r"$\tau$", 4.0, 3.5)) 14 | pgm.add_node(daft.Node("alpha", r"$\alpha$", 6, 4.0)) 15 | pgm.add_node(daft.Node("lambda1", r"$\lambda_1$", 5.5, 3.2,)) 16 | pgm.add_node(daft.Node("lambda2", r"$\lambda_2$", 6.5, 3.2)) 17 | pgm.add_node(daft.Node("lambda", r"$\lambda$", 5.0, 2.0)) 18 | pgm.add_node(daft.Node("obs", "obs", 5.0, 1.0, 1.2, observed=True)) 19 | 20 | 21 | 22 | pgm.add_edge("tau", "lambda") 23 | pgm.add_edge("alpha", "lambda1") 24 | pgm.add_edge("alpha", "lambda2") 25 | pgm.add_edge("lambda1", "lambda") 26 | pgm.add_edge("lambda2", "lambda") 27 | 28 | pgm.add_edge("lambda", "obs") 29 | pgm.render() 30 | plt.figure( figsize=(12,5) ) 31 | plt.show() -------------------------------------------------------------------------------- /ExamplesFromChapters/Chapter2/ORingFailure.py: -------------------------------------------------------------------------------- 1 | import pymc as mc 2 | 3 | 4 | challenger_data = np.genfromtxt("../../Chapter2_MorePyMC/data/challenger_data.csv", skip_header = 1, usecols=[1,2], missing_values="NA", delimiter=",") 5 | #drop the NA values 6 | challenger_data = challenger_data[ ~np.isnan(challenger_data[:,1]) ] 7 | 8 | 9 | temperature = challenger_data[:,0] 10 | D = challenger_data[:,1] #defect or not? 11 | 12 | beta = mc.Normal( "beta", 0, 0.001, value = 0 ) 13 | alpha = mc.Normal( "alpha", 0, 0.001, value = 0 ) 14 | 15 | @mc.deterministic 16 | def p( temp = temperature, alpha = alpha, beta = beta): 17 | return 1.0/( 1. + np.exp( beta*temperature + alpha) ) 18 | 19 | 20 | observed = mc.Bernoulli( "bernoulli_obs", p, value = D, observed=True) 21 | 22 | model = mc.Model( [observed, beta, alpha] ) 23 | 24 | #mysterious code to be explained in Chapter 3 25 | map_ = mc.MAP(model) 26 | map_.fit() 27 | mcmc = mc.MCMC( model ) 28 | mcmc.sample( 260000, 220000, 2 ) 29 | -------------------------------------------------------------------------------- /ExamplesFromChapters/Chapter1/SMS_behaviour.py: -------------------------------------------------------------------------------- 1 | import pymc as mc 2 | 3 | count_data = np.loadtxt("../../Chapter1_Introduction/data/txtdata.csv") 4 | n_count_data = len(count_data) 5 | 6 | alpha = 1.0/count_data.mean() #recall count_data is 7 | #the variable that holds our txt counts 8 | 9 | lambda_1 = mc.Exponential( "lambda_1", alpha ) 10 | lambda_2 = mc.Exponential( "lambda_2", alpha ) 11 | 12 | tau = mc.DiscreteUniform( "tau", lower = 0, upper = n ) 13 | 14 | @mc.deterministic 15 | def lambda_( tau = tau, lambda_1 = lambda_1, lambda_2 = lambda_2 ): 16 | out = np.zeros( n_count_data ) 17 | out[:tau] = lambda_1 #lambda before tau is lambda1 18 | out[tau:] = lambda_2 #lambda after tau is lambda1 19 | return out 20 | 21 | observation = mc.Poisson( "obs", lambda_, value = count_data, observed = True) 22 | model = mc.Model( [observation, lambda_1, lambda_2, tau] ) 23 | 24 | 25 | mcmc = mc.MCMC(model) 26 | mcmc.sample( 100000, 50000, 1 ) -------------------------------------------------------------------------------- /sandbox/Chapter10_/data/gh_forks.csv: -------------------------------------------------------------------------------- 1 | 0.000000000000000000e+00 2 | 1.000000000000000000e+00 3 | 2.000000000000000000e+00 4 | 4.000000000000000000e+00 5 | 8.000000000000000000e+00 6 | 1.600000000000000000e+01 7 | 3.200000000000000000e+01 8 | 6.400000000000000000e+01 9 | 1.280000000000000000e+02 10 | 2.560000000000000000e+02 11 | 5.120000000000000000e+02 12 | 1.024000000000000000e+03 13 | 2.048000000000000000e+03 14 | 4.096000000000000000e+03 15 | 8.192000000000000000e+03 16 | 1.638400000000000000e+04 17 | 3.276800000000000000e+04 18 | 2.738548000000000000e+06 19 | 3.345390000000000000e+05 20 | 1.592060000000000000e+05 21 | 7.483600000000000000e+04 22 | 3.653200000000000000e+04 23 | 1.794800000000000000e+04 24 | 8.394000000000000000e+03 25 | 3.841000000000000000e+03 26 | 1.580000000000000000e+03 27 | 6.050000000000000000e+02 28 | 2.220000000000000000e+02 29 | 6.900000000000000000e+01 30 | 1.700000000000000000e+01 31 | 4.000000000000000000e+00 32 | 2.000000000000000000e+00 33 | 0.000000000000000000e+00 34 | 0.000000000000000000e+00 35 | -------------------------------------------------------------------------------- /sandbox/Chapter10_/data/gh_stars.csv: -------------------------------------------------------------------------------- 1 | 0.000000000000000000e+00 2 | 1.000000000000000000e+00 3 | 2.000000000000000000e+00 4 | 4.000000000000000000e+00 5 | 8.000000000000000000e+00 6 | 1.600000000000000000e+01 7 | 3.200000000000000000e+01 8 | 6.400000000000000000e+01 9 | 1.280000000000000000e+02 10 | 2.560000000000000000e+02 11 | 5.120000000000000000e+02 12 | 1.024000000000000000e+03 13 | 2.048000000000000000e+03 14 | 4.096000000000000000e+03 15 | 8.192000000000000000e+03 16 | 1.638400000000000000e+04 17 | 3.276800000000000000e+04 18 | 2.738541000000000000e+06 19 | 1.704779000000000000e+06 20 | 4.935290000000000000e+05 21 | 2.120990000000000000e+05 22 | 1.069730000000000000e+05 23 | 5.810100000000000000e+04 24 | 3.187700000000000000e+04 25 | 1.737000000000000000e+04 26 | 9.239000000000000000e+03 27 | 4.578000000000000000e+03 28 | 2.150000000000000000e+03 29 | 8.720000000000000000e+02 30 | 2.860000000000000000e+02 31 | 8.400000000000000000e+01 32 | 2.200000000000000000e+01 33 | 5.000000000000000000e+00 34 | 1.000000000000000000e+00 35 | -------------------------------------------------------------------------------- /sandbox/Chapter10_/data/gh_forks_02112013.csv: -------------------------------------------------------------------------------- 1 | 0.000000000000000000e+00 2 | 1.000000000000000000e+00 3 | 2.000000000000000000e+00 4 | 4.000000000000000000e+00 5 | 8.000000000000000000e+00 6 | 1.600000000000000000e+01 7 | 3.200000000000000000e+01 8 | 6.400000000000000000e+01 9 | 1.280000000000000000e+02 10 | 2.560000000000000000e+02 11 | 5.120000000000000000e+02 12 | 1.024000000000000000e+03 13 | 2.048000000000000000e+03 14 | 4.096000000000000000e+03 15 | 8.192000000000000000e+03 16 | 1.638400000000000000e+04 17 | 3.276800000000000000e+04 18 | 2.305360000000000000e+06 19 | 2.473584000000000000e+06 20 | 2.528307000000000000e+06 21 | 2.569002000000000000e+06 22 | 2.594631000000000000e+06 23 | 2.609437000000000000e+06 24 | 2.617785000000000000e+06 25 | 2.621941000000000000e+06 26 | 2.624019000000000000e+06 27 | 2.624923000000000000e+06 28 | 2.625293000000000000e+06 29 | 2.625435000000000000e+06 30 | 2.625486000000000000e+06 31 | 2.625494000000000000e+06 32 | 2.625496000000000000e+06 33 | 2.625498000000000000e+06 34 | 2.625498000000000000e+06 35 | -------------------------------------------------------------------------------- /sandbox/Chapter10_/data/gh_stars_02112013.csv: -------------------------------------------------------------------------------- 1 | 0.000000000000000000e+00 2 | 1.000000000000000000e+00 3 | 2.000000000000000000e+00 4 | 4.000000000000000000e+00 5 | 8.000000000000000000e+00 6 | 1.600000000000000000e+01 7 | 3.200000000000000000e+01 8 | 6.400000000000000000e+01 9 | 1.280000000000000000e+02 10 | 2.560000000000000000e+02 11 | 5.120000000000000000e+02 12 | 1.024000000000000000e+03 13 | 2.048000000000000000e+03 14 | 4.096000000000000000e+03 15 | 8.192000000000000000e+03 16 | 1.638400000000000000e+04 17 | 3.276800000000000000e+04 18 | 9.241220000000000000e+05 19 | 2.138996000000000000e+06 20 | 2.337881000000000000e+06 21 | 2.461031000000000000e+06 22 | 2.531702000000000000e+06 23 | 2.571640000000000000e+06 24 | 2.595213000000000000e+06 25 | 2.608768000000000000e+06 26 | 2.616559000000000000e+06 27 | 2.621043000000000000e+06 28 | 2.623388000000000000e+06 29 | 2.624607000000000000e+06 30 | 2.625171000000000000e+06 31 | 2.625367000000000000e+06 32 | 2.625423000000000000e+06 33 | 2.625440000000000000e+06 34 | 2.625444000000000000e+06 35 | -------------------------------------------------------------------------------- /LICENSE.txt: -------------------------------------------------------------------------------- 1 | Copyright (c) 2013 Cameron Davidson-Pilon 2 | 3 | Permission is hereby granted, free of charge, to any person 4 | obtaining a copy of this software and associated documentation 5 | files (the "Software"), to deal in the Software without 6 | restriction, including without limitation the rights to use, 7 | copy, modify, merge, publish, distribute, sublicense, and/or sell 8 | copies of the Software, and to permit persons to whom the 9 | Software is furnished to do so, subject to the following 10 | conditions: 11 | 12 | The above copyright notice and this permission notice shall be 13 | included in all copies or substantial portions of the Software. 