├── .gitignore
├── LICENSE
├── README.md
├── __init__.py
├── exp
    ├── __init__.py
    ├── loss_function_sample_size.ipynb
    ├── solve_sym_pos_matrix.ipynb
    └── tgp_np_gradient_check.ipynb
└── tgp
    ├── .idea
        ├── test.py
        ├── test2.py
        └── zero.py
    ├── __init__.py
    ├── gradient_check.py
    ├── np
        ├── __init__.py
        └── gaussian_process.py
    └── tf
        ├── gaussian_process.py
        └── troubleshoot.ipynb


/.gitignore:
--------------------------------------------------------------------------------
 1 | # Untitled notebooks
 2 | Untitled*
 3 | 
 4 | # Byte-compiled / optimized / DLL files
 5 | __pycache__/
 6 | *.py[cod]
 7 | *$py.class
 8 | 
 9 | # C extensions
10 | *.so
11 | 
12 | # Distribution / packaging
13 | .Python
14 | env/
15 | build/
16 | develop-eggs/
17 | dist/
18 | downloads/
19 | eggs/
20 | .eggs/
21 | lib/
22 | lib64/
23 | parts/
24 | sdist/
25 | var/
26 | *.egg-info/
27 | .installed.cfg
28 | *.egg
29 | 
30 | # PyInstaller
31 | #  Usually these files are written by a python script from a template
32 | #  before PyInstaller builds the exe, so as to inject date/other infos into it.
33 | *.manifest
34 | *.spec
35 | 
36 | # Installer logs
37 | pip-log.txt
38 | pip-delete-this-directory.txt
39 | 
40 | # Unit test / coverage reports
41 | htmlcov/
42 | .tox/
43 | .coverage
44 | .coverage.*
45 | .cache
46 | nosetests.xml
47 | coverage.xml
48 | *,cover
49 | .hypothesis/
50 | 
51 | # Translations
52 | *.mo
53 | *.pot
54 | 
55 | # Django stuff:
56 | *.log
57 | 
58 | # Sphinx documentation
59 | docs/_build/
60 | 
61 | # PyBuilder
62 | target/
63 | 
64 | #Ipython Notebook
65 | .ipynb_checkpoints
66 | 


--------------------------------------------------------------------------------
/LICENSE:
--------------------------------------------------------------------------------
 1 | The MIT License (MIT)
 2 | 
 3 | Copyright (c) 2016 Rui Shu
 4 | 
 5 | Permission is hereby granted, free of charge, to any person obtaining a copy
 6 | of this software and associated documentation files (the "Software"), to deal
 7 | in the Software without restriction, including without limitation the rights
 8 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
 9 | copies of the Software, and to permit persons to whom the Software is
10 | furnished to do so, subject to the following conditions:
11 | 
12 | The above copyright notice and this permission notice shall be included in all
13 | copies or substantial portions of the Software.
14 | 
15 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
16 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
17 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
18 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
19 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
20 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
21 | SOFTWARE.
22 | 


--------------------------------------------------------------------------------
/README.md:
--------------------------------------------------------------------------------
1 | # tensorflow-gp
2 | Implementation of gaussian processes and bayesian optimization in tensorflow
3 | 


--------------------------------------------------------------------------------
/__init__.py:
--------------------------------------------------------------------------------
https://raw.githubusercontent.com/RuiShu/tensorflow-gp/45f48c93475de7e49658745b34536a74c9cb6380/__init__.py


--------------------------------------------------------------------------------
/exp/__init__.py:
--------------------------------------------------------------------------------
https://raw.githubusercontent.com/RuiShu/tensorflow-gp/45f48c93475de7e49658745b34536a74c9cb6380/exp/__init__.py


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/exp/loss_function_sample_size.ipynb:
--------------------------------------------------------------------------------
 1 | {
 2 |  "cells": [
 3 |   {
 4 |    "cell_type": "code",
 5 |    "execution_count": 7,
 6 |    "metadata": {
 7 |     "collapsed": false
 8 |    },
 9 |    "outputs": [],
10 |    "source": [
11 |     "import sys\n",
12 |     "sys.path.append('/Users/void/Documents/github/tensorflow-gp')import numpy as np\n",
13 |     "import tensorflow as tf\n",
14 |     "import scipy.linalg as la\n",
15 |     "from src.np.gaussian_process import GaussianProcess as GP"
16 |    ]
17 |   }
18 |  ],
19 |  "metadata": {
20 |   "kernelspec": {
21 |    "display_name": "Python 2",
22 |    "language": "python",
23 |    "name": "python2"
24 |   },
25 |   "language_info": {
26 |    "codemirror_mode": {
27 |     "name": "ipython",
28 |     "version": 2
29 |    },
30 |    "file_extension": ".py",
31 |    "mimetype": "text/x-python",
32 |    "name": "python",
33 |    "nbconvert_exporter": "python",
34 |    "pygments_lexer": "ipython2",
35 |    "version": "2.7.10"
36 |   }
37 |  },
38 |  "nbformat": 4,
39 |  "nbformat_minor": 0
40 | }
41 | 