14 | 15 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, 16 | EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES 17 | OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND 18 | NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT 19 | HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, 20 | WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING 21 | FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 22 | OTHER DEALINGS IN THE SOFTWARE. 23 | -------------------------------------------------------------------------------- /ExamplesFromChapters/Chapter3/ClusteringWithGaussians.py: -------------------------------------------------------------------------------- 1 | 2 | import pymc as mc 3 | 4 | 5 | data = np.loadtxt( "../../Chapter3_MCMC/data/mixture_data.csv", delimiter="," ) 6 | 7 | 8 | p = mc.Uniform( "p", 0, 1) 9 | 10 | assignment = mc.Categorical("assignment", [p, 1-p], size = data.shape[0] ) 11 | 12 | taus = 1.0/mc.Uniform( "stds", 0, 100, size= 2)**2 #notice the size! 13 | centers = mc.Normal( "centers", [150, 150], [0.001, 0.001], size =2 ) 14 | 15 | """ 16 | The below determinsitic functions map a assingment, in this case 0 or 1, 17 | to a set of parameters, located in the (1,2) arrays `taus` and `centers.` 18 | """ 19 | 20 | @mc.deterministic 21 | def center_i( assignment = assignment, centers = centers ): 22 | return centers[ assignment] 23 | 24 | @mc.deterministic 25 | def tau_i( assignment = assignment, taus = taus ): 26 | return taus[ assignment] 27 | 28 | #and to combine it with the observations: 29 | observations = mc.Normal( "obs", center_i, tau_i, value = data, observed = True ) 30 | 31 | #below we create a model class 32 | model = mc.Model( [p, assignment, taus, centers ] ) 33 | 34 | 35 | map_ = mc.MAP( model ) 36 | map_.fit() 37 | mcmc = mc.MCMC( model ) 38 | mcmc.sample( 100000, 50000 ) -------------------------------------------------------------------------------- /Chapter4_TheGreatestTheoremNeverTold/top_pic_comments.py: -------------------------------------------------------------------------------- 1 | import sys 2 | 3 | import numpy as np 4 | from IPython.core.display import Image 5 | 6 | import praw 7 | 8 | 9 | reddit = praw.Reddit("BayesianMethodsForHackers") 10 | subreddit = reddit.get_subreddit( "pics" ) 11 | 12 | top_submissions = subreddit.get_top() 13 | 14 | 15 | n_pic = int( sys.argv[1] ) if sys.argv[1] else 1 16 | 17 | i = 0 18 | while i < n_pic: 19 | top_submission = top_submissions.next() 20 | while "i.imgur.com" not in top_submission.url: 21 | #make sure it is linking to an image, not a webpage. 22 | top_submission = top_submissions.next() 23 | i+=1 24 | 25 | print "Title of submission: \n", top_submission.title 26 | top_post_url = top_submission.url 27 | #top_submission.replace_more_comments(limit=5, threshold=0) 28 | print top_post_url 29 | 30 | upvotes = [] 31 | downvotes = [] 32 | contents = [] 33 | _all_comments = top_submission.comments 34 | all_comments=[] 35 | for comment in _all_comments: 36 | try: 37 | upvotes.append( comment.ups ) 38 | downvotes.append( comment.downs ) 39 | contents.append( comment.body ) 40 | except Exception as e: 41 | continue 42 | 43 | votes = np.array( [ upvotes, downvotes] ).T 44 | 45 | 46 | 47 | 48 | 49 | 50 | 51 | 52 | 53 | 54 | 55 | 56 | 57 | 58 | 59 | 60 | 61 | 62 | 63 | 64 | -------------------------------------------------------------------------------- /book_layout.txt: -------------------------------------------------------------------------------- 1 | # Bayesian Methods for Hackers Layout 2 | 3 | \section{ Preamble} 4 | 5 | 6 | \chapter1{ Introduction } 7 | 8 | 9 | \chapter2{More PyMC / Modeling in PyMC} 10 | #flexible about what this section is. Basically it's more intro to the 11 | syntax of PyMC, with examples + distributions. 12 | 13 | \chapter3{ Intro to MCMC and Diagnogstics } 14 | 15 | 16 | \chapter4{ The greatest theorem never told } 17 | #This is about the law of large numbers and how a bayesian uses it for estimates. 18 | 19 | 20 | 21 | \chapter5{ Would you rather lose an arm or a leg? } 22 | #Introduction to loss functions and point estimation. 23 | 24 | 25 | 26 | >>>>>>>>> 27 | Below is subject to change 28 | 29 | \chapter6{What should my prior look like?} 30 | \subsection{Noninformative priors...} 31 | \subsection{Noninformative priors do not exist} 32 | \subsection{Good choices of priors } 33 | 34 | \chapter7{ Bayesian Networks } 35 | #I do not know too much about this. 36 | 37 | 38 | \chapter8{ Gaussian Processes } 39 | # pymc.gp 40 | 41 | 42 | \chapter9{ Large Scale systems } 43 | #how can we scale PyMC to larger systems/datasets? 44 | 45 | \chapter10{More hacking with PyMC} 46 | #some examples from PyMC. 47 | # Potential class? 48 | 49 | 50 | 51 | 52 | \section{Appendix} 53 | \subsection{A} 54 | #Chart of distributions and their support 55 | \subsection{B} 56 | #Appendix on MCMC 57 | \section{C} 58 | #Proofs 59 | -------------------------------------------------------------------------------- /Chapter5_LossFunctions/data/Test_haloCounts.csv: -------------------------------------------------------------------------------- 1 | SkyID,NumberHalos 2 | Sky1,1 3 | Sky2,1 4 | Sky3,1 5 | Sky4,1 6 | Sky5,1 7 | Sky6,1 8 | Sky7,1 9 | Sky8,1 10 | Sky9,1 11 | Sky10,1 12 | Sky11,1 13 | Sky12,1 14 | Sky13,1 15 | Sky14,1 16 | Sky15,1 17 | Sky16,1 18 | Sky17,1 19 | Sky18,1 20 | Sky19,1 21 | Sky20,1 22 | Sky21,1 23 | Sky22,1 24 | Sky23,1 25 | Sky24,1 26 | Sky25,1 27 | Sky26,1 28 | Sky27,1 29 | Sky28,1 30 | Sky29,1 31 | Sky30,1 32 | Sky31,1 33 | Sky32,1 34 | Sky33,1 35 | Sky34,1 36 | Sky35,1 37 | Sky36,1 38 | Sky37,1 39 | Sky38,1 40 | Sky39,1 41 | Sky40,1 42 | Sky41,2 43 | Sky42,2 44 | Sky43,2 45 | Sky44,2 46 | Sky45,2 47 | Sky46,2 48 | Sky47,2 49 | Sky48,2 50 | Sky49,2 51 | Sky50,2 52 | Sky51,2 53 | Sky52,2 54 | Sky53,2 55 | Sky54,2 56 | Sky55,2 57 | Sky56,2 58 | Sky57,2 59 | Sky58,2 60 | Sky59,2 61 | Sky60,2 62 | Sky61,2 63 | Sky62,2 64 | Sky63,2 65 | Sky64,2 66 | Sky65,2 67 | Sky66,2 68 | Sky67,2 69 | Sky68,2 70 | Sky69,2 71 | Sky70,2 72 | Sky71,2 73 | Sky72,2 74 | Sky73,2 75 | Sky74,2 76 | Sky75,2 77 | Sky76,2 78 | Sky77,2 79 | Sky78,2 80 | Sky79,2 81 | Sky80,2 82 | Sky81,3 83 | Sky82,3 84 | Sky83,3 85 | Sky84,3 86 | Sky85,3 87 | Sky86,3 88 | Sky87,3 89 | Sky88,3 90 | Sky89,3 91 | Sky90,3 92 | Sky91,3 93 | Sky92,3 94 | Sky93,3 95 | Sky94,3 96 | Sky95,3 97 | Sky96,3 98 | Sky97,3 99 | Sky98,3 100 | Sky99,3 101 | Sky100,3 102 | Sky101,3 103 | Sky102,3 104 | Sky103,3 105 | Sky104,3 106 | Sky105,3 107 | Sky106,3 108 | Sky107,3 109 | Sky108,3 110 | Sky109,3 111 | Sky110,3 112 | Sky111,3 113 | Sky112,3 114 | Sky113,3 115 | Sky114,3 116 | Sky115,3 117 | Sky116,3 118 | Sky117,3 119 | Sky118,3 120 | Sky119,3 121 | Sky120,3 122 | -------------------------------------------------------------------------------- /Chapter2_MorePyMC/separation_plot.py: -------------------------------------------------------------------------------- 1 | # separation plot 2 | # Author: Cameron Davidson-Pilon,2013 3 | # see http://mdwardlab.com/sites/default/files/GreenhillWardSacks.pdf 4 | 5 | 6 | import matplotlib.pyplot as plt 7 | import numpy as np 8 | 9 | 10 | 11 | def separation_plot( p, y, **kwargs ): 12 | """ 13 | This function creates a separation plot for logitisc and probit classification. 14 | See http://mdwardlab.com/sites/default/files/GreenhillWardSacks.pdf 15 | 16 | p: The proportions/probabilities, can be a nxM matrix which represents M models. 17 | y: the 0-1 response variables. 18 | 19 | """ 20 | assert p.shape[0] == y.shape[0], "p.shape[0] != y.shape[0]" 21 | n = p.shape[0] 22 | 23 | try: 24 | M = p.shape[1] 25 | except: 26 | p = p.reshape( n, 1 ) 27 | M = p.shape[1] 28 | 29 | #colors = np.array( ["#fdf2db", "#e44a32"] ) 30 | colors_bmh = np.array( ["#eeeeee", "#348ABD"] ) 31 | 32 | 33 | fig = plt.figure( )#figsize = (8, 1.3*M) ) 34 | 35 | for i in range(M): 36 | ax = fig.add_subplot(M, 1, i+1) 37 | ix = np.argsort( p[:,i] ) 38 | #plot the different bars 39 | bars = ax.bar( np.arange(n), np.ones(n), width=1., 40 | color = colors_bmh[ y[ix].astype(int) ], 41 | edgecolor = 'none') 42 | ax.plot( np.arange(n), p[ix,i], "k", 43 | linewidth = 1.,drawstyle="steps-post" ) 44 | #create expected value bar. 45 | ax.vlines( [(1-p[ix,i]).sum()], [0], [1] ) 46 | #ax.grid(False) 47 | #ax.axis('off') 48 | plt.xlim( 0, n-1) 49 | 50 | plt.tight_layout() 51 | 52 | return 53 | 54 | 55 | -------------------------------------------------------------------------------- /styles/custom.css: -------------------------------------------------------------------------------- 1 | 46 | -------------------------------------------------------------------------------- /Chapter1_Introduction/data/txtdata.csv: -------------------------------------------------------------------------------- 1 | 1.300000000000000000e+01 2 | 2.400000000000000000e+01 3 | 8.000000000000000000e+00 4 | 2.400000000000000000e+01 5 | 7.000000000000000000e+00 6 | 3.500000000000000000e+01 7 | 1.400000000000000000e+01 8 | 1.100000000000000000e+01 9 | 1.500000000000000000e+01 10 | 1.100000000000000000e+01 11 | 2.200000000000000000e+01 12 | 2.200000000000000000e+01 13 | 1.100000000000000000e+01 14 | 5.700000000000000000e+01 15 | 1.100000000000000000e+01 16 | 1.900000000000000000e+01 17 | 2.900000000000000000e+01 18 | 6.000000000000000000e+00 19 | 1.900000000000000000e+01 20 | 1.200000000000000000e+01 21 | 2.200000000000000000e+01 22 | 1.200000000000000000e+01 23 | 1.800000000000000000e+01 24 | 7.200000000000000000e+01 25 | 3.200000000000000000e+01 26 | 9.000000000000000000e+00 27 | 7.000000000000000000e+00 28 | 1.300000000000000000e+01 29 | 1.900000000000000000e+01 30 | 2.300000000000000000e+01 31 | 2.700000000000000000e+01 32 | 2.000000000000000000e+01 33 | 6.000000000000000000e+00 34 | 1.700000000000000000e+01 35 | 1.300000000000000000e+01 36 | 1.000000000000000000e+01 37 | 1.400000000000000000e+01 38 | 6.000000000000000000e+00 39 | 1.600000000000000000e+01 40 | 1.500000000000000000e+01 41 | 7.000000000000000000e+00 42 | 2.000000000000000000e+00 43 | 1.500000000000000000e+01 44 | 1.500000000000000000e+01 45 | 1.900000000000000000e+01 46 | 7.000000000000000000e+01 47 | 4.900000000000000000e+01 48 | 7.000000000000000000e+00 49 | 5.300000000000000000e+01 50 | 2.200000000000000000e+01 51 | 2.100000000000000000e+01 52 | 3.100000000000000000e+01 53 | 1.900000000000000000e+01 54 | 1.100000000000000000e+01 55 | 1.800000000000000000e+01 56 | 2.000000000000000000e+01 57 | 1.200000000000000000e+01 58 | 3.500000000000000000e+01 59 | 1.700000000000000000e+01 60 | 2.300000000000000000e+01 61 | 1.700000000000000000e+01 62 | 4.000000000000000000e+00 63 | 2.000000000000000000e+00 64 | 3.100000000000000000e+01 65 | 3.000000000000000000e+01 66 | 1.300000000000000000e+01 67 | 2.700000000000000000e+01 68 | 0.000000000000000000e+00 69 | 3.900000000000000000e+01 70 | 3.700000000000000000e+01 71 | 5.000000000000000000e+00 72 | 1.400000000000000000e+01 73 | 1.300000000000000000e+01 74 | 2.200000000000000000e+01 75 | -------------------------------------------------------------------------------- /Chapter3_MCMC/github_pull.py: -------------------------------------------------------------------------------- 1 | #github data scrapper 2 | 3 | """ 4 | variables of interest: 5 | indp. variables 6 | - language, given as a binary variable. Need 4 positions for 5 langagues 7 | - #number of days created ago, 1 position 8 | - has wiki? Boolean, 1 position 9 | - followers, 1 position 10 | - following, 1 position 11 | - constant 12 | 13 | dep. variables 14 | -stars/watchers 15 | -forks 16 | 17 | """ 18 | from json import loads 19 | import datetime 20 | import numpy as np 21 | from requests import get 22 | 23 | 24 | 25 | MAX = 8000000 26 | today = datetime.datetime.today() 27 | randint = np.random.randint 28 | N = 120 #sample size. 29 | auth = ("username", "password" ) 30 | 31 | language_mappings = {"Python": 0, "JavaScript": 1, "Ruby": 2, "Java":3, "Shell":4, "PHP":5} 32 | 33 | #define data matrix: 34 | X = np.zeros( (N , 12), dtype = int ) 35 | 36 | for i in xrange(N): 37 | is_fork = True 38 | is_valid_language = False 39 | 40 | while is_fork == True or is_valid_language == False: 41 | is_fork = True 42 | is_valid_language = False 43 | 44 | params = {"since":randint(0, MAX ) } 45 | r = get("https://api.github.com/repositories", params = params, auth=auth ) 46 | results = loads( r.text )[0] 47 | #im only interested in the first one, and if it is not a fork. 48 | is_fork = results["fork"] 49 | 50 | r = get( results["url"], auth = auth) 51 | 52 | #check the language 53 | repo_results = loads( r.text ) 54 | try: 55 | language_mappings[ repo_results["language" ] ] 56 | is_valid_language = True 57 | except: 58 | pass 59 | 60 | 61 | 62 | #languages 63 | X[ i, language_mappings[ repo_results["language" ] ] ] = 1 64 | 65 | #delta time 66 | X[ i, 6] = ( today - datetime.datetime.strptime( repo_results["created_at"][:10], "%Y-%m-%d" ) ).days 67 | 68 | #haswiki 69 | X[i, 7] = repo_results["has_wiki"] 70 | 71 | #get user information 72 | r = get( results["owner"]["url"] , auth = auth) 73 | user_results = loads( r.text ) 74 | X[i, 8] = user_results["following"] 75 | X[i, 9] = user_results["followers"] 76 | 77 | #get dep. data 78 | X[i, 10] = repo_results["watchers_count"] 79 | X[i, 11] = repo_results["forks_count"] 80 | print 81 | print " -------------- " 82 | print i, ": ", results["full_name"], repo_results["language" ], repo_results["watchers_count"], repo_results["forks_count"] 83 | print " -------------- " 84 | print 85 | 86 | np.savetxt("data/github_data.csv", X, delimiter=",", fmt="%d" ) 87 | 88 | 89 | 90 | -------------------------------------------------------------------------------- /Chapter6_Priorities/BanditsD3.html: -------------------------------------------------------------------------------- 1 | 2 | 3 | 45 | 46 | 47 | 48 | 49 | 50 | 51 |
52 |
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89 | 90 | 91 | -------------------------------------------------------------------------------- /sandbox/Chapter10_/github_datapull.py: -------------------------------------------------------------------------------- 1 | 2 | try: 3 | import numpy as np 4 | from requests import get 5 | from bs4 import BeautifulSoup 6 | 7 | 8 | 9 | 10 | stars_to_explore = ( 2**np.arange( -1, 16 ) ).astype("int") 11 | forks_to_explore = ( 2**np.arange( -1, 16 ) ).astype("int") 12 | repo_with_stars = np.ones_like( stars_to_explore ) 13 | repo_with_forks = np.ones_like( forks_to_explore ) 14 | 15 | URL = "https://github.com/search" 16 | print "Scrapping data from Github. Sorry Github..." 17 | print "The data is contained in variables `foo_to_explore` and `repo_with_foo`" 18 | print 19 | print "stars first..." 20 | payload = {"q":""} 21 | for i, _star in enumerate(stars_to_explore): 22 | payload["q"] = "stars:>=%d"%_star 23 | r = get( URL, params = payload ) 24 | soup = BeautifulSoup( r.text ) 25 | try: 26 | h3 = soup.find( class_="sort-bar").find( "h3" ).text #hopefully the github search results page plays nicely. 27 | value = int( h3.split(" ")[2].replace(",", "" ) ) 28 | except AttributeError as e: 29 | #there might be less than 10 repos, so I'll count the number of display results 30 | value = len( soup.findAll(class_= "mega-icon-public-repo" ) ) 31 | 32 | repo_with_stars[i] = value 33 | print "number of repos with greater than or equal to %d stars: %d"%(_star, value ) 34 | 35 | #repo_with_stars = repo_with_stars.astype("float")/repo_with_stars[0] 36 | 37 | 38 | print 39 | print "forks second..." 40 | payload = {"q":""} 41 | for i, _fork in enumerate(stars_to_explore): 42 | payload["q"] = "forks:>=%d"%_fork 43 | r = get( URL, params = payload ) 44 | soup = BeautifulSoup( r.text ) 45 | try: 46 | h3 = soup.find( class_="sort-bar").find( "h3" ).text #hopefully the github search results page plays nicely. 