--------------------------------------------------------------------------------
/exp/solve_sym_pos_matrix.ipynb:
--------------------------------------------------------------------------------
  1 | {
  2 |  "cells": [
  3 |   {
  4 |    "cell_type": "markdown",
  5 |    "metadata": {},
  6 |    "source": [
  7 |     "# Comparing matrix inversion v. solving\n",
  8 |     "\n",
  9 |     "KX = Y\n",
 10 |     "\n",
 11 |     "where K is pretty big, X is pretty big, and Y is pretty big. We're solving for X"
 12 |    ]
 13 |   },
 14 |   {
 15 |    "cell_type": "code",
 16 |    "execution_count": 1,
 17 |    "metadata": {
 18 |     "collapsed": true
 19 |    },
 20 |    "outputs": [],
 21 |    "source": [
 22 |     "# Set up matrix K and Y\n",
 23 |     "import numpy as np\n",
 24 |     "from scipy.linalg import solve\n",
 25 |     "from numpy.linalg import inv\n",
 26 |     "import time\n",
 27 |     "import matplotlib.pyplot as plt\n",
 28 |     "% matplotlib inline"
 29 |    ]
 30 |   },
 31 |   {
 32 |    "cell_type": "code",
 33 |    "execution_count": 2,
 34 |    "metadata": {
 35 |     "collapsed": true
 36 |    },
 37 |    "outputs": [],
 38 |    "source": [
 39 |     "n = 1000\n",
 40 |     "K = np.random.randn(n, n)\n",
 41 |     "K = K.dot(K.T)\n",
 42 |     "Y = np.random.randn(n, n)"
 43 |    ]
 44 |   },
 45 |   {
 46 |    "cell_type": "code",
 47 |    "execution_count": 3,
 48 |    "metadata": {
 49 |     "collapsed": true
 50 |    },
 51 |    "outputs": [],
 52 |    "source": [
 53 |     "def generate(n):\n",
 54 |     "    K = np.random.randn(n, n)\n",
 55 |     "    K = K.dot(K.T)\n",
 56 |     "    Y = np.random.randn(n, n)\n",
 57 |     "    return K, Y"
 58 |    ]
 59 |   },
 60 |   {
 61 |    "cell_type": "code",
 62 |    "execution_count": 4,
 63 |    "metadata": {
 64 |     "collapsed": true
 65 |    },
 66 |    "outputs": [],
 67 |    "source": [
 68 |     "def solve_by_inv(K, Y):\n",
 69 |     "    # Solve by matrix inversion\n",
 70 |     "    t = time.time()\n",
 71 |     "    X = inv(K).dot(Y)\n",
 72 |     "    t = time.time() - t\n",
 73 |     "    err = abs(K.dot(X) - Y).mean()\n",
 74 |     "    return err, t"
 75 |    ]
 76 |   },
 77 |   {
 78 |    "cell_type": "code",
 79 |    "execution_count": 5,
 80 |    "metadata": {
 81 |     "collapsed": true
 82 |    },
 83 |    "outputs": [],
 84 |    "source": [
 85 |     "def solve_by_sol(K, Y):\n",
 86 |     "    # Solve by matrix inversion\n",
 87 |     "    t = time.time()\n",
 88 |     "    X = solve(K, Y, sym_pos=True)\n",
 89 |     "    t = time.time() - t\n",
 90 |     "    err = abs(K.dot(X) - Y).mean()\n",
 91 |     "    return err, t    "
 92 |    ]
 93 |   },
 94 |   {
 95 |    "cell_type": "code",
 96 |    "execution_count": 6,
 97 |    "metadata": {
 98 |     "collapsed": false
 99 |    },
100 |    "outputs": [
101 |     {
102 |      "name": "stdout",
103 |      "output_type": "stream",
104 |      "text": [
105 |       "Solution check: 2.55433963354e-11\n",
106 |       "Computation time: 0.166968822479\n"
107 |      ]
108 |     }
109 |    ],
110 |    "source": [
111 |     "# Solve by matrix inversion\n",
112 |     "err, t = solve_by_inv(K, Y)\n",
113 |     "print \"Solution check:\", err\n",
114 |     "print \"Computation time:\", t"
115 |    ]
116 |   },
117 |   {
118 |    "cell_type": "code",
119 |    "execution_count": 7,
120 |    "metadata": {
121 |     "collapsed": false
122 |    },
123 |    "outputs": [
124 |     {
125 |      "name": "stdout",
126 |      "output_type": "stream",
127 |      "text": [
128 |       "Solution check: 1.64575786881e-11\n",
129 |       "Computation time: 0.114394187927\n"
130 |      ]
131 |     }
132 |    ],
133 |    "source": [
134 |     "# Solve by solving\n",
135 |     "err, t = solve_by_sol(K, Y)\n",
136 |     "print \"Solution check:\", err\n",
137 |     "print \"Computation time:\", t"
138 |    ]
139 |   },
140 |   {
141 |    "cell_type": "code",
142 |    "execution_count": 14,
143 |    "metadata": {
144 |     "collapsed": false,
145 |     "scrolled": true
146 |    },
147 |    "outputs": [
148 |     {
149 |      "name": "stdout",
150 |      "output_type": "stream",
151 |      "text": [
152 |       "10\n",
153 |       "********************************************************************************\n",
154 |       "Error: 4.42049175042e-15 \t3.43683415061e-15\n",
155 |       "Time: 9.20295715332e-05 \t0.0001060962677\n",
156 |       "********************************************************************************\n",
157 |       "Error: 3.29209819128e-13 \t1.7948229708e-13\n",
158 |       "Time: 3.09944152832e-05 \t6.29425048828e-05\n",
159 |       "********************************************************************************\n",
160 |       "Error: 4.79287616539e-15 \t3.7774384315e-15\n",
161 |       "Time: 2.88486480713e-05 \t5.79357147217e-05\n",
162 |       "18\n",
163 |       "********************************************************************************\n",
164 |       "Error: 8.63665575662e-14 \t5.66552234493e-14\n",
165 |       "Time: 4.10079956055e-05 \t7.20024108887e-05\n",
166 |       "********************************************************************************\n",
167 |       "Error: 1.8808092381e-13 \t1.27801132187e-13\n",
168 |       "Time: 3.50475311279e-05 \t6.07967376709e-05\n",
169 |       "********************************************************************************\n",
170 |       "Error: 5.53955163847e-15 \t2.85114786932e-15\n",
171 |       "Time: 3.40938568115e-05 \t6.00814819336e-05\n",
172 |       "35\n",
173 |       "********************************************************************************\n",
174 |       "Error: 9.55214531162e-13 \t7.06246148581e-13\n",
175 |       "Time: 0.00029993057251 \t0.000163078308105\n",
176 |       "********************************************************************************\n",
177 |       "Error: 9.10603868917e-14 \t5.75306378854e-14\n",
178 |       "Time: 0.000164985656738 \t0.000113964080811\n",
179 |       "********************************************************************************\n",
180 |       "Error: 1.80277426722e-11 \t9.85386184063e-12\n",
181 |       "Time: 0.000129222869873 \t0.000195026397705\n",
182 |       "68\n",
183 |       "********************************************************************************\n",
184 |       "Error: 3.22948889123e-12 \t1.7591507325e-12\n",
185 |       "Time: 0.000412940979004 \t0.000247001647949\n",
186 |       "********************************************************************************\n",
187 |       "Error: 3.11033180812e-13 \t1.89298640525e-13\n",
188 |       "Time: 0.000715017318726 \t0.000301837921143\n",
189 |       "********************************************************************************\n",
190 |       "Error: 3.09719012001e-12 \t1.70594262638e-12\n",
191 |       "Time: 0.000520944595337 \t0.00047492980957\n",
192 |       "129\n",
193 |       "********************************************************************************\n",
194 |       "Error: 1.68938517692e-10 \t9.88073725983e-11\n",
195 |       "Time: 0.00245594978333 \t0.00132703781128\n",
196 |       "********************************************************************************\n",
197 |       "Error: 2.85277239044e-12 \t1.74371486702e-12\n",
198 |       "Time: 0.00215888023376 \t0.00173306465149\n",
199 |       "********************************************************************************\n",
200 |       "Error: 3.85807851936e-13 \t2.35591375268e-13\n",
201 |       "Time: 0.00109601020813 \t0.00109505653381\n",
202 |       "244\n",
203 |       "********************************************************************************\n",
204 |       "Error: 1.42796057749e-09 \t9.20738798286e-10\n",
205 |       "Time: 0.00374412536621 \t0.00209999084473\n",
206 |       "********************************************************************************\n",
207 |       "Error: 2.38886458949e-10 \t1.39761291498e-10\n",
208 |       "Time: 0.0028510093689 \t0.00250101089478\n",
209 |       "********************************************************************************\n",
210 |       "Error: 4.71068022907e-13 \t3.10499473008e-13\n",
211 |       "Time: 0.00812816619873 \t0.00343108177185\n",
212 |       "464\n",
213 |       "********************************************************************************\n",
214 |       "Error: 1.2198434094e-11 \t7.78292422394e-12\n",
215 |       "Time: 0.0160710811615 \t0.0093309879303\n",
216 |       "********************************************************************************\n",
217 |       "Error: 2.07141102474e-12 \t1.36553636803e-12\n",
218 |       "Time: 0.0166411399841 \t0.00949811935425\n",
219 |       "********************************************************************************\n",
220 |       "Error: 2.90398855521e-11 \t1.8192453841e-11\n",
221 |       "Time: 0.0132720470428 \t0.00915384292603\n",
222 |       "879\n",
223 |       "********************************************************************************\n",
224 |       "Error: 1.00970254969e-09 \t6.40454072489e-10\n",
225 |       "Time: 0.0777299404144 \t0.0480480194092\n",
226 |       "********************************************************************************\n",
227 |       "Error: 2.19341119894e-10 \t1.3761695871e-10\n",
228 |       "Time: 0.0762650966644 \t0.0459249019623\n",
229 |       "********************************************************************************\n",
230 |       "Error: 7.73593810326e-11 \t4.52258853839e-11\n",
231 |       "Time: 0.0735318660736 \t0.0467600822449\n",
232 |       "1668\n",
233 |       "********************************************************************************\n",
234 |       "Error: 1.7599371871e-10 \t1.10621402707e-10\n",
235 |       "Time: 0.593911886215 \t0.29734992981\n",
236 |       "********************************************************************************\n",
237 |       "Error: 5.9789171951e-10 \t3.73527719942e-10\n",
238 |       "Time: 0.759345054626 \t0.336894035339\n",
239 |       "********************************************************************************\n",
240 |       "Error: 8.17685037585e-11 \t5.42736781058e-11\n",
241 |       "Time: 0.756484031677 \t0.284887075424\n",
242 |       "3162\n",
243 |       "********************************************************************************\n",
244 |       "Error: 1.64172481528e-09 \t1.00572685299e-09\n",
245 |       "Time: 3.15070295334 \t2.03040194511\n",
246 |       "********************************************************************************\n",
247 |       "Error: 1.06867099803e-08 \t6.74737991947e-09\n",
248 |       "Time: 2.91052508354 \t2.09549403191\n",
249 |       "********************************************************************************\n",
250 |       "Error: 8.36690771438e-10 \t5.61995860124e-10\n",
251 |       "Time: 3.53569293022 \t2.42399406433\n"
252 |      ]
253 |     }
254 |    ],
255 |    "source": [
256 |     "ns = np.power(10, np.linspace(1, 3.5, num=10)).astype(int)\n",
257 |     "trials = 3\n",
258 |     "inv_err = np.zeros(trials*len(ns))\n",
259 |     "sol_err = np.zeros(trials*len(ns))\n",
260 |     "inv_t = np.zeros(trials*len(ns))\n",
261 |     "sol_t = np.zeros(trials*len(ns))\n",
262 |     "x = np.zeros(trials*len(ns))\n",
263 |     "\n",
264 |     "i = 0\n",
265 |     "for n in ns:\n",
266 |     "    print n\n",
267 |     "    for _ in xrange(trials):\n",
268 |     "        K, Y = generate(n)\n",
269 |     "        err1, t1 = solve_by_inv(K, Y)\n",
270 |     "        err2, t2 = solve_by_sol(K, Y)\n",
271 |     "        inv_err[i] = err1\n",
272 |     "        sol_err[i] = err2\n",
273 |     "        inv_t[i] = t1\n",
274 |     "        sol_t[i] = t2\n",
275 |     "        x[i] = n\n",
276 |     "        i += 1\n",
277 |     "        print \"*\"*80\n",
278 |     "        print \"Error:\", err1, \"\\t\", err2\n",
279 |     "        print \"Time:\", t1, \"\\t\", t2"
280 |    ]
281 |   },
282 |   {
283 |    "cell_type": "code",
284 |    "execution_count": 15,
285 |    "metadata": {
286 |     "collapsed": false
287 |    },
288 |    "outputs": [
289 |     {
290 |      "data": {
291 |       "image/png": 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nw8qVUMD/l7F2HN5BzMQYrqhwBXGd4yhWqJjfj2ECx+tPhIiMEJFEEVmTzTYf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\nRK5CYII=\n",
292 |       "text/plain": [
293 |        "<matplotlib.figure.Figure at 0x10e433410>"
294 |       ]
295 |      },
296 |      "metadata": {},
297 |      "output_type": "display_data"
298 |     }
299 |    ],
300 |    "source": [
301 |     "y1 = np.array([inv_err[x == n].mean() for n in ns])\n",
302 |     "y2 = np.array([sol_err[x == n].mean() for n in ns])\n",
303 |     "plt.axis((x.min(), x.max(), 0, max(y1.max(),y2.max())))\n",
304 |     "plt.plot(ns, y1, color='r')\n",
305 |     "plt.plot(ns, y2, color='g')\n",
306 |     "plt.title(\"Error rate\")\n",
307 |     "plt.show()"
308 |    ]
309 |   },
310 |   {
311 |    "cell_type": "code",
312 |    "execution_count": 16,
313 |    "metadata": {
314 |     "collapsed": false,
315 |     "scrolled": true
316 |    },
317 |    "outputs": [
318 |     {
319 |      "data": {
320 |       "image/png": 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AtGQJPPIILFwI55/vdjWlYuTakby49EU+v+tzbj0/77lQCqvAIS4iocBU4DHPGXmRDBky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\n7PQllYIruV2S8RJ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321 |       "text/plain": [
322 |        "<matplotlib.figure.Figure at 0x10fd72590>"
323 |       ]
324 |      },
325 |      "metadata": {},
326 |      "output_type": "display_data"
327 |     }
328 |    ],
329 |    "source": [
330 |     "y1 = np.array([inv_t[x == n].mean() for n in ns])\n",
331 |     "y2 = np.array([sol_t[x == n].mean() for n in ns])\n",
332 |     "plt.axis((x.min(), x.max(), 0, max(y1.max(),y2.max())))\n",
333 |     "plt.plot(ns, y1, color='r')\n",
334 |     "plt.plot(ns, y2, color='g')\n",
335 |     "plt.title(\"Compute time\")\n",
336 |     "plt.show()"
337 |    ]
338 |   }
339 |  ],
340 |  "metadata": {
341 |   "kernelspec": {
342 |    "display_name": "Python 2",
343 |    "language": "python",
344 |    "name": "python2"
345 |   },
346 |   "language_info": {
347 |    "codemirror_mode": {
348 |     "name": "ipython",
349 |     "version": 2
350 |    },
351 |    "file_extension": ".py",
352 |    "mimetype": "text/x-python",
353 |    "name": "python",
354 |    "nbconvert_exporter": "python",
355 |    "pygments_lexer": "ipython2",
356 |    "version": "2.7.10"
357 |   }
358 |  },
359 |  "nbformat": 4,
360 |  "nbformat_minor": 0
361 | }
362 | 