47 | value = int( h3.split(" ")[2].replace(",", "" ) ) 48 | except AttributeError as e: 49 | #there might be less than 10 repos, so I'll count the number of display results 50 | value = len( soup.findAll(class_= "mega-icon-public-repo" ) ) 51 | 52 | repo_with_forks[i] = value 53 | print "number of repos with greater than or equal to %d forks: %d"%(_fork, value ) 54 | 55 | #repo_with_forks = repo_with_forks.astype("float")/repo_with_forks[0] 56 | 57 | np.savetxt( "data/gh_forks.csv", np.concatenate( [forks_to_explore, repo_with_forks], axis=1) ) 58 | np.savetxt( "data/gh_stars.csv", np.concatenate( [stars_to_explore, repo_with_stars], axis=1) ) 59 | 60 | except ImportError as e: 61 | print e 62 | print "requests / BeautifulSoup not found. Using data pulled on Feburary 11, 2013" 63 | _data = np.genfromtxt( "data/gh_forks.csv", delimiter = "," ) #cehck this. 64 | forks_to_explore = _data[:,0] 65 | repo_with_forks = _data[:,1] 66 | 67 | _data = np.genfromtxt( "data/gh_stars.csv", delimiter = "," ) #cehck this. 68 | stars_to_explore = _data[:,0] 69 | repo_with_stars = _data[:,1] 70 | 71 | 72 | -------------------------------------------------------------------------------- /Chapter3_MCMC/data/github_data.csv: -------------------------------------------------------------------------------- 1 | Python, Javascript, Ruby, Java, Shell, PHP, days_since_creation, has_wiki, author_following, author_followers, starred_count, forked_count 2 | 0,1,0,0,0,0,523,1,0,0,2,1 3 | 0,1,0,0,0,0,778,1,193,95,1,0 4 | 0,0,0,1,0,0,531,1,1,4,3,0 5 | 0,0,1,0,0,0,396,1,1,2,2,0 6 | 0,0,0,0,1,0,846,1,3,5,1,0 7 | 0,0,1,0,0,0,520,1,155,56,1,0 8 | 0,1,0,0,0,0,384,1,0,0,2,0 9 | 1,0,0,0,0,0,705,1,33,9,1,0 10 | 0,0,0,0,0,1,726,1,0,7,11,1 11 | 1,0,0,0,0,0,413,1,0,2,1,0 12 | 1,0,0,0,0,0,141,1,3,0,1,0 13 | 1,0,0,0,0,0,1410,1,65,82,1,0 14 | 0,0,0,0,0,1,175,1,0,0,0,0 15 | 0,0,1,0,0,0,365,1,49,85,1,0 16 | 0,0,0,0,0,1,580,1,9,4,1,0 17 | 0,0,0,1,0,0,471,1,1,0,1,0 18 | 0,1,0,0,0,0,353,1,5,2,2,1 19 | 0,0,1,0,0,0,973,1,0,0,1,0 20 | 0,0,1,0,0,0,591,1,0,0,1,0 21 | 0,0,1,0,0,0,85,1,0,0,0,0 22 | 0,1,0,0,0,0,431,1,0,0,1,0 23 | 1,0,0,0,0,0,188,1,1,1,0,0 24 | 0,0,1,0,0,0,144,1,0,0,0,0 25 | 0,1,0,0,0,0,102,1,0,0,0,0 26 | 0,1,0,0,0,0,249,1,0,0,2,0 27 | 0,1,0,0,0,0,395,1,2,0,1,0 28 | 0,1,0,0,0,0,433,1,12,69,1,0 29 | 0,0,0,1,0,0,615,1,0,0,1,0 30 | 0,0,1,0,0,0,707,1,0,0,1,0 31 | 0,0,0,1,0,0,256,1,0,1,1,0 32 | 0,0,1,0,0,0,363,1,0,0,1,0 33 | 0,0,1,0,0,0,1818,1,98,162,16,6 34 | 0,1,0,0,0,0,86,1,13,7,0,0 35 | 0,1,0,0,0,0,284,1,1,3,2,1 36 | 0,0,0,1,0,0,867,1,9,5,2,0 37 | 0,0,1,0,0,0,1203,1,1,0,1,0 38 | 0,1,0,0,0,0,436,1,34,4,0,0 39 | 0,1,0,0,0,0,720,1,6,73,6,0 40 | 0,0,1,0,0,0,948,1,0,84,18,4 41 | 1,0,0,0,0,0,383,1,0,0,2,1 42 | 0,0,0,1,0,0,62,1,0,0,0,0 43 | 0,0,0,1,0,0,927,1,0,0,40,17 44 | 0,1,0,0,0,0,1303,1,0,0,3,0 45 | 0,1,0,0,0,0,113,1,0,0,0,0 46 | 0,0,1,0,0,0,810,1,4,5,1,0 47 | 0,0,0,0,0,1,43,1,7,11,2,0 48 | 0,0,0,0,0,1,369,1,0,0,1,0 49 | 0,1,0,0,0,0,449,1,106,4398,399,60 50 | 0,1,0,0,0,0,200,1,0,0,0,0 51 | 0,1,0,0,0,0,122,1,4,2,0,0 52 | 0,0,1,0,0,0,738,1,0,0,1,0 53 | 0,1,0,0,0,0,705,1,0,0,2,0 54 | 0,0,1,0,0,0,291,1,0,0,1,0 55 | 0,1,0,0,0,0,621,1,3,23,1,0 56 | 0,0,1,0,0,0,368,1,0,0,1,0 57 | 0,0,1,0,0,0,851,1,0,0,1,0 58 | 0,0,0,1,0,0,58,1,0,0,0,0 59 | 0,0,0,1,0,0,706,1,0,8,2,1 60 | 0,0,0,0,0,1,817,1,0,1,1,1 61 | 0,0,0,0,1,0,1475,1,0,4,1,0 62 | 0,0,1,0,0,0,584,1,0,0,1,0 63 | 1,0,0,0,0,0,841,1,0,7,1,0 64 | 0,0,0,0,0,1,382,1,0,74,1,0 65 | 0,0,1,0,0,0,213,1,1,0,1,0 66 | 0,0,1,0,0,0,93,1,0,0,0,0 67 | 0,1,0,0,0,0,356,1,1,10,2,0 68 | 0,0,1,0,0,0,123,1,0,1,0,0 69 | 0,0,1,0,0,0,113,1,35,63,0,0 70 | 0,0,0,0,0,1,302,1,13,2,3,1 71 | 0,1,0,0,0,0,550,0,19,18,2,0 72 | 0,0,1,0,0,0,721,1,2,0,1,0 73 | 0,0,1,0,0,0,160,1,5,6,11,6 74 | 1,0,0,0,0,0,399,1,7,6,1,0 75 | 0,1,0,0,0,0,206,1,15,116,2,0 76 | 0,0,0,1,0,0,319,1,0,0,2,1 77 | 0,1,0,0,0,0,111,1,2,3,0,0 78 | 0,0,0,0,0,1,632,1,10,3,2,1 79 | 0,0,0,0,0,1,1044,1,16,23,3,1 80 | 0,0,0,0,0,1,194,1,0,0,0,0 81 | 0,1,0,0,0,0,908,1,56,503,43,8 82 | 0,0,1,0,0,0,89,1,0,0,0,0 83 | 0,1,0,0,0,0,1311,1,107,119,4,1 84 | 0,1,0,0,0,0,78,1,0,0,0,0 85 | 0,0,1,0,0,0,564,1,0,2,1,0 86 | 0,0,1,0,0,0,1049,1,0,0,1,0 87 | 0,0,0,1,0,0,322,1,0,0,2,1 88 | 0,0,1,0,0,0,1443,1,11,7,3,8 89 | 0,0,1,0,0,0,310,1,1,0,1,0 90 | 0,0,0,0,0,1,515,1,0,2,1,0 91 | 0,0,1,0,0,0,563,1,0,0,1,0 92 | 1,0,0,0,0,0,344,1,0,0,1,0 93 | 0,1,0,0,0,0,132,1,2,2,0,0 94 | 0,0,1,0,0,0,837,1,0,0,1,0 95 | 0,1,0,0,0,0,459,1,1,4,1,0 96 | 0,0,0,0,0,1,768,1,8,2,3,0 97 | 0,0,0,0,0,1,410,1,0,4,2,1 98 | 1,0,0,0,0,0,380,1,0,0,9,0 99 | 0,0,0,1,0,0,859,1,14,22,1,0 100 | 1,0,0,0,0,0,628,1,0,1,1,0 101 | 0,0,1,0,0,0,206,0,55,50,21,2 102 | 0,0,0,1,0,0,117,1,1,2,0,0 103 | 0,0,0,0,1,0,237,1,0,0,1,0 104 | 0,0,1,0,0,0,462,1,0,1,1,0 105 | 1,0,0,0,0,0,628,1,2,3,1,0 106 | 0,0,0,1,0,0,504,1,1,6,1,0 107 | 0,0,1,0,0,0,283,1,0,0,1,0 108 | 0,1,0,0,0,0,654,0,4,7,1,0 109 | 0,1,0,0,0,0,97,1,0,0,0,0 110 | 1,0,0,0,0,0,396,1,3,11,1,0 111 | 0,0,0,0,1,0,179,1,0,0,0,0 112 | 0,1,0,0,0,0,1743,1,3,0,1,0 113 | 0,0,1,0,0,0,949,1,1,4,75,24 114 | 0,0,0,1,0,0,307,1,0,0,1,1 115 | 0,0,1,0,0,0,264,1,0,0,1,0 116 | 0,0,1,0,0,0,193,1,4,5,0,0 117 | 0,0,0,0,1,0,1148,1,4,37,2,1 118 | 0,0,1,0,0,0,150,1,0,0,0,0 119 | 0,0,0,0,1,0,250,1,19,9,1,0 120 | 0,0,1,0,0,0,1726,1,7,287,1,0 121 | 0,1,0,0,0,0,340,1,0,0,1,0 122 | -------------------------------------------------------------------------------- /Chapter6_Priorities/other_strats.py: -------------------------------------------------------------------------------- 1 | #other strats. 2 | # TODO: UBC strat, epsilon-greedy 3 | 4 | import scipy.stats as stats 5 | import numpy as np 6 | from pymc import rbeta 7 | 8 | rand = np.random.rand 9 | beta = stats.beta 10 | 11 | 12 | class GeneralBanditStrat( object ): 13 | 14 | """ 15 | Implements a online, learning strategy to solve 16 | the Multi-Armed Bandit problem. 17 | 18 | parameters: 19 | bandits: a Bandit class with .pull method 20 | choice_function: accepts a self argument (which gives access to all the variables), and 21 | returns and int between 0 and n-1 22 | methods: 23 | sample_bandits(n): sample and train on n pulls. 24 | 25 | attributes: 26 | N: the cumulative number of samples 27 | choices: the historical choices as a (N,) array 28 | bb_score: the historical score as a (N,) array 29 | 30 | """ 31 | 32 | def __init__(self, bandits, choice_function): 33 | 34 | self.bandits = bandits 35 | n_bandits = len( self.bandits ) 36 | self.wins = np.zeros( n_bandits ) 37 | self.trials = np.zeros(n_bandits ) 38 | self.N = 0 39 | self.choices = [] 40 | self.score = [] 41 | self.choice_function = choice_function 42 | 43 | def sample_bandits( self, n=1 ): 44 | 45 | score = np.zeros( n ) 46 | choices = np.zeros( n ) 47 | 48 | for k in range(n): 49 | #sample from the bandits's priors, and select the largest sample 50 | choice = self.choice_function(self) 51 | 52 | #sample the chosen bandit 53 | result = self.bandits.pull( choice ) 54 | 55 | #update priors and score 56 | self.wins[ choice ] += result 57 | self.trials[ choice ] += 1 58 | score[ k ] = result 59 | self.N += 1 60 | choices[ k ] = choice 61 | 62 | self.score = np.r_[ self.score, score ] 63 | self.choices = np.r_[ self.choices, choices ] 64 | return 65 | 66 | 67 | def bayesian_bandit_choice(self): 68 | return np.argmax( rbeta( 1 + self.wins, 1 + self.trials - self.wins) ) 69 | 70 | def max_mean( self ): 71 | """pick the bandit with the current best observed proportion of winning """ 72 | return np.argmax( self.wins / ( self.trials +1 ) ) 73 | 74 | def lower_credible_choice( self ): 75 | """pick the bandit with the best LOWER BOUND. See chapter 5""" 76 | def lb(a,b): 77 | return a/(a+b) - 1.65*np.sqrt( (a*b)/( (a+b)**2*(a+b+1) ) ) 78 | a = self.wins + 1 79 | b = self.trials - self.wins + 1 80 | return np.argmax( lb(a,b) ) 81 | 82 | def upper_credible_choice( self ): 83 | """pick the bandit with the best LOWER BOUND. See chapter 5""" 84 | def lb(a,b): 85 | return a/(a+b) + 1.65*np.sqrt( (a*b)/( (a+b)**2*(a+b+1) ) ) 86 | a = self.wins + 1 87 | b = self.trials - self.wins + 1 88 | return np.argmax( lb(a,b) ) 89 | 90 | def random_choice( self): 91 | return np.random.randint( 0, len( self.wins ) ) 92 | 93 | 94 | def ucb_bayes( self ): 95 | C = 0 96 | n = 10000 97 | alpha =1 - 1./( (self.N+1) ) 98 | return np.argmax( beta.ppf( alpha, 99 | 1 + self.wins, 100 | 1 + self.trials - self.wins ) ) 101 | 102 | 103 | 104 | 105 | class Bandits(object): 106 | """ 107 | This class represents N bandits machines. 108 | 109 | parameters: 110 | p_array: a (n,) Numpy array of probabilities >0, <1. 111 | 112 | methods: 113 | pull( i ): return the results, 0 or 1, of pulling 114 | the ith bandit. 115 | """ 116 | def __init__(self, p_array): 117 | self.p = p_array 118 | self.optimal = np.argmax(p_array) 119 | 120 | def pull( self, i ): 121 | #i is which arm to pull 122 | return rand() < self.p[i] 123 | 124 | def __len__(self): 125 | return len(self.p) 126 | -------------------------------------------------------------------------------- /Chapter6_Priorities/ystockquote.py: -------------------------------------------------------------------------------- 1 | # 2 | # ystockquote : Python module - retrieve stock quote data from Yahoo Finance 3 | # 4 | # Copyright (c) 2007,2008,2013 Corey Goldberg (cgoldberg@gmail.com) 5 | # 6 | # license: GNU LGPL 7 | # 8 | # This library is free software; you can redistribute it and/or 9 | # modify it under the terms of the GNU Lesser General Public 10 | # License as published by the Free Software Foundation; either 11 | # version 2.1 of the License, or (at your option) any later version. 