--------------------------------------------------------------------------------
/exp/tgp_np_gradient_check.ipynb:
--------------------------------------------------------------------------------
  1 | {
  2 |  "cells": [
  3 |   {
  4 |    "cell_type": "markdown",
  5 |    "metadata": {},
  6 |    "source": [
  7 |     "# Sanity Check for Gradients"
  8 |    ]
  9 |   },
 10 |   {
 11 |    "cell_type": "code",
 12 |    "execution_count": 1,
 13 |    "metadata": {
 14 |     "collapsed": false
 15 |    },
 16 |    "outputs": [],
 17 |    "source": [
 18 |     "import sys\n",
 19 |     "sys.path.append('/Users/void/Documents/github/tensorflow-gp')\n",
 20 |     "import numpy as np\n",
 21 |     "from tgp.np.gaussian_process import GaussianProcess as GP\n",
 22 |     "from tgp.gradient_check import check_grad\n",
 23 |     "import matplotlib.pyplot as plt\n",
 24 |     "import time\n",
 25 |     "%load_ext autoreload\n",
 26 |     "%autoreload 2\n",
 27 |     "%matplotlib inline"
 28 |    ]
 29 |   },
 30 |   {
 31 |    "cell_type": "code",
 32 |    "execution_count": 2,
 33 |    "metadata": {
 34 |     "collapsed": true
 35 |    },
 36 |    "outputs": [],
 37 |    "source": [
 38 |     "np.random.seed(42)\n",
 39 |     "# make some random data\n",
 40 |     "n = 2\n",
 41 |     "X = np.random.uniform(0, 1, (n, 1))\n",
 42 |     "y = np.sin(X)"
 43 |    ]
 44 |   },
 45 |   {
 46 |    "cell_type": "code",
 47 |    "execution_count": 3,
 48 |    "metadata": {
 49 |     "collapsed": false
 50 |    },
 51 |    "outputs": [
 52 |     {
 53 |      "data": {
 54 |       "text/plain": [
 55 |        "<tgp.np.gaussian_process.GaussianProcess at 0x1038f2290>"
 56 |       ]
 57 |      },
 58 |      "execution_count": 3,
 59 |      "metadata": {},
 60 |      "output_type": "execute_result"
 61 |     }
 62 |    ],
 63 |    "source": [
 64 |     "gp = GP(ls=[.5],\n",
 65 |     "        amp=1.,\n",
 66 |     "        noise=0.,\n",
 67 |     "        keps=1e-9)\n",
 68 |     "gp.fit(X, y, train=False)"
 69 |    ]
 70 |   },
 71 |   {
 72 |    "cell_type": "markdown",
 73 |    "metadata": {},
 74 |    "source": [
 75 |     "### Gradients w.r.t. K"
 76 |    ]
 77 |   },
 78 |   {
 79 |    "cell_type": "code",
 80 |    "execution_count": 4,
 81 |    "metadata": {
 82 |     "collapsed": false
 83 |    },
 84 |    "outputs": [
 85 |     {
 86 |      "name": "stdout",
 87 |      "output_type": "stream",
 88 |      "text": [
 89 |       "[[ 1.          0.51481205]\n",
 90 |       " [ 0.51481205  1.        ]]\n",
 91 |       "ls grad:\n",
 92 |       "[[ 0.          1.36724483]\n",
 93 |       " [ 1.36724483  0.        ]]\n",
 94 |       "amp grad:\n",
 95 |       "[[ 2.          1.02962411]\n",
 96 |       " [ 1.02962411  2.        ]]\n",
 97 |       "noise grad:\n",
 98 |       "[[ 0.  0.]\n",
 99 |       " [ 0.  0.]]\n"
100 |      ]
101 |     }
102 |    ],
103 |    "source": [
104 |     "K, grads = gp.K(X, grad=True)\n",
105 |     "print K\n",
106 |     "print \"ls grad:\"\n",
107 |     "for ls_grad in grads['ls']:\n",
108 |     "    print ls_grad\n",
109 |     "print \"amp grad:\"\n",
110 |     "print grads['amp']\n",
111 |     "print \"noise grad:\"\n",
112 |     "print grads['noise']"
113 |    ]
114 |   },
115 |   {
116 |    "cell_type": "code",
117 |    "execution_count": 5,
118 |    "metadata": {
119 |     "collapsed": false
120 |    },
121 |    "outputs": [
122 |     {
123 |      "name": "stdout",
124 |      "output_type": "stream",
125 |      "text": [
126 |       "Numerical v. analytical gradient difference:\n",
127 |       "[[  0.00000000e+00  -2.49078536e-11]\n",
128 |       " [ -2.49078536e-11   0.00000000e+00]]\n",
129 |       "Max deviation: 2.49078535575e-11\n",
130 |       "(array([[[ 0.        ,  1.36724483],\n",
131 |       "        [ 1.36724483,  0.        ]]]), array([[[ 0.        ,  1.36724483],\n",
132 |       "        [ 1.36724483,  0.        ]]]))\n"
133 |      ]
134 |     }
135 |    ],
136 |    "source": [
137 |     "name = 'ls'\n",
138 |     "f = lambda x: (gp.K(X), gp.K(X, grad=True)[1][name])\n",
139 |     "print check_grad(f, gp.params[name], h=1e-5, verbose=True)"
140 |    ]
141 |   },
142 |   {
143 |    "cell_type": "code",
144 |    "execution_count": 6,
145 |    "metadata": {
146 |     "collapsed": false
147 |    },
148 |    "outputs": [
149 |     {
150 |      "name": "stdout",
151 |      "output_type": "stream",
152 |      "text": [
153 |       "Numerical v. analytical gradient difference:\n",
154 |       "[[ -2.00017780e-12   9.48352508e-12]\n",
155 |       " [  9.48352508e-12  -2.00017780e-12]]\n",
156 |       "Max deviation: 9.48352507635e-12\n",
157 |       "(array([[ 2.        ,  1.02962411],\n",
158 |       "       [ 1.02962411,  2.        ]]), array([[ 2.        ,  1.02962411],\n",
159 |       "       [ 1.02962411,  2.        ]]))\n"
160 |      ]
161 |     }
162 |    ],
163 |    "source": [
164 |     "name = 'amp'\n",
165 |     "f = lambda x: (gp.K(X), gp.K(X, grad=True)[1][name])\n",
166 |     "print check_grad(f, gp.params[name], h=1e-5, verbose=True)"
167 |    ]
168 |   },
169 |   {
170 |    "cell_type": "code",
171 |    "execution_count": 7,
172 |    "metadata": {
173 |     "collapsed": false
174 |    },
175 |    "outputs": [
176 |     {
177 |      "name": "stdout",
178 |      "output_type": "stream",
179 |      "text": [
180 |       "Numerical v. analytical gradient difference:\n",
181 |       "[[ 0.  0.]\n",
182 |       " [ 0.  0.]]\n",
183 |       "Max deviation: 0.0\n",
184 |       "(array([[ 0.,  0.],\n",
185 |       "       [ 0.,  0.]]), array([[ 0.,  0.],\n",
186 |       "       [ 0.,  0.]]))\n"
187 |      ]
188 |     }
189 |    ],
190 |    "source": [
191 |     "name = 'noise'\n",
192 |     "f = lambda x: (gp.K(X), gp.K(X, grad=True)[1][name])\n",
193 |     "print check_grad(f, gp.params[name], h=1e-5, verbose=True)"
194 |    ]
195 |   },
196 |   {
197 |    "cell_type": "markdown",
198 |    "metadata": {},
199 |    "source": [
200 |     "### Gradients w.r.t. L"
201 |    ]
202 |   },
203 |   {
204 |    "cell_type": "code",
205 |    "execution_count": 8,
206 |    "metadata": {
207 |     "collapsed": false
208 |    },
209 |    "outputs": [
210 |     {
211 |      "name": "stdout",
212 |      "output_type": "stream",
213 |      "text": [
214 |       "(0.0,) \t0.000395059585571\n",
215 |       "(0.0,) \t0.00114607810974\n",
216 |       "(0.0,) \t0.000312089920044\n"
217 |      ]
218 |     }
219 |    ],
220 |    "source": [
221 |     "# Before checking gradient, here's a little demo of the different ways of computing the log determinant\n",
222 |     "big_matrix = np.eye(100) # np.random.randn(30, 30)\n",
223 |     "big_matrix = big_matrix.T.dot(big_matrix)\n",
224 |     "t1 = time.time()\n",
225 |     "ans1 = np.log(np.diag(np.linalg.cholesky(big_matrix)**2)).sum()\n",
226 |     "t1 = time.time() - t1\n",
227 |     "t2 = time.time()\n",
228 |     "ans2 = np.linalg.slogdet(big_matrix)[1]\n",
229 |     "t2 = time.time() - t2\n",
230 |     "t3 = time.time()\n",
231 |     "ans3 = 2*np.log(np.diag(np.linalg.cholesky(big_matrix))).sum()\n",
232 |     "t3 = time.time() - t3\n",
233 |     "print (ans1,), \"\\t\", t1\n",
234 |     "print (ans2,), \"\\t\", t2\n",
235 |     "print (ans3,), \"\\t\", t3"
236 |    ]
237 |   },
238 |   {
239 |    "cell_type": "markdown",
240 |    "metadata": {},
241 |    "source": [
242 |     "### Check if L changes significantly as a function of sample size\n",
243 |     "\n",
244 |     "It does change. I have modified the loss function so that it is divided by the number of samples"
245 |    ]
246 |   },
247 |   {
248 |    "cell_type": "code",
249 |    "execution_count": 9,
250 |    "metadata": {
251 |     "collapsed": false
252 |    },
253 |    "outputs": [
254 |     {
255 |      "name": "stdout",
256 |      "output_type": "stream",
257 |      "text": [
258 |       "9.20589046451\n"
259 |      ]
260 |     }
261 |    ],
262 |    "source": [
263 |     "# make some random data\n",
264 |     "np.random.seed(42)\n",
265 |     "n = 1000\n",
266 |     "X = np.random.uniform(0, 1, (n, 1))\n",
267 |     "y = np.sin(X)\n",
268 |     "\n",
269 |     "gp = GP(ls=[.1],\n",
270 |     "        amp=1.,\n",
271 |     "        noise=0.0,\n",
272 |     "        keps=1e-9)\n",
273 |     "print gp.L(X, y, grad=True)[0]"
274 |    ]
275 |   },
276 |   {
277 |    "cell_type": "code",
278 |    "execution_count": 10,
279 |    "metadata": {
280 |     "collapsed": false
281 |    },
282 |    "outputs": [
283 |     {
284 |      "name": "stdout",
285 |      "output_type": "stream",
286 |      "text": [
287 |       "Numerical v. analytical gradient difference:\n",
288 |       "0.00415114502771\n",
289 |       "Max deviation: 0.00415114502771\n",
290 |       "Ana gradient: 1.87503868876\n",
291 |       "Num gradient: 1.87088754373\n"
292 |      ]
293 |     }
294 |    ],
295 |    "source": [
296 |     "name = 'ls'\n",
297 |     "f = lambda x: (gp.L(X, y), gp.L(X, y, grad=True)[1][name])\n",
298 |     "ana_grad, num_grad = check_grad(f, gp.params[name], h=1e-5, verbose=1)\n",
299 |     "print \"Ana gradient:\", ana_grad[0]\n",
300 |     "print \"Num gradient:\", num_grad[0]"
301 |    ]
302 |   },
303 |   {
304 |    "cell_type": "code",
305 |    "execution_count": 11,
306 |    "metadata": {
307 |     "collapsed": false
308 |    },
309 |    "outputs": [
310 |     {
311 |      "name": "stdout",
312 |      "output_type": "stream",
313 |      "text": [
314 |       "Numerical v. analytical gradient difference:\n",
315 |       "0.0119308041244\n",
316 |       "Max deviation: 0.0119308041244\n",
317 |       "Ana gradient: -0.0264338891645\n",
318 |       "Num gradient: -0.0383646932889\n"
319 |      ]
320 |     }
321 |    ],
322 |    "source": [
323 |     "name = 'amp'\n",
324 |     "f = lambda x: (gp.L(X, y), gp.L(X, y, grad=True)[1][name])\n",
325 |     "ana_grad, num_grad = check_grad(f, gp.params[name], h=1e-5, verbose=1)\n",
326 |     "print \"Ana gradient:\", ana_grad\n",
327 |     "print \"Num gradient:\", num_grad"
328 |    ]
329 |   },
330 |   {
331 |    "cell_type": "code",
332 |    "execution_count": 12,
333 |    "metadata": {
334 |     "collapsed": false,
335 |     "scrolled": true
336 |    },
337 |    "outputs": [
338 |     {
339 |      "name": "stdout",
340 |      "output_type": "stream",
341 |      "text": [
342 |       "Numerical v. analytical gradient difference:\n",
343 |       "0.0\n",
344 |       "Max deviation: 0.0\n",
345 |       "Ana gradient: 0.0\n",
346 |       "Num gradient: 0.0\n"
347 |      ]
348 |     }
349 |    ],
350 |    "source": [
351 |     "name = 'noise'\n",
352 |     "f = lambda x: (gp.L(X, y), gp.L(X, y, grad=True)[1][name])\n",
353 |     "ana_grad, num_grad = check_grad(f, gp.params[name], h=1e-5, verbose=1)\n",
354 |     "print \"Ana gradient:\", ana_grad\n",
355 |     "print \"Num gradient:\", num_grad"
356 |    ]
357 |   },
358 |   {
359 |    "cell_type": "code",
360 |    "execution_count": 18,
361 |    "metadata": {
362 |     "collapsed": false,
363 |     "scrolled": true
364 |    },
365 |    "outputs": [
366 |     {
367 |      "name": "stdout",
368 |      "output_type": "stream",
369 |      "text": [
370 |       "Batch size larger than sample size. Reducing it to. 67\n",
371 |       "Epoch: 1 Negative log likelihood: 10.4488791064\n",
372 |       "Epoch: 2 Negative log likelihood: 8.77794575183\n",
373 |       "Epoch: 3 Negative log likelihood: 7.02011137203\n",
374 |       "Epoch: 4 Negative log likelihood: 4.67777952181\n",
375 |       "Epoch: 5 Negative log likelihood: 1.94095366678\n",
376 |       "Epoch: 6 Negative log likelihood: 0.133018449251\n",
377 |       "Epoch: 7 Negative log likelihood: -0.589810677274\n",
378 |       "Epoch: 8 Negative log likelihood: -0.886640464514\n",
379 |       "Epoch: 9 Negative log likelihood: -1.03350597035\n",
380 |       "Epoch: 10 Negative log likelihood: -1.11859571878\n",
381 |       "********************************************************************************\n",
382 |       "Final negative log likelihood -1.11859571878\n",
383 |       "Final parameters:\n",
384 |       "amp : 0.269161863125\n",
385 |       "noise : 0.05\n",
386 |       "ls : [ 0.25104884]\n",
387 |       "keps : 1e-09\n",
388 |       "********************************************************************************\n"
389 |      ]
390 |     },
391 |     {
392 |      "data": {
393 |       "text/plain": [
394 |        "<tgp.np.gaussian_process.GaussianProcess at 0x102cd5350>"
395 |       ]
396 |      },
397 |      "execution_count": 18,
398 |      "metadata": {},
399 |      "output_type": "execute_result"
400 |     }
401 |    ],
402 |    "source": [
403 |     "# make some random data\n",
404 |     "np.random.seed(45)\n",
405 |     "n = 67\n",
406 |     "X = np.random.uniform(0., 1, (n, 1))\n",
407 |     "y = np.squeeze(np.sin(X*10)) + np.random.randn(len(X))*.1\n",
408 |     "\n",
409 |     "gp = GP(ls=[.5],\n",
410 |     "       amp=.1,\n",
411 |     "       noise=5e-2)\n",
412 |     "gp.fit(X, y, nepochs=10, batch_size=1000, learning_rate=1e-3, learning_rate_decay=.999, verbose=1)"
413 |    ]
414 |   },
415 |   {
416 |    "cell_type": "code",
417 |    "execution_count": 19,
418 |    "metadata": {
419 |     "collapsed": false
420 |    },
421 |    "outputs": [
422 |     {
423 |      "data": {
424 |       "text/plain": [
425 |        "[<matplotlib.lines.Line2D at 0x1038d6b10>]"
426 |       ]
427 |      },
428 |      "execution_count": 19,
429 |      "metadata": {},
430 |      "output_type": "execute_result"
431 |     },
432 |     {
433 |      "data": {
434 |       "image/png": 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IFqUUU2+bw89pvniaoU29dYy/f2SNn4WImnUw9SAlmQsI8i/lTDLsXgP/PAu7a3CfZUcI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\nAElFTkSuQmCC\n",
435 |       "text/plain": [
436 |        "<matplotlib.figure.Figure at 0x1091ca550>"
437 |       ]
438 |      },
439 |      "metadata": {},
440 |      "output_type": "display_data"
441 |     }
442 |    ],
443 |    "source": [
444 |     "X_ = np.linspace(0, 1, 1000).reshape(-1, 1)\n",
445 |     "y_, var = gp.predict(X_)\n",
446 |     "plt.scatter(X, y, c='r')\n",
447 |     "plt.plot(X_, y_ + var**.5, c='g')\n",
448 |     "plt.plot(X_, y_ - var**.5, c='g')\n",
449 |     "plt.plot(X_, y_, c='y', linewidth=2)"
450 |    ]
451 |   },
452 |   {
453 |    "cell_type": "markdown",
454 |    "metadata": {},
455 |    "source": [
456 |     "### Higher Dimensions"
457 |    ]
458 |   },
459 |   {
460 |    "cell_type": "code",
461 |    "execution_count": null,
462 |    "metadata": {
463 |     "collapsed": false
464 |    },
465 |    "outputs": [],
466 |    "source": [
467 |     "np.random.seed(45)\n",
468 |     "n = 1000\n",
469 |     "dim = 7\n",
470 |     "X = np.random.uniform(0, 1, (n, dim))\n",
471 |     "ls = [.1, .2, .4, .8, 1.6, 3.2, 6.4]\n",
472 |     "amp = 10.\n",
473 |     "noise = 0.001\n",
474 |     "sqdist = GP.compute_sqdist(X/ls)\n",
475 |     "K = amp**2 * np.exp(-0.5 * sqdist)\n",
476 |     "A = np.linalg.cholesky( K + np.eye(n)*1e-9 )\n",
477 |     "y = A.dot(np.random.randn(n, 1))"
478 |    ]
479 |   },
480 |   {
481 |    "cell_type": "code",
482 |    "execution_count": null,
483 |    "metadata": {
484 |     "collapsed": false
485 |    },
486 |    "outputs": [],
487 |    "source": [
488 |     "shuffle = np.random.permutation(len(X))\n",
489 |     "X = X[shuffle]\n",
490 |     "y = y[shuffle]\n",
491 |     "mask = len(X)/3*2\n",
492 |     "X_train, y_train = X[:mask], y[:mask]\n",
493 |     "X_test, y_test = X[mask:], y[mask:]"
494 |    ]
495 |   },
496 |   {
497 |    "cell_type": "code",
498 |    "execution_count": null,
499 |    "metadata": {
500 |     "collapsed": false
501 |    },
502 |    "outputs": [],
503 |    "source": [
504 |     "gp = GP(lsr=(.1, .2, 7),\n",
505 |     "       amp=1.,\n",
506 |     "       noise=1e-2)\n",
507 |     "gp.fit(X_train, y_train, \n",
508 |     "       nepochs=500, batch_size=500, learning_rate=1e-2, \n",
509 |     "       learning_rate_decay=.999, \n",
510 |     "       verbose=2)\n",
511 |     "y_, var = gp.predict(X_train)\n",
512 |     "print \"mse:\", ((y_train - y_)**2).mean()/np.var(y_train)\n",
513 |     "y_, var = gp.predict(X_test)\n",
514 |     "print \"mse:\", ((y_test - y_)**2).mean()/np.var(y_test)\n",
515 |     "print \"mse:\", ((y_test - y_train.mean())**2).mean()/np.var(y_test)"
516 |    ]
517 |   },
518 |   {
519 |    "cell_type": "code",
520 |    "execution_count": null,
521 |    "metadata": {
522 |     "collapsed": true
523 |    },
524 |    "outputs": [],
525 |    "source": [
526 |     "from sklearn.ensemble import RandomForestRegressor as RF"
527 |    ]
528 |   },
529 |   {
530 |    "cell_type": "code",
531 |    "execution_count": null,
532 |    "metadata": {
533 |     "collapsed": false
534 |    },
535 |    "outputs": [],
536 |    "source": [
537 |     "rf = RF(n_estimators=1000).fit(X_train, np.squeeze(y_train))\n",
538 |     "\n",
539 |     "y_ = rf.predict(X_train)\n",
540 |     "print \"mse:\", ((np.squeeze(y_train) - y_)**2).mean()/np.var(y_train)\n",
541 |     "y_ = rf.predict(X_test)\n",
542 |     "print \"mse:\", ((np.squeeze(y_test) - y_)**2).mean()/np.var(y_test)"
543 |    ]
544 |   }
545 |  ],
546 |  "metadata": {
547 |   "kernelspec": {
548 |    "display_name": "Python 2",
549 |    "language": "python",
550 |    "name": "python2"
551 |   },
552 |   "language_info": {
553 |    "codemirror_mode": {
554 |     "name": "ipython",
555 |     "version": 2
556 |    },
557 |    "file_extension": ".py",
558 |    "mimetype": "text/x-python",
559 |    "name": "python",
560 |    "nbconvert_exporter": "python",
561 |    "pygments_lexer": "ipython2",
562 |    "version": "2.7.10"
563 |   }
564 |  },
565 |  "nbformat": 4,
566 |  "nbformat_minor": 0
567 | }
568 | 