12 | # 13 | # Requires: Python 2.7/3.2+ 14 | 15 | 16 | __version__ = '0.2.2' 17 | 18 | 19 | try: 20 | # py3 21 | from urllib.request import Request, urlopen 22 | from urllib.parse import urlencode 23 | except ImportError: 24 | # py2 25 | from urllib2 import Request, urlopen 26 | from urllib import urlencode 27 | 28 | 29 | def _request(symbol, stat): 30 | url = 'http://finance.yahoo.com/d/quotes.csv?s=%s&f=%s' % (symbol, stat) 31 | req = Request(url) 32 | resp = urlopen(req) 33 | return str(resp.read().decode('utf-8').strip()) 34 | 35 | 36 | def get_all(symbol): 37 | """ 38 | Get all available quote data for the given ticker symbol. 39 | 40 | Returns a dictionary. 41 | """ 42 | values = _request(symbol, 'l1c1va2xj1b4j4dyekjm3m4rr5p5p6s7').split(',') 43 | return dict( 44 | price=values[0], 45 | change=values[1], 46 | volume=values[2], 47 | avg_daily_volume=values[3], 48 | stock_exchange=values[4], 49 | market_cap=values[5], 50 | book_value=values[6], 51 | ebitda=values[7], 52 | dividend_per_share=values[8], 53 | dividend_yield=values[9], 54 | earnings_per_share=values[10], 55 | fifty_two_week_high=values[11], 56 | fifty_two_week_low=values[12], 57 | fifty_day_moving_avg=values[13], 58 | two_hundred_day_moving_avg=values[14], 59 | price_earnings_ratio=values[15], 60 | price_earnings_growth_ratio=values[16], 61 | price_sales_ratio=values[17], 62 | price_book_ratio=values[18], 63 | short_ratio=values[19], 64 | ) 65 | 66 | 67 | def get_price(symbol): 68 | return _request(symbol, 'l1') 69 | 70 | 71 | def get_change(symbol): 72 | return _request(symbol, 'c1') 73 | 74 | 75 | def get_volume(symbol): 76 | return _request(symbol, 'v') 77 | 78 | 79 | def get_avg_daily_volume(symbol): 80 | return _request(symbol, 'a2') 81 | 82 | 83 | def get_stock_exchange(symbol): 84 | return _request(symbol, 'x') 85 | 86 | 87 | def get_market_cap(symbol): 88 | return _request(symbol, 'j1') 89 | 90 | 91 | def get_book_value(symbol): 92 | return _request(symbol, 'b4') 93 | 94 | 95 | def get_ebitda(symbol): 96 | return _request(symbol, 'j4') 97 | 98 | 99 | def get_dividend_per_share(symbol): 100 | return _request(symbol, 'd') 101 | 102 | 103 | def get_dividend_yield(symbol): 104 | return _request(symbol, 'y') 105 | 106 | 107 | def get_earnings_per_share(symbol): 108 | return _request(symbol, 'e') 109 | 110 | 111 | def get_52_week_high(symbol): 112 | return _request(symbol, 'k') 113 | 114 | 115 | def get_52_week_low(symbol): 116 | return _request(symbol, 'j') 117 | 118 | 119 | def get_50day_moving_avg(symbol): 120 | return _request(symbol, 'm3') 121 | 122 | 123 | def get_200day_moving_avg(symbol): 124 | return _request(symbol, 'm4') 125 | 126 | 127 | def get_price_earnings_ratio(symbol): 128 | return _request(symbol, 'r') 129 | 130 | 131 | def get_price_earnings_growth_ratio(symbol): 132 | return _request(symbol, 'r5') 133 | 134 | 135 | def get_price_sales_ratio(symbol): 136 | return _request(symbol, 'p5') 137 | 138 | 139 | def get_price_book_ratio(symbol): 140 | return _request(symbol, 'p6') 141 | 142 | 143 | def get_short_ratio(symbol): 144 | return _request(symbol, 's7') 145 | 146 | 147 | def get_historical_prices(symbol, start_date, end_date): 148 | """ 149 | Get historical prices for the given ticker symbol. 150 | Date format is 'YYYY-MM-DD' 151 | 152 | Returns a nested list (first item is list of column headers). 153 | """ 154 | params = urlencode({ 155 | 's': symbol, 156 | 'a': int(start_date[5:7]) - 1, 157 | 'b': int(start_date[8:10]), 158 | 'c': int(start_date[0:4]), 159 | 'd': int(end_date[5:7]) - 1, 160 | 'e': int(end_date[8:10]), 161 | 'f': int(end_date[0:4]), 162 | 'g': 'd', 163 | 'ignore': '.csv', 164 | }) 165 | url = 'http://ichart.yahoo.com/table.csv?%s' % params 166 | req = Request(url) 167 | resp = urlopen(req) 168 | content = str(resp.read().decode('utf-8').strip()) 169 | days = content.splitlines() 170 | return [day.split(',') for day in days] -------------------------------------------------------------------------------- /Chapter7_BayesianMachineLearning/MachineLearning.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "metadata": { 3 | "name": "MachineLearning" 4 | }, 5 | "nbformat": 3, 6 | "nbformat_minor": 0, 7 | "worksheets": [ 8 | { 9 | "cells": [ 10 | { 11 | "cell_type": "markdown", 12 | "metadata": {}, 13 | "source": [ 14 | "List of topics to cover:\n", 15 | "\n", 16 | "- Bayesian solution to overfitting\n", 17 | " - Salisman's solution to the Don't Overfit\n", 18 | "- Predictive distributions; \"how do I evaluate testing data?\"\n", 19 | "- model fitting, BIC + visualization tools\n", 20 | "- Gaussian Processes\n", 21 | "\n", 22 | "\n", 23 | "Would be nice/cool to cover:\n", 24 | "\n", 25 | "- classification models (using the books text)\n", 26 | "- Bayesian networks?" 27 | ] 28 | }, 29 | { 30 | "cell_type": "code", 31 | "collapsed": false, 32 | "input": [], 33 | "language": "python", 34 | "metadata": {}, 35 | "outputs": [], 36 | "prompt_number": 6 37 | }, 38 | { 39 | "cell_type": "code", 40 | "collapsed": false, 41 | "input": [], 42 | "language": "python", 43 | "metadata": {}, 44 | "outputs": [], 45 | "prompt_number": 6 46 | }, 47 | { 48 | "cell_type": "code", 49 | "collapsed": false, 50 | "input": [], 51 | "language": "python", 52 | "metadata": {}, 53 | "outputs": [], 54 | "prompt_number": 6 55 | }, 56 | { 57 | "cell_type": "code", 58 | "collapsed": false, 59 | "input": [], 60 | "language": "python", 61 | "metadata": {}, 62 | "outputs": [], 63 | "prompt_number": 6 64 | }, 65 | { 66 | "cell_type": "code", 67 | "collapsed": false, 68 | "input": [ 69 | "from IPython.core.display import HTML\n", 70 | "def css_styling():\n", 71 | " styles = open(\"../styles/custom.css\", \"r\").read()\n", 72 | " return HTML(styles)\n", 73 | "css_styling()" 74 | ], 75 | "language": "python", 76 | "metadata": {}, 77 | "outputs": [ 78 | { 79 | "html": [ 80 | "\n", 125 | "" 140 | ], 141 | "output_type": "pyout", 142 | "prompt_number": 10, 143 | "text": [ 144 | "" 145 | ] 146 | } 147 | ], 148 | "prompt_number": 10 149 | }, 150 | { 151 | "cell_type": "code", 152 | "collapsed": false, 153 | "input": [], 154 | "language": "python", 155 | "metadata": {}, 156 | "outputs": [] 157 | } 158 | ], 159 | "metadata": {} 160 | } 161 | ] 162 | } 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2.045002706098395606e+02 255 | 2.152174652951992471e+02 256 | 1.987922144174747530e+02 257 | 2.241648159527295547e+02 258 | 2.205483546065124472e+02 259 | 1.558159484378380171e+02 260 | 1.676495617850407598e+02 261 | 1.850186838826528231e+02 262 | 2.464145786167696599e+02 263 | 2.486409397084338195e+02 264 | 1.767515487795867273e+02 265 | 1.869117804626637849e+02 266 | 1.870810635558241586e+02 267 | 1.958352409681716324e+02 268 | 1.614541679698469920e+02 269 | 1.820210126509980739e+02 270 | 2.199473579766136595e+02 271 | 2.133444798833926654e+02 272 | 2.090551017466646613e+02 273 | 2.046156673206388064e+02 274 | 1.992916910824319530e+02 275 | 1.946361653458499745e+02 276 | 2.421374635348616948e+02 277 | 2.110007927344491918e+02 278 | 1.662765715442542671e+02 279 | 1.949143298584492641e+02 280 | 1.875771759652629953e+02 281 | 2.219149956242236783e+02 282 | 1.876747717865994218e+02 283 | 1.971850332862213122e+02 284 | 1.482140589550791105e+02 285 | 2.064803608972869711e+02 286 | 2.134641290909328859e+02 287 | 1.919518147378720414e+02 288 | 1.800465916326361935e+02 289 | 2.203791380076491464e+02 290 | 2.223561248500241163e+02 291 | 2.278082046953573752e+02 292 | 2.181685881622520640e+02 293 | 1.863762249820889565e+02 294 | 1.775192919731025256e+02 295 | 1.764703438636786075e+02 296 | 2.315749158793883566e+02 297 | 2.171688340729648985e+02 298 | 2.423196685427484454e+02 299 | 1.963990296752487268e+02 300 | 2.228190673247157747e+02 301 | -------------------------------------------------------------------------------- /Chapter6_Priorities/d3bandits.js: -------------------------------------------------------------------------------- 1 | var ARMS = [0,0,0,0,0,0]; 2 | var _PROBS = [ rbeta(2,9), rbeta(5,9), rbeta(5,9) ]; 3 | var BB_RUN = 0; 4 | 5 | d3.select( "#reveal-div" ) 6 | .selectAll("p") 7 | .data( _PROBS ) 8 | .enter() 9 | .append("p") 10 | .text( function(d,i){ return "Arm " + (i + 1) + ": " +d.toFixed(4); } ) 11 | 12 | 13 | function pdfbeta(x_array,a,b){ 14 | //x is an array 15 | _beta = Beta(a,b); 16 | function _pdfbeta(x){ 17 | return ( Math.pow(x,a-1)*Math.pow(1-x, b - 1) )/_beta 18 | } 19 | 20 | return x_array.map( _pdfbeta ) 21 | } 22 | 23 | function Beta(a,b){ 24 | //stirlings approx 25 | // use logs and exponentials to avoid underflow 26 | // with logs is still giving me errors 27 | 28 | //var n = Math.pow(a, a - 0.5)*Math.pow(b, b-0.5) 29 | 30 | var log_n = Math.log(a)*(a - 0.5) + Math.log(b)*( b-0.5) 31 | //var d = Math.pow( a + b, a+ b-0.5) 32 | var log_d = Math.log( a + b)*(a+ b-0.5) 33 | return Math.sqrt( 2*Math.PI)*Math.exp(log_n - log_d) 34 | } 35 | 36 | 37 | function rbeta(a,b){ 38 | //from Simulation and MC, Wiley 39 | 40 | var p = a/b; 41 | if (Math.min(a,b) <= 1){ 42 | var lambda = Math.min(a,b) 43 | }else{ 44 | var lambda = Math.sqrt( (2*a*b - a - b)/(a+b-2) ) 45 | } 46 | 47 | while (1){ 48 | var R1 = Math.random(); 49 | var R2 = Math.random(); 50 | var y = Math.pow( ( 1./R1 - 1.), 1./lambda ); 51 | if ( 4*R1*R2*R2 < (Math.pow(y, a - lambda)*Math.pow( (1.+ p)/(1 + p*y) , a + b ) )){ 52 | return (p*y)/(1+ p*y) 53 | } 54 | } 55 | } 56 | 57 | function rbeta_array( arm_counts){ 58 | // to be used with ARMS with uniform prior. 59 | samples = [] 60 | for (var i=0; i < arm_counts.length/2; i++){ 61 | samples.push( 62 | rbeta(arm_counts[2*i + 1]+1, 1+arm_counts[2*i] - arm_counts[2*i+1] ) 63 | ) 64 | } 65 | return samples 66 | } 67 | 68 | function draw_arm( p ){ 69 | if ( Math.random() < p){ return 1 } else { return 0 } 70 | } 71 | 72 | 73 | function update_arm( arm_number ){ 74 | var result = draw_arm(_PROBS[arm_number] ); 75 | ARMS[2*arm_number] += 1; 76 | ARMS[2*arm_number+1] += result; 77 | redraw(arm_number); 78 | return 79 | } 80 | 81 | 82 | function bayesian_bandits(){ 83 | //for (var i = 0; i < n_pulls; i++ ){ 84 | //sample from Beta distributions 85 | var samples = rbeta_array(ARMS); 86 | var select = samples.indexOf( d3.max( samples) ); 87 | update_arm( select ); 88 | if (BB_RUN < 300){ 89 | BB_RUN += 1; 90 | window.setTimeout( bayesian_bandits, 100 ) 91 | } 92 | else{ 93 | return 94 | } 95 | //} 96 | } 97 | 98 | var x_array = []; 99 | var _N = 100; 100 | var max_data = 10 101 | for ( var i =0; i < _N; i++ ){ 102 | x_array.push( .01*i ) 103 | } 104 | 105 | var colors = ["#348ABD", "#A60628", "#7A68A6"]; 106 | var fill_colors = [ "rgba(52, 128, 189,0.1)", "rgba(166, 6, 40, 0.1 )", "rgba( 122, 104, 166,0.1 )"]; 107 | 108 | var w = 600, 109 | h = 150, 110 | margin = 15, 111 | y = d3.scale.linear().domain([0, max_data]).range([h - margin,0 + margin ]), 112 | x = d3.scale.linear().domain([0,_N]).range([0 + margin, w - margin]) 113 | 114 | var vis = d3.select("#beta-graphs") 115 | .append("svg:svg") 116 | .attr("width", w ) 117 | .attr("height", h ) 118 | 119 | var g = vis.append("svg:g") 120 | 121 | var line = d3.svg.line() 122 | .x(function(d, i) { return x(i); }) 123 | .y(y) 124 | 125 | 126 | for ( var i =0; i < 3; i++){ 127 | var _data = pdfbeta(x_array, 1 + ARMS[2*i+1],1+ARMS[2*i] - ARMS[2*i+1] ); 128 | g.selectAll('path.line') 129 | .data( [_data] ) 130 | .enter() 131 | .append("svg:path") 132 | .attr("stroke", colors[i] ) 133 | //.attr("fill", fill_colors[i] ) 134 | //.attr("fill", fill_colors[i] ) 135 | //.attr("stroke-width", 0 ) 136 | .attr("d", line ) 137 | .attr("id", "line-" + i ); 138 | } 139 | 140 | 141 | g.append("svg:line") 142 | .attr("x1", x(0)) 143 | .attr("y1", y(0)) 144 | .attr("x2", x(w)) 145 | .attr("y2", y(0)) 146 | 147 | g.append("svg:line") 148 | .attr("x1", x(0)) 149 | .attr("y1", y(0)) 150 | .attr("x2", x(0)) 151 | .attr("y2", y(max_data)) 152 | 153 | g.selectAll(".xLabel") 154 | .data( d3.range(0,1.2,.2) ) 155 | .enter().append("svg:text") 156 | .attr("class", "xLabel") 157 | .text(String) 158 | .attr("x", function(d) { return x(100*d) }) 159 | .attr("y", h) 160 | .attr("text-anchor", "middle") 161 | .attr("dy", 0.0 ) 162 | /* 163 | g.selectAll(".yLabel") 164 | .data(y.ticks(4)) 165 | .enter().append("svg:text") 166 | .attr("class", "yLabel") 167 | .text(String) 168 | .attr("x", 0) 169 | .attr("y", function(d) { return y(d) }) 170 | .attr("text-anchor", "right") 171 | .attr("dy", 4) 172 | */ 173 | g.selectAll(".xTicks") 174 | .data(x.ticks(5)) 175 | .enter().append("svg:line") 176 | .attr("class", "xTicks") 177 | .attr("x1", function(d) { return x(d); }) 178 | .attr("y1", y(0)) 179 | .attr("x2", function(d) { return x(d); }) 180 | .attr("y2", y(-0.1)) 181 | 182 | vis.append("text") 183 | .attr("x", (w / 2)) 184 | .attr("y", 15 ) 185 | .attr("text-anchor", "middle") 186 | .style("font-size", "17px") 187 | .text("Posterior Distributions"); 188 | 189 | /* 190 | g.selectAll(".yTicks") 191 | .data(y.ticks(4)) 192 | .enter().append("svg:line") 193 | .attr("class", "yTicks") 194 | .attr("y1", function(d) { return -1 * y(d); }) 195 | .attr("x1", x(-0.3)) 196 | .attr("y2", function(d) { return -1 * y(d); }) 197 | .attr("x2", x(0)) 198 | */ 199 | 200 | 201 | 202 | 203 | 204 | 205 | var data = ARMS; 206 | var labellist = ["Arm 1", "", "Arm 2", "", "Arm 3", ""]; 207 | 208 | var w_bar = 600, 209 | h_bar = 170, 210 | labelpad = 50, 211 | x_bar = d3.scale.linear().domain([0, 100]).range([0, w_bar]), 212 | y_bar = d3.scale.ordinal().domain(d3.range(data.length)).rangeBands([0, h_bar], .2); 213 | 214 | var vis = d3.select("#paired-bar-chart") 215 | .append("svg:svg") 216 | .attr("width", w_bar + 40) 217 | .attr("height", h_bar + 20) 218 | .append("svg:g") 219 | 220 | var bars = vis.selectAll("g.bar") 221 | .data(data) 222 | .enter().append("svg:g") 223 | .attr("class", "bar") 224 | .attr("transform", function(d, i) { return "translate(" + labelpad + "," + y_bar(i) + ")"; }) 225 | 226 | 227 | bars.append("svg:rect") 228 | .attr("fill", function(d, i) { return (i%2)? colors[i]: fill_colors[i]; } ) //Alternate colors 229 | .attr("width", function(d,i){ return x_bar(d)*0.5 }) 230 | .attr("height", y_bar.rangeBand()); 231 | 232 | bars.append("svg:text") 233 | .attr("x", 0) 234 | .attr("y", 10 + y_bar.rangeBand() / 2) 235 | .attr("dx", -6) 236 | .attr("dy", ".50em") 237 | .attr("text-anchor", "end") 238 | .text(function(d, i) { return labellist[i]; }); 239 | 240 | var counts = bars.append("svg:text") 241 | .attr("x", 0) 242 | .attr("y", 10 + y_bar.rangeBand() / 2) 243 | .attr("dx", -6) 244 | .attr("dy", "-.40em") 245 | .attr("text-anchor", "end") 246 | .text(function(d, i) { return ""; }); 247 | 248 | 249 | var rules = vis.selectAll("g.rule") 250 | .data(x.ticks(10)) 251 | .enter().append("svg:g") 252 | .attr("class", "rule") 253 | .attr("transform", function(d) { return "translate(" + x_bar(d) + ", 0)"; }); 254 | 255 | 256 | rules.append("svg:line") 257 | .attr("y1", 0) 258 | .attr("y2", h_bar) 259 | .attr("x1", labelpad) 260 | .attr("x2", labelpad) 261 | .attr("stroke", "white") 262 | .attr("stroke-opacity", .3); 263 | 264 | 265 | 266 | function redraw(arm_number){ 267 | 268 | var _data = [] 269 | for ( var i =0; i < 3; i++){ 270 | _data.push( pdfbeta(x_array, 1 + ARMS[2*i+1],1+ARMS[2*i] - ARMS[2*i+1] ) ); 271 | 272 | } 273 | //update what is max. 274 | max_data = d3.max( [ 275 | 10, 276 | d3.max(_data[0]), 277 | d3.max(_data[1]), 278 | d3.max(_data[2]) ]) 279 | 280 | y = d3.scale.linear().domain([0, max_data]).range([h - margin,0 + margin ]) 281 | line = d3.svg.line() 282 | .x(function(d, i) { return x(i); }) 283 | .y(y) 284 | 285 | for ( var i =0; i < 3; i++){ 286 | g.select("#line-" + i) 287 | .data( [_data[i]] ) 288 | .attr("d", line ) 289 | } 290 | 291 | 292 | 293 | 294 | 295 | 296 | bars.data(ARMS) 297 | .enter().append("svg:g") 298 | .attr("class", "bar") 299 | .attr("transform", function(d, i) { return "translate(" + labelpad + "," + y(i) + ")"; }); 300 | 301 | 302 | bars.append("svg:rect") 303 | .attr("fill", function(d, ix) {_ix = Math.floor(ix/2); return (ix%2)? fill_colors[_ix]: colors[_ix]; } ) //Alternate colors 304 | .attr("width", function(d,i){ return x_bar(d)*0.5 }) 305 | .attr("height", y_bar.rangeBand()); 306 | 307 | 308 | counts 309 | .attr("x", 0) 310 | .attr("y", 10 + y_bar.rangeBand() / 2) 311 | .attr("dx", function( d,i) { return !(i%2) ? 50 + 3.2*data[i] : 67 + 3.2*data[i] ;}) 312 | .attr("dy", "-.40em") 313 | .attr("text-anchor", "end") 314 | .text(function(d, i) { return !(i%2) ? data[i] + " pulls" : data[i] + " rewards" ;}); 315 | 316 | //update scoreboard 317 | var rewards = ARMS[1] + ARMS[3] + ARMS[5]; 318 | var pulls = ARMS[0] + ARMS[2] + ARMS[4]; 319 | document.getElementById("rewards").innerHTML = rewards ; 320 | document.getElementById("pulls").innerHTML = pulls ; 321 | document.getElementById("ratio").innerHTML = (rewards/pulls).toFixed(3) ; 322 | 323 | } 324 | 325 | 326 | d3.select( "#reveal-div" ) 327 | .selectAll("p") 328 | .data( _PROBS ) 329 | .enter() 330 | .append("span") 331 | .attr( "style", "margin-left:15; margin-right: 30px; margin-top:0" ) 332 | .text( function(d,i){ return d.toFixed(4) ; } ) 333 | //redraw() //to initialize 334 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | #Bayesian Methods for Hackers 2 | #### *Using Python and PyMC* 3 | 4 | 5 | 6 | 7 | The Bayesian method is the natural approach to inference, yet it is hidden from readers behind chapters of slow, mathematical analysis. The typical text on Bayesian inference involves two to three chapters on probability theory, then enters what Bayesian inference is. Unfortunately, due to mathematical intractability of most Bayesian models, the reader is only shown simple, artificial examples. This can leave the user with a *so-what* feeling about Bayesian inference. In fact, this was the author's own prior opinion. 8 | 9 | 10 |