--------------------------------------------------------------------------------
/tgp/.idea/test.py:
--------------------------------------------------------------------------------
 1 | import tensorflow as tf
 2 | 
 3 | sess1 = tf.Session(config=tf.ConfigProto(
 4 |     inter_op_parallelism_threads=1, intra_op_parallelism_threads=1
 5 | ))
 6 | sess2 = tf.Session(config=tf.ConfigProto(
 7 |     inter_op_parallelism_threads=1, intra_op_parallelism_threads=1
 8 | ))
 9 | 
10 | a = tf.Variable(1.)
11 | d = tf.Variable([1., 1.])
12 | add = tf.assign_add(a, 1.)
13 | b = tf.assign(tf.Variable(a, trainable=True), a)
14 | c = tf.convert_to_tensor(a)
15 | sess1.run(tf.initialize_all_variables())
16 | sess2.run(tf.initialize_all_variables())
17 | print sess1.run(a)
18 | print sess1.run(b)
19 | sess1.run(add)
20 | sess1.run(add)
21 | sess1.run(add)
22 | print sess1.run(b)
23 | print sess1.run(c)
24 | print tf.trainable_variables()
25 | 
26 | loss_a = tf.square(a)
27 | loss_b = (b - d[0])*(10 - d[0])
28 | loss_c = tf.square(c)
29 | 
30 | print sess1.run(loss_b)
31 | train = tf.train.GradientDescentOptimizer(0.01).minimize(loss_b)
32 | 
33 | for _ in xrange(100):
34 |     sess1.run(train)
35 | 
36 | 
37 | print sess1.run(a)
38 | print sess1.run(b)
39 | print sess1.run(c)
40 | print sess1.run(loss_b)
41 | print sess1.run(d)
42 | print sess2.run(b)
43 | 