11 | 12 | After some recent success of Bayesian methods in machine-learning competitions, I decided to investigate the subject again. Even with my mathematical background, it took me three straight-days of reading examples and trying to put the pieces together to understand the methods. There was simply not enough literature bridging theory to practice. The problem with my misunderstanding was the disconnect between Bayesian mathematics and probabilistic programming. That being said, I suffered then so the reader would not have to now. This book attempts to bridge the gap. 13 | 14 | If Bayesian inference is the destination, then mathematical analysis is a particular path to towards it. On the other hand, computing power is cheap enough that we can afford to take an alternate route via probabilistic programming. The latter path is much more useful, as it denies the necessity of mathematical intervention at each step, that is, we remove often-intractable mathematical analysis as a prerequisite to Bayesian inference. Simply put, this latter computational path proceeds via small intermediate jumps from beginning to end, where as the first path proceeds by enormous leaps, often landing far away from our target. Furthermore, without a strong mathematical background, the analysis required by the first path cannot even take place. 15 | 16 | *Bayesian Methods for Hackers* is designed as a introduction to Bayesian inference from a computational/understanding-first, and mathematics-second, point of view. Of course as an introductory book, we can only leave it at that: an introductory book. For the mathematically trained, they may cure the curiosity this text generates with other texts designed with mathematical analysis in mind. For the enthusiast with less mathematical-background, or one who is not interested in the mathematics but simply the practice of Bayesian methods, this text should be sufficient and entertaining. 17 | 18 | 19 | The choice of PyMC as the probabilistic programming language is two-fold. As of this writing, there is currently no central resource for examples and explanations in the PyMC universe. The official documentation assumes prior knowledge of Bayesian inference and probabilistic programming. We hope this book encourages users at every level to look at PyMC. Secondly, with recent core developments and popularity of the scientific stack in Python, PyMC is likely to become a core component soon enough. 20 | 21 | PyMC does have dependencies to run, namely NumPy and (optionally) SciPy. To not limit the user, the examples in this book will rely only on PyMC, NumPy, SciPy and Matplotlib only. 22 | 23 | 24 | Contents 25 | ------ 26 | 27 | (The below chapters are rendered via the *nbviewer* at 28 | [nbviewer.ipython.org/](http://nbviewer.ipython.org/), and is read-only and rendered in real-time. 29 | Interactive notebooks + examples can be downloaded by cloning! ) 30 | 31 | 32 | * [**Prologue:**](http://nbviewer.ipython.org/urls/raw.github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Prologue/Prologue.ipynb) Why we do it. 33 | 34 | * [**Chapter 1: Introduction to Bayesian Methods**](http://nbviewer.ipython.org/urls/raw.github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Chapter1_Introduction/Chapter1_Introduction.ipynb) 35 | Introduction to the philosophy and practice of Bayesian methods and answering the question, "What is probabilistic programming?" Examples include: 36 | - Inferring human behaviour changes from text message rates 37 | 38 | * [**Chapter 2: A little more on PyMC**](http://nbviewer.ipython.org/urls/raw.github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Chapter2_MorePyMC/MorePyMC.ipynb) 39 | We explore modeling Bayesian problems using Python's PyMC library through examples. How do we create Bayesian models? Examples include: 40 | - Detecting the frequency of cheating students, while avoiding liars 41 | - Calculating probabilities of the Challenger space-shuttle disaster 42 | 43 | * [**Chapter 3: Opening the Black Box of MCMC**](http://nbviewer.ipython.org/urls/raw.github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Chapter3_MCMC/IntroMCMC.ipynb) 44 | We discuss how MCMC operates and diagnostic tools. Examples include: 45 | - Bayesian clustering with mixture models 46 | 47 | * [**Chapter 4: The Greatest Theorem Never Told**](http://nbviewer.ipython.org/urls/raw.github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Chapter4_TheGreatestTheoremNeverTold/LawOfLargeNumbers.ipynb) 48 | We explore an incredibly useful, and dangerous, theorem: The Law of Large Numbers. Examples include: 49 | - Exploring a Kaggle dataset and the pitfalls of naive analysis 50 | - How to sort Reddit comments from best to worst (not as easy as you think) 51 | 52 | * [**Chapter 5: Would you rather lose an arm or a leg?**](http://nbviewer.ipython.org/urls/raw.github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Chapter5_LossFunctions/LossFunctions.ipynb) 53 | The introduction of loss functions and their (awesome) use in Bayesian methods. Examples include: 54 | - Solving the *Price is Right*'s Showdown 55 | - Optimizing financial predictions 56 | - Winning solution to the Kaggle Dark World's competition 57 | 58 | * [**Chapter 6: Getting our *prior*-ities straight**](http://nbviewer.ipython.org/urls/raw.github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Chapter6_Priorities/Priors.ipynb) 59 | Probably the most important chapter. We draw on expert opinions to answer questions. Examples include: 60 | - Multi-Armed Bandits and the Bayesian Bandit solution. 61 | - What is the relationship between data sample size and prior? 62 | - Estimating financial unknowns using expert priors 63 | 64 | We explore useful tips to be objective in analysis as well as common pitfalls of priors. 65 | 66 | * **Chapter X1: Bayesian methods in Machine Learning and Model Validation** 67 | We explore how to resolve the overfitting problem plus popular ML methods. Also included are probablistic explainations of ridge regression and LASSO regression. 68 | - Tim Saliman's winning solution to Kaggle's *Don't Overfit* problem 69 | 70 | * **Chapter X2: More PyMC Hackery** 71 | We explore the gritty details of PyMC. Examples include: 72 | - Analysis on real-time GitHub repo stars and forks. 73 | 74 | 75 | 76 | **More questions about PyMC?** 77 | Please post your modeling, convergence, or any other PyMC question on [cross-validated](http://stats.stackexchange.com/), the statistics stack-exchange. 78 | 79 | 80 | Using the book 81 | ------- 82 | 83 | The book can be read in three different ways, starting from most recommended to least recommended: 84 | 85 | 1. The most recommended option is to clone the repository to download the .ipynb files to your local machine. If you have IPython installed, you can view the 86 | chapters in your browser *plus* edit and run the code provided (and try some practice questions). This is the preferred option to read 87 | this book, though it comes with some dependencies. 88 | - IPython v0.13 (or greater) is a requirement to view the ipynb files. It can be downloaded [here](http://ipython.org/) 89 | - For Linux users, you should not have a problem installing NumPy, SciPy, Matplotlib and PyMC. For Windows users, check out [pre-compiled versions](http://www.lfd.uci.edu/~gohlke/pythonlibs/) if you have difficulty. 90 | - In the styles/ directory are a number of files (.matplotlirc) that used to make things pretty. These are not only designed for the book, but they offer many improvements over the default settings of matplotlib and the IPython notebook. 91 | - while technically not required, it may help to run the IPython notebook with `ipython notebook --pylab inline` flag if you encounter io errors. 92 | 2. The second, preferred, option is to use the nbviewer.ipython.org site, which display IPython notebooks in the browser ([example](http://nbviewer.ipython.org/urls/raw.github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Chapter1_Introduction/Chapter1_Introduction.ipynb)). 93 | The contents are updated synchronously as commits are made to the book. You can use the Contents section above to link to the chapters. 94 | 95 | 3. **PDF versions are coming.** PDFs are the least-prefered method to read the book, as pdf's are static and non-interactive. If PDFs are desired, they can be created dynamically using Chrome's builtin print-to-pdf feature or using the [nbconvert](https://github.com/ipython/nbconvert) utility. 96 | 97 | 98 | Installation and configuration 99 | ------ 100 | If you would like to run the IPython notebooks locally, (option 1. above), you'll need to install the following: 101 | - IPython 0.13 is a requirement to view the ipynb files. It can be downloaded [here](http://ipython.org/ipython-doc/dev/install/index.html) 102 | - For Linux users, you should not have a problem installing NumPy, SciPy and PyMC. For Windows users, check out [pre-compiled versions](http://www.lfd.uci.edu/~gohlke/pythonlibs/) if you have difficulty. 103 | - also recommended, for data-mining exercises, are [PRAW](https://github.com/praw-dev/praw) and [requests](https://github.com/kennethreitz/requests). 104 | 105 | - In the styles/ directory are a number of files that are customized for the notebook. 106 | These are not only designed for the book, but they offer many improvements over the 107 | default settings of matplotlib and the IPython notebook. The in notebook style has not been finalized yet. 108 | 109 | 110 | 111 | Development 112 | ------ 113 | 114 | This book has an unusual development design. The content is open-sourced, meaning anyone can be an author. 115 | Authors submit content or revisions using the GitHub interface. 116 | 117 | ### How to contribute 118 | 119 | ####What to contribute? 120 | 121 | - The current chapter list is not finalized. If you see something that is missing (MCMC, MAP, Bayesian networks, good prior choices, Potential classes etc.), 122 | feel free to start there. 123 | - Cleaning up Python code and making code more PyMC-esque 124 | - Giving better explanations 125 | - Spelling/grammar mistakes 126 | - Suggestions 127 | - Contributing to the IPython notebook styles 128 | 129 | 130 | ####Commiting 131 | 132 | - All commits are welcome, even if they are minor ;) 133 | - If you are unfamiliar with Github, you can email me contributions to the email below. 134 | 135 | 136 | Contributions and Thanks 137 | ----- 138 | 139 | 140 | Thanks to all our contributing authors, including (in chronological order): 141 | - [Cameron Davidson-Pilon](http://www.camdp.com) 142 | - [Stef Gibson](http://stefgibson.com) 143 | - [Vincent Ohprecio](http://bigsnarf.wordpress.com/) 144 | - [Lars Buitinck](https://github.com/larsman) 145 | - [Paul Magwene](http://github.com/pmagwene) 146 | - [Matthias Bussonnier](https://github.com/Carreau) 147 | - [Jens Rantil](https://github.com/JensRantil) 148 | - [y-p](https://github.com/y-p) 149 | - [Ethan Brown](http://www.etano.net/) 150 | - [Jonathan Whitmore](http://jonathanwhitmore.com/) 151 | - [Mattia Rigotti](https://github.com/matrig) 152 | - [Colby Lemon](https://github.com/colibius) 153 | - [Gustav W Delius](https://github.com/gustavdelius) 154 | - [Matthew Conlen](http://www.mathisonian.com/) 155 | - [Jim Radford](https://github.com/radford) 156 | - [Vannessa Sabino](http://baniverso.com/) 157 | - [Thomas Bratt](https://github.com/thomasbratt) 158 | - [Nisan Haramati](https://github.com/nisanharamati) 159 | - [Thomas Bratt](https://github.com/thomasbratt) 160 | - [Robert Grant](https://github.com/bgrant) 161 | - [Yaroslav Halchenko](https://github.com/yarikoptic) 162 | - [Alex Garel](https://github.com/alexgarel) 163 | - [Oleksandr Lysenko](https://twitter.com/sash_ko) 164 | - [liori](https://github.com/liori) 165 | - [ducky427](https://github.com/ducky427) 166 | - [Pablo de Oliveira Castro](https://github.com/pablooliveira) 167 | - [sergeyfogelson](https://github.com/sergeyfogelson) 168 | - [Mattia Rigotti](http://neurotheory.columbia.edu/~mrigotti/) 169 | 170 | 171 | We would like to thank the Python community for building an amazing architecture. We would like to thank the 172 | statistics community for building an amazing architecture. 173 | 174 | Similarly, the book is only possible because of the [PyMC](http://github.com/pymc-devs/pymc) library. A big thanks to the core devs of PyMC: Chris Fonnesbeck, Anand Patil, David Huard and John Salvatier. 175 | 176 | One final thanks. This book was generated by IPython Notebook, a wonderful tool for developing in Python. We thank the IPython 177 | community for developing the Notebook interface. All IPython notebook files are available for download on the GitHub repository. 178 | 179 | 180 | 181 | ####Contact 182 | Contact the main author, Cam Davidson-Pilon at cam.davidson.pilon@gmail.com or [@cmrndp](https://twitter.com/cmrn_dp) 183 | 184 | 185 | ![Imgur](http://i.imgur.com/Zb79QZb.png) 186 | -------------------------------------------------------------------------------- /Chapter5_LossFunctions/data/Train_Skies/Train_Skies/Training_Sky200.csv: -------------------------------------------------------------------------------- 1 | GalaxyID,x,y,e1,e2 2 | Galaxy1,1977.18,2284.96,0.135144,-0.075196 3 | Galaxy2,4187.01,3033.95,-0.289684,-0.009205 4 | Galaxy3,1849.42,1870.43,-0.128524,0.188735 5 | Galaxy4,1305.95,2440.36,-0.160642,-0.158346 6 | Galaxy5,2750.99,628.40,0.144453,-0.207262 7 | Galaxy6,232.89,2303.53,0.078057,-0.437543 8 | Galaxy7,2612.18,3763.64,-0.244929,-0.170409 9 | Galaxy8,2343.68,696.38,-0.091899,-0.056466 10 | Galaxy9,1347.46,2430.44,-0.118368,-0.133801 11 | Galaxy10,3059.47,3522.40,0.567381,0.262042 12 | Galaxy11,525.64,3536.97,0.237223,-0.106512 13 | Galaxy12,2689.56,955.63,-0.126659,-0.188333 14 | Galaxy13,488.40,4103.84,-0.264981,0.028407 15 | Galaxy14,2462.76,68.95,0.186851,0.087643 16 | Galaxy15,1751.51,2893.69,-0.159142,-0.350449 17 | Galaxy16,837.03,4112.89,-0.073740,-0.116542 18 | Galaxy17,1329.02,3690.04,-0.015756,-0.439716 19 | Galaxy18,3129.31,1580.80,0.115302,-0.150052 20 | Galaxy19,1528.66,2605.11,0.325420,-0.185407 21 | Galaxy20,3705.80,1939.42,0.154496,-0.318856 22 | Galaxy21,2912.97,1396.94,0.605121,-0.167950 23 | Galaxy22,2422.36,2698.40,0.055310,-0.287335 24 | Galaxy23,1282.99,1312.29,-0.190086,0.217821 25 | Galaxy24,3414.15,369.69,0.126505,0.161918 26 | Galaxy25,4109.78,2711.26,-0.357916,0.344080 27 | Galaxy26,1799.94,1571.47,0.370868,-0.006458 28 | Galaxy27,1079.35,3306.13,0.180853,-0.205937 29 | Galaxy28,1475.48,579.65,-0.007217,0.029759 30 | Galaxy29,2305.35,1687.76,-0.020087,-0.238240 31 | Galaxy30,2125.44,1404.53,0.256425,0.211617 32 | Galaxy31,2645.83,1232.90,0.107564,-0.133721 33 | Galaxy32,2740.30,128.29,-0.275907,-0.240346 34 | Galaxy33,345.14,1585.68,0.157808,-0.251283 35 | Galaxy34,2540.53,997.99,0.050012,-0.003349 36 | Galaxy35,1535.33,3324.26,-0.329937,-0.205468 37 | Galaxy36,3598.68,3123.36,-0.123360,-0.874771 38 | Galaxy37,341.48,3812.43,0.206939,0.022255 39 | Galaxy38,1131.28,1631.04,-0.039327,0.660914 40 | Galaxy39,1208.29,590.20,0.074814,-0.211530 41 | Galaxy40,3205.92,1148.99,0.357477,-0.196860 42 | Galaxy41,2366.50,3279.92,-0.239987,-0.258418 43 | Galaxy42,951.88,3934.53,0.038660,-0.077037 44 | Galaxy43,1528.15,3674.78,-0.048536,-0.068555 45 | Galaxy44,1614.13,382.33,0.282453,-0.328420 46 | Galaxy45,1442.38,2721.67,-0.249329,0.251646 47 | Galaxy46,3836.53,1673.49,0.129003,0.551354 48 | Galaxy47,97.19,403.08,-0.228413,-0.385924 49 | Galaxy48,3465.82,2665.68,0.534817,0.283285 50 | Galaxy49,2857.74,1717.25,0.146345,-0.064359 51 | 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