--------------------------------------------------------------------------------
/tgp/.idea/test2.py:
--------------------------------------------------------------------------------
 1 | import tensorflow as tf
 2 | sess1 = tf.Session(config=tf.ConfigProto(
 3 |     inter_op_parallelism_threads=1, intra_op_parallelism_threads=1
 4 | ))
 5 | sess2 = tf.Session(config=tf.ConfigProto(
 6 |     inter_op_parallelism_threads=1, intra_op_parallelism_threads=1
 7 | ))
 8 | 
 9 | a = tf.Variable(1.)
10 | b = tf.assign(tf.Variable(2.), a+10)
11 | sess1.run(tf.initialize_all_variables())
12 | sess2.run(tf.initialize_all_variables())
13 | sess1.run(tf.assign(a, 100))
14 | print sess1.run(a)
15 | print sess1.run(b)
16 | print sess2.run(a)
17 | print sess2.run(b)
18 | 


--------------------------------------------------------------------------------
/tgp/.idea/zero.py:
--------------------------------------------------------------------------------
1 | import tensorflow as tf
2 | # sess = tf.Session()
3 | # sess.run(tf.div(0,0))
4 | 


--------------------------------------------------------------------------------
/tgp/__init__.py:
--------------------------------------------------------------------------------
https://raw.githubusercontent.com/RuiShu/tensorflow-gp/45f48c93475de7e49658745b34536a74c9cb6380/tgp/__init__.py


--------------------------------------------------------------------------------
/tgp/gradient_check.py:
--------------------------------------------------------------------------------
 1 | import numpy as np
 2 | 
 3 | def check_grad(f, x, h=1e-4, verbose=0):
 4 |     """ checks whether the computed gradient is correct
 5 |     
 6 |     Parameters
 7 |     ----------
 8 |     f : lambda function
 9 |         Takes in a particular argument x and computes the loss and gradient 
10 |         w.r.t. x
11 |     x : np.array
12 |         A parameter (or array of parameters) to be passed into f
13 |     h : float
14 |         The discrete step used for central difference 
15 |     """
16 |     max_dev = -np.inf
17 |     if type(x) == np.ndarray and x.shape is not ():
18 |         it = np.nditer(x, flags=['multi_index'], op_flags=['readwrite'])
19 |         _, ana_grad = f(x)
20 |         num_grad = np.zeros_like(ana_grad)
21 |         while not it.finished:
22 |             ix = it.multi_index
23 |             x[ix] += h/2
24 |             fxph, _ = f(x) 
25 |             x[ix] -= h
26 |             fxmh, _ = f(x) 
27 |             x[ix] += h/2
28 |             num_grad[ix] = (fxph - fxmh) / h
29 |             if verbose > 1:
30 |                 print "Numeric:", num_grad[ix]
31 |                 print "Analytic:", ana_grad[ix]
32 |             if verbose > 0:
33 |                 diff = ana_grad[ix] - num_grad[ix]
34 |                 if abs(diff).max() > max_dev:
35 |                     max_dev = abs(diff).max()
36 |                 print "Numerical v. analytical gradient difference:\n", diff
37 |             it.iternext()
38 |     elif type(x) == np.ndarray and x.shape is ():
39 |         _, ana_grad = f(x)
40 |         original = x
41 |         x += h/2
42 |         fxph, _ = f(x)
43 |         x -= h
44 |         fxmh, _ = f(x)
45 |         x += h/2
46 |         num_grad = (fxph - fxmh) / h
47 |         if verbose > 1:
48 |             print "Numeric:", num_grad
49 |             print "Analytic:", ana_grad
50 |         if verbose > 0:
51 |             diff = ana_grad - num_grad
52 |             if abs(diff).max() > max_dev:
53 |                 max_dev = abs(diff).max()
54 |             print "Numerical v. analytical gradient difference:\n", diff
55 |     if verbose:
56 |         print "Max deviation:", max_dev
57 |     return ana_grad, num_grad
58 | 
59 | if __name__ == "__main__":
60 |     f = lambda x: (x.sum(), np.ones_like(x))
61 |     check_grad(f, x=np.random.randn(3, 3), verbose=True)
62 | 


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/tgp/np/__init__.py:
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https://raw.githubusercontent.com/RuiShu/tensorflow-gp/45f48c93475de7e49658745b34536a74c9cb6380/tgp/np/__init__.py


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/tgp/np/gaussian_process.py:
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  1 | """
  2 | gaussian_process.py
  3 | -------------------
  4 | This module performs basic Gaussian process regression using the squared
  5 | exponential kernel. 
  6 | 
  7 | Author: Rui Shu
  8 | """
  9 | 
 10 | import numpy as np
 11 | from numpy.linalg import cholesky as chol 
 12 | 
 13 | class GaussianProcess(object):
 14 |     def __init__(self, ls=None, amp=None, noise=None, 
 15 |                  lsr=(.1, .2, 1), ampr=(1., 2.), noiser=(.1, .2), 
 16 |                  keps=1e-9):
 17 |         """ Gaussian Process Class
 18 | 
 19 |         Initialization of Gaussian process hyperparameters
 20 | 
 21 |         Parameters
 22 |         ----------
 23 |         ls : (n_dim,) array/list of floats
 24 |             Array of length scales to be used
 25 |         amp : float
 26 |             Amplitude parameter in kernel
 27 |         noise : float
 28 |             Noise parameter in kernel
 29 |         lsr : 3-tuple (float, float, int)
 30 |             The range for random initializtion, and ndim number of ls's
 31 |         ampr : 2-tuple (float, float)
 32 |             The range of random initialization for amp 
 33 |         noiser : 2-tuple (float, float)
 34 |             The range of random initialization for noise 
 35 |         keps : float
 36 |             Small constant added to diag of kernel matrix for stability
 37 |         """
 38 |         # parameters for non-learning
 39 |         self.params = {}
 40 |         self.params['ls'] = (np.array(ls) if ls is not None
 41 |                              else np.random.uniform(*tuple(lsr)))
 42 |         self.params['amp'] = (np.array(amp) if amp is not None
 43 |                               else np.random.uniform(*tuple(ampr)))
 44 |         self.params['noise'] = (np.array(noise) if noise is not None
 45 |                                 else np.random.uniform(*tuple(noiser)))
 46 |         self.params['keps'] = keps
 47 |         # self.Ki stores the inverse of the kernel
 48 |         self.Ki = None
 49 |         
 50 |     def fit(self, X, y, nepochs=1000, batch_size=None, train=True,
 51 |             learning_rate=1e-1, learning_rate_decay=1.,
 52 |             verbose=0):
 53 |         """ Feeds in input data and trains parameters of the GP if desired
 54 |         
 55 |         Parameters
 56 |         ----------
 57 |         X : (n_samples, n_dim) float matrix
 58 |             independent variables
 59 |         y : (n_samples,) float matrix
 60 |             response variable
 61 |         train : boolean
 62 |             Whether to train parameters or not
 63 |         """
 64 |         # Preprocess:
 65 |         X = np.atleast_2d(X).astype(float)
 66 |         y = y.reshape(-1, 1).astype(float)
 67 |         # Scale to unit hypercube
 68 |         y_m = y.mean()
 69 |         y_scale = y.max() - y.min()
 70 |         X_m = X.min(axis=0)
 71 |         X_scale = X.max(axis=0) - X.min()
 72 |         # Check for scale being 0
 73 |         y_scale = y_scale if y_scale > 0 else 1.
 74 |         X_scale[X_scale <= 0] = 1.
 75 |         self.transform = {'ym': y_m,
 76 |                           'ys': y_scale,
 77 |                           'Xm': X_m,
 78 |                           'Xs': X_scale}
 79 |         X = (X - X_m)/X_scale
 80 |         y = (y - y_m)/y_scale
 81 | 
 82 |         if train:
 83 |             self.train(X, y, nepochs, batch_size, 
 84 |                        learning_rate, learning_rate_decay,
 85 |                        verbose)
 86 |         
 87 |         K = self.K(X)
 88 |         self.Ki = np.linalg.inv(K)
 89 |         self.X = X
 90 |         self.y = y
 91 |         return self
 92 |         
 93 |     def train(self, X, y, nepochs, batch_size, learning_rate,
 94 |               learning_rate_decay, verbose):
 95 |         """ Update parameters via gradient ascend to maximize marginal log
 96 |         likelihood.
 97 |         """
 98 |         batch_size = len(X) if batch_size is None else batch_size
 99 |         if batch_size > len(X):
100 |             string = "Batch size larger than sample size. Reducing it to. {0:d}"
101 |             print string.format(len(X))
102 |             batch_size = len(X)
103 |         batch_count = 0
104 | 
105 |         # Compute the frequency with which print statements should arrive
106 |         # I expect at least 10 epoch print outs
107 |         
108 |         for epoch in xrange(1, nepochs+1):
109 |             shuffle = np.random.permutation(len(X))
110 |             X = X[shuffle]
111 |             y = y[shuffle]
112 |             nbatch = len(X)/batch_size  # good enough approximation
113 |             for i in xrange(nbatch):
114 |                 batch_count += 1
115 |                 X_batch = X[i*batch_size : (i+1)*batch_size]
116 |                 y_batch = y[i*batch_size : (i+1)*batch_size]
117 |                 L, dL = self.L(X_batch, y_batch, grad=True)
118 |                 print dL['ls']
119 |                 for key in ['ls', 'amp']:
120 |                     self.params[key] += learning_rate * dL[key]
121 |                     if verbose > 2:
122 |                         print key, ":", self.params[key]
123 |                         print key, "gradient:", dL[key]
124 |                 if batch_count % 100 == 0 and verbose > 1:
125 |                     print "...Batch:", batch_count, "Negative log likelihood:", -L
126 |             if epoch % (nepochs/10) == 0 and verbose > 0:
127 |                 print "Epoch:", epoch, "Negative log likelihood:", -L
128 | 
129 |         if verbose > 0:
130 |             print "*"*80
131 |             print "Final negative log likelihood", -L
132 |             print "Final parameters:"
133 |             for key in self.params:
134 |                 print key, ":", self.params[key]
135 |             print "*"*80
136 |                 
137 |     def L(self, X, y, grad=False):
138 |         """ Computes the log likelihood and returns the gradient w.r.t. ls, amp,
139 |         and noise if desired.
140 |         """
141 |         # Set up cache
142 |         cache = {}
143 |         K = self.K(X)
144 |         Ki = np.linalg.inv(K)
145 |         Kiy = Ki.dot(y)
146 |         norm = len(X)
147 |         cache['K'] = K
148 |         cache['Ki'] = Ki
149 |         cache['Kiy'] = Kiy
150 |         cache['norm'] = norm
151 |         # Compute L and dL
152 |         L = -0.5*y.T.dot(Kiy).sum() - np.log(np.diag(chol(K))).sum()
153 |         L -= len(X)/2 * np.log(2*np.pi)
154 |         if grad:
155 |             return L/norm, self.L_grad(X, y, cache)
156 |         else:
157 |             return L/norm
158 | 
159 |     def L_grad(self, X, y, cache=None):
160 |         """ Computes the gradient of the log likelihood w.r.t. ls, amp, and
161 |         noise.
162 |         """
163 |         if cache is None:
164 |             K = self.K(X)
165 |             Ki = np.linalg.inv(K)
166 |             Kiy = Ki.dot(y)
167 |             norm = len(X)
168 |         else:
169 |             K = cache['K']
170 |             Ki = cache['Ki']
171 |             Kiy = cache['Kiy']
172 |             norm = cache['norm']
173 |         pre = Kiy.dot(Kiy.T) - Ki
174 |         dK = self.K_grad(X)
175 |         grads = {}
176 |         grads['ls'] = np.zeros(len(dK['ls']))
177 |         for i in xrange(len(dK['ls'])):
178 |             grads['ls'][i] = np.sum(np.diag(pre.dot(dK['ls'][i])))/norm/2
179 |         grads['amp'] = np.sum(np.diag(pre.dot(dK['amp'])))/norm/2
180 |         grads['noise'] = np.sum(np.diag(pre.dot(dK['noise'])))/norm/2
181 |         return grads
182 |     
183 |     def K(self, X, grad=False):
184 |         """ Computes the covariance matrix using X and returns the gradient
185 |         w.r.t. ls, amp, and noise if desired.
186 |         """
187 |         keps = self.params['keps']
188 |         noise = self.params['noise']
189 |         K = (
190 |             self.compute_kernel(X) +
191 |             (keps + noise**2)*np.eye(len(X))
192 |         )
193 |         if grad:
194 |             return K, self.K_grad(X)
195 |         else:
196 |             return K
197 |         
198 |     def K_grad(self, X):
199 |         """ Computes the gradient of the covariance matrix element-wise
200 |         w.r.t. ls, amp, and noise.
201 |         """
202 |         ls = self.params['ls']
203 |         amp = self.params['amp']
204 |         noise = self.params['noise']
205 |         grads = {}
206 |         # Compute dK w.r.t. noise
207 |         grads['noise'] = 2*noise*np.eye(len(X))
208 |         # Compute dK w.r.t. amp
209 |         sqdist = self.compute_sqdist(X/ls)
210 |         grads['amp'] = 2*amp * np.exp(-0.5*sqdist)
211 |         # Compute dK w.r.t. ls
212 |         grads['ls'] = []
213 |         precompute = amp**2 * np.exp(-0.5*sqdist)
214 |         for i in xrange(X.shape[1]):
215 |             val = precompute/ls[i]**3
216 |             val *= self.compute_sqdist(X[:, i, None])
217 |             grads['ls'].append(val)
218 |         grads['ls'] = np.array(grads['ls'])
219 |         return grads
220 | 
221 |     def compute_kernel(self, X, Y=None):
222 |         """ Compue the kernel matrix for X x Y, keeping in mind the scaling
223 |         w.r.t. ls
224 |         """
225 |         ls = self.params['ls']
226 |         amp = self.params['amp']
227 |         noise = self.params['noise']
228 |         if Y is None:
229 |             sqdist = self.compute_sqdist(X/ls)
230 |         else:
231 |             sqdist = self.compute_sqdist(X/ls, Y/ls)
232 |         return amp**2 * np.exp(-0.5*sqdist)
233 | 
234 |     @staticmethod
235 |     def compute_sqdist(X, Y=None):
236 |         """ Compute the square distance between the rows of X v. Y
237 |         """
238 |         if Y is None:
239 |             a = (X**2).sum(axis=1).reshape(-1, 1)
240 |             b = a.T
241 |             c = X.dot(X.T)
242 |         else:
243 |             a = (X**2).sum(axis=1).reshape(-1, 1)
244 |             b = (Y**2).sum(axis=1)
245 |             c = X.dot(Y.T)
246 |         return a + b - 2*c
247 | 
248 |     def predict(self, X_):
249 |         """ Predict w.r.t. X_
250 |         """
251 |         # Push X_ into hypercube
252 |         X_ = (X_ - self.transform['Xm'])/self.transform['Xs']
253 |         K_ = self.compute_kernel(self.X, X_)
254 |         y_ = K_.T.dot(self.Ki).dot(self.y)
255 |         # Compute variance
256 |         var = self.params['amp']**2 - (K_.T * K_.T.dot(self.Ki)).sum(axis=1)
257 |         var = (var * self.transform['ys']**2).reshape(-1, 1)
258 |         # Convert y_ back to original input space
259 |         y_ = y_ * self.transform['ys'] + self.transform['ym']
260 |         return y_, var
261 | 
262 | def main():
263 |     import matplotlib.pyplot as plt
264 |     # make some random data
265 |     # np.random.seed(45)
266 |     n = 10
267 |     X = np.random.uniform(0., 1, (n, 1))
268 |     y = np.squeeze(np.sin(X*10)) + np.random.randn(len(X))*.1
269 | 
270 |     gp = GaussianProcess(ls=[.1],
271 |                          amp=.1,
272 |                          noise=2e-2)
273 |     gp.fit(X, y, nepochs=100, batch_size=1000,
274 |            learning_rate=1e-2, learning_rate_decay=.999,
275 |            verbose=1)
276 |     X_ = np.linspace(0, 1, 1000).reshape(-1, 1)
277 |     y_, var = gp.predict(X_)
278 |     plt.scatter(X, y, c='r')
279 |     plt.plot(X_, y_ + var**.5, c='g')
280 |     plt.plot(X_, y_ - var**.5, c='g')
281 |     plt.plot(X_, y_, c='y', linewidth=2)
282 |     plt.show()
283 |     
284 | if __name__ == "__main__":
285 |     main()
286 |                     
287 |         
288 | 


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/tgp/tf/gaussian_process.py:
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  1 | import sys
  2 | sys.path.append('/Users/void/Documents/github/tensorflow-gp')
  3 | from tgp.np.gaussian_process import GaussianProcess as GP
  4 | import numpy as np
  5 | import tensorflow as tf
  6 | 
  7 | class DoubleAdamOptimizer(tf.train.AdamOptimizer):
  8 |   def _valid_dtypes(self):
  9 |     return set([tf.float32, tf.float64])
 10 | 
 11 | class GaussianProcess(object):
 12 |     def __init__(self, ls=.1, amp=.1, noise=1e-2, sess=tf.Session(), dim=1):
 13 |       self.sess = sess
 14 |       self.ls = tf.Variable(np.array(ls))
 15 |       self.amp = tf.Variable(np.array(amp))
 16 |       self.noise = tf.Variable(np.array(noise))
 17 |       # construct loss computation graph
 18 |       self.xp = tf.placeholder(tf.float64, [None, dim])
 19 |       self.yp = tf.placeholder(tf.float64, [None, 1])
 20 |       self.x_p = tf.placeholder(tf.float64, [None, dim])
 21 |       self.L = self.construct_loss_graph()
 22 |       # construct prediction computation graph
 23 |       self.y_, self.var_ = self.construct_prediction_graph()
 24 |       # set up optimizer
 25 |       opt = DoubleAdamOptimizer(
 26 |         learning_rate=tf.constant(1e-3, tf.float64),
 27 |         beta1=tf.constant(0.9, tf.float64),
 28 |         beta2=tf.constant(0.999, tf.float64),
 29 |         epsilon=tf.constant(1e-8, tf.float64)
 30 |       )
 31 |       self.opt_op = opt.minimize(self.L, var_list=[self.ls, self.amp])
 32 |       self.grad_ls = tf.gradients(self.L, self.ls)
 33 |       self.grad_amp = tf.gradients(self.L, self.amp)
 34 |       self.init = tf.initialize_all_variables()
 35 |       
 36 |     def construct_covariance_graph(self, xs, ys=None):
 37 |       add_noise = True if ys is None else False
 38 |       ys = xs if ys is None else ys
 39 |       # Compute covariance matrix K
 40 |       xsq = tf.reduce_sum(tf.square(xs), 1)
 41 |       ysq = tf.reduce_sum(tf.square(ys), 1)
 42 |       xsq = tf.reshape(xsq, tf.pack([tf.shape(xsq)[0], 1]))
 43 |       ysq = tf.reshape(ysq, tf.pack([1, tf.shape(ysq)[0]]))
 44 |       sqdist = xsq + ysq - 2*tf.matmul(xs, tf.transpose(ys))
 45 |       K = tf.square(self.amp) * tf.exp(-0.5*sqdist)
 46 |       if add_noise:
 47 |         ones = tf.ones(tf.pack([tf.shape(xs)[0]]), dtype=tf.float64)
 48 |         K = K + tf.diag(ones)*(1e-9 + tf.square(self.noise))
 49 |         # compute loss
 50 |         Ki = tf.matrix_inverse(K)
 51 |         return K, Ki
 52 |       else:
 53 |         return K
 54 |       
 55 |     def construct_loss_graph(self):
 56 |       x = self.xp
 57 |       y = self.yp
 58 |       xs = x/self.ls
 59 |       K, Ki = self.construct_covariance_graph(xs)
 60 |       yT = tf.transpose(y)
 61 |       Kiy = tf.matmul(Ki, y)
 62 |       lK = tf.log(tf.matrix_determinant(K))
 63 |       L = tf.matmul(yT, Kiy) + lK
 64 |       ones = tf.ones(tf.pack([tf.shape(xs)[0]]), dtype=tf.float64)
 65 |       L = L/tf.reduce_sum(ones) * 0.5
 66 |       return L
 67 | 
 68 |     def construct_prediction_graph(self):
 69 |       x = self.xp
 70 |       y = self.yp
 71 |       x_ = self.x_p
 72 |       xs = x/self.ls
 73 |       xs_ = x_/self.ls
 74 |       _, Ki = self.construct_covariance_graph(xs)
 75 |       K_ = self.construct_covariance_graph(xs, xs_)
 76 |       # compute variance
 77 |       K_T = tf.transpose(K_)
 78 |       K_Ki = tf.matmul(K_T, Ki)
 79 |       var_ = tf.square(self.amp) - tf.reduce_sum(K_T * K_Ki, 1)
 80 |       # compute prediction
 81 |       y_ = tf.matmul(K_T, tf.matmul(Ki, y))
 82 |       return y_, var_
 83 |     
 84 |     def solve(self, X, y, epochs=20, batch_size=50, train=True):
 85 |       self.X = X
 86 |       self.y = y
 87 |       self.sess.run(self.init)
 88 |       if train:
 89 |         iterations = epochs * len(X) / batch_size
 90 |         epochiter = iterations/epochs
 91 |         for i in xrange(iterations):
 92 |           idx = np.random.choice(np.arange(len(X)), batch_size, replace=False)
 93 |           X_mini = X[idx]
 94 |           y_mini = y[idx]
 95 |           fd = {self.xp: X_mini, self.yp: y_mini}
 96 |           if i % epochiter == 0:
 97 |             print self.sess.run(self.L, feed_dict=fd)
 98 |           self.sess.run(self.opt_op, fd)
 99 | 
100 |     def predict(self, X_):
101 |       fd = {self.xp: self.X, self.yp: self.y, self.x_p: X_}
102 |       y_ = self.sess.run(self.y_, feed_dict=fd)
103 |       var_ = self.sess.run(self.var_, feed_dict=fd)
104 |       return y_, var_
105 |         
106 | def main():
107 |   import matplotlib.pyplot as plt
108 |   dim = 1
109 |   X = np.random.uniform(0, 1, (10, dim))
110 |   y = (np.sin((X[:, 0])*10) - X[:,0]*3).reshape(-1, 1)
111 | 
112 |   ls = [.1]*dim
113 |   sess = tf.Session()
114 |   gp = GaussianProcess(dim=dim, sess=sess, ls=ls, noise=0.1)
115 |   gp.solve(X, y, epochs=100, batch_size=len(X), train=False)
116 |   print sess.run(gp.ls)
117 |   
118 |   X_ = np.linspace(0, 1, 1000).reshape(-1, 1)
119 |   y_, var_ = gp.predict(X_)
120 |   std_ = np.sqrt(var_).reshape(-1, 1)
121 | 
122 |   plt.scatter(X, y)
123 |   plt.plot(X_, y_, c='r')
124 |   plt.plot(X_, y_+2*std_, c='g')
125 |   plt.plot(X_, y_-2*std_, c='g')
126 |   plt.show()
127 |   
128 | 
129 | if __name__ == "__main__":
130 |   main()
131 | 


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/tgp/tf/troubleshoot.ipynb:
--------------------------------------------------------------------------------
  1 | {
  2 |  "cells": [
  3 |   {
  4 |    "cell_type": "code",
  5 |    "execution_count": 8,
  6 |    "metadata": {
  7 |     "collapsed": true
  8 |    },
  9 |    "outputs": [],
 10 |    "source": [
 11 |     "from gaussian_process import GaussianProcess as GP\n",
 12 |     "import matplotlib.pyplot as plt\n",
 13 |     "import numpy as np\n",
 14 |     "import tensorflow as tf\n",
 15 |     "%matplotlib inline"
 16 |    ]
 17 |   },
 18 |   {
 19 |    "cell_type": "code",
 20 |    "execution_count": 24,
 21 |    "metadata": {
 22 |     "collapsed": false
 23 |    },
 24 |    "outputs": [
 25 |     {
 26 |      "data": {
 27 |       "image/png": 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 28 |       "text/plain": [
 29 |        "<matplotlib.figure.Figure at 0x1181da7d0>"
 30 |       ]
 31 |      },
 32 |      "metadata": {},
 33 |      "output_type": "display_data"
 34 |     }
 35 |    ],
 36 |    "source": [
 37 |     "# X = np.linspace(0., 1., 300).reshape(-1, 1).astype(np.float64)\n",
 38 |     "dim = 1\n",
 39 |     "X = np.random.uniform(0, 1, (10, dim))\n",
 40 |     "y = (np.sin((X[:, 0])*10) - X[:,0]*3).reshape(-1, 1)\n",
 41 |     "plt.scatter(X, y)\n",
 42 |     "plt.show()"
 43 |    ]
 44 |   },
 45 |   {
 46 |    "cell_type": "code",
 47 |    "execution_count": 37,
 48 |    "metadata": {
 49 |     "collapsed": false,
 50 |     "scrolled": true
 51 |    },
 52 |    "outputs": [
 53 |     {
 54 |      "name": "stdout",
 55 |      "output_type": "stream",
 56 |      "text": [
 57 |       "[[-0.15558379]]\n",
 58 |       "[[-0.16170398]]\n",
 59 |       "[[-0.16779481]]\n",
 60 |       "[[-0.17385392]]\n",
 61 |       "[[-0.17987888]]\n",
 62 |       "[[-0.18586716]]\n",
 63 |       "[[-0.19181617]]\n",
 64 |       "[[-0.19772328]]\n",
 65 |       "[[-0.20358581]]\n",
 66 |       "[[-0.20940105]]\n",
 67 |       "[[-0.21516629]]\n",
 68 |       "[[-0.22087881]]\n",
 69 |       "[[-0.22653591]]\n",
 70 |       "[[-0.2321349]]\n",
 71 |       "[[-0.23767316]]\n",
 72 |       "[[-0.2431481]]\n",
 73 |       "[[-0.24855719]]\n",
 74 |       "[[-0.25389799]]\n",
 75 |       "[[-0.25916812]]\n",
 76 |       "[[-0.26436531]]\n",
 77 |       "[[-0.2694874]]\n",
 78 |       "[[-0.27453232]]\n",
 79 |       "[[-0.27949814]]\n",
 80 |       "[[-0.28438304]]\n",
 81 |       "[[-0.28918533]]\n",
 82 |       "[[-0.29390346]]\n",
 83 |       "[[-0.29853604]]\n",
 84 |       "[[-0.30308177]]\n",
 85 |       "[[-0.30753955]]\n",
 86 |       "[[-0.31190839]]\n",
 87 |       "[[-0.31618746]]\n",
 88 |       "[[-0.32037607]]\n",
 89 |       "[[-0.32447368]]\n",
 90 |       "[[-0.32847988]]\n",
 91 |       "[[-0.33239443]]\n",
 92 |       "[[-0.3362172]]\n",
 93 |       "[[-0.33994819]]\n",
 94 |       "[[-0.34358756]]\n",
 95 |       "[[-0.34713557]]\n",
 96 |       "[[-0.3505926]]\n",
 97 |       "[[-0.35395917]]\n",
 98 |       "[[-0.35723589]]\n",
 99 |       "[[-0.36042348]]\n",
100 |       "[[-0.36352276]]\n",
101 |       "[[-0.36653465]]\n",
102 |       "[[-0.36946014]]\n",
103 |       "[[-0.37230032]]\n",
104 |       "[[-0.37505636]]\n",
105 |       "[[-0.37772949]]\n",
106 |       "[[-0.380321]]\n",
107 |       "[[-0.38283225]]\n",
108 |       "[[-0.38526466]]\n",
109 |       "[[-0.38761969]]\n",
110 |       "[[-0.38989885]]\n",
111 |       "[[-0.39210368]]\n",
112 |       "[[-0.39423576]]\n",
113 |       "[[-0.39629672]]\n",
114 |       "[[-0.39828818]]\n",
115 |       "[[-0.40021181]]\n",
116 |       "[[-0.40206928]]\n",
117 |       "[[-0.4038623]]\n",
118 |       "[[-0.40559257]]\n",
119 |       "[[-0.40726179]]\n",
120 |       "[[-0.40887168]]\n",
121 |       "[[-0.41042396]]\n",
122 |       "[[-0.41192034]]\n",
123 |       "[[-0.41336254]]\n",
124 |       "[[-0.41475226]]\n",
125 |       "[[-0.41609118]]\n",
126 |       "[[-0.41738098]]\n",
127 |       "[[-0.41862333]]\n",
128 |       "[[-0.41981988]]\n",
129 |       "[[-0.42097225]]\n",
130 |       "[[-0.42208205]]\n",
131 |       "[[-0.42315085]]\n",
132 |       "[[-0.42418023]]\n",
133 |       "[[-0.42517169]]\n",
134 |       "[[-0.42612676]]\n",
135 |       "[[-0.42704689]]\n",
136 |       "[[-0.42793353]]\n",
137 |       "[[-0.42878809]]\n",
138 |       "[[-0.42961194]]\n",
139 |       "[[-0.43040641]]\n",
140 |       "[[-0.43117282]]\n",
141 |       "[[-0.43191243]]\n",
142 |       "[[-0.43262647]]\n",
143 |       "[[-0.43331614]]\n",
144 |       "[[-0.43398258]]\n",
145 |       "[[-0.43462691]]\n",
146 |       "[[-0.43525021]]\n",
147 |       "[[-0.43585352]]\n",
148 |       "[[-0.43643784]]\n",
149 |       "[[-0.43700413]]\n",
150 |       "[[-0.43755331]]\n",
151 |       "[[-0.43808626]]\n",
152 |       "[[-0.43860383]]\n",
153 |       "[[-0.43910683]]\n",
154 |       "[[-0.43959602]]\n",
155 |       "[[-0.44007215]]\n",
156 |       "[[-0.44053592]]\n"
157 |      ]
158 |     }
159 |    ],
160 |    "source": [
161 |     "sess = tf.Session()\n",
162 |     "gp = GP(sess=sess, ls=.1, noise=0.1, amp=1.)\n",
163 |     "gp.solve(X, y, epochs=100, batch_size=len(X), train=True)\n",
164 |     "X_ = np.linspace(0, 1, 1000).reshape(-1, 1)\n",
165 |     "y_, var_ = gp.predict(X_)\n",
166 |     "std_ = np.sqrt(var_).reshape(-1, 1)"
167 |    ]
168 |   },
169 |   {
170 |    "cell_type": "code",
171 |    "execution_count": 38,
172 |    "metadata": {
173 |     "collapsed": false
174 |    },
175 |    "outputs": [
176 |     {
177 |      "data": {
178 |       "text/plain": [
179 |        "<matplotlib.collections.PathCollection at 0x11acb9250>"
180 |       ]
181 |      },
182 |      "execution_count": 38,
183 |      "metadata": {},
184 |      "output_type": "execute_result"
185 |     },
186 |     {
187 |      "data": {
188 |       "image/png": 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dCxF3Y4euHuLQ1UM8CH3A80We54WiL9CkdBMq5a2UrJLwiRsnqD2lNifeP0G2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\n",
189 |       "text/plain": [
190 |        "<matplotlib.figure.Figure at 0x11b723610>"
191 |       ]
192 |      },
193 |      "metadata": {},
194 |      "output_type": "display_data"
195 |     }
196 |    ],
197 |    "source": [
198 |     "plt.plot(X_, y_)\n",
199 |     "plt.plot(X_, y_ + 2*std_, 'g')\n",
200 |     "plt.plot(X_, y_ - 2*std_, 'g')\n",
201 |     "plt.scatter(X, y)"
202 |    ]
203 |   }
204 |  ],
205 |  "metadata": {
206 |   "kernelspec": {
207 |    "display_name": "Python 2",
208 |    "language": "python",
209 |    "name": "python2"
210 |   },
211 |   "language_info": {
212 |    "codemirror_mode": {
213 |     "name": "ipython",
214 |     "version": 2
215 |    },
216 |    "file_extension": ".py",
217 |    "mimetype": "text/x-python",
218 |    "name": "python",
219 |    "nbconvert_exporter": "python",
220 |    "pygments_lexer": "ipython2",
221 |    "version": "2.7.10"
222 |   }
223 |  },
224 |  "nbformat": 4,
225 |  "nbformat_minor": 0
226 | }
227 | 


--------------------------------------------------------------------------------