├── .gitignore ├── LICENSE ├── README.md ├── notebooks ├── Bayesian-LinearRegression.ipynb ├── FirstOrdervsSeconOrderBounds.ipynb ├── PAC2-Ensemble-MultiModalData-NeuralNetwork.ipynb ├── PAC2-Ensemble-SinusoidalData-NeuralNetwork.ipynb ├── PAC2-Variational-LinearRegression.ipynb └── PAC2-Variational-SinusoidalData-NeuralNetwork.ipynb ├── results ├── output-PAC2-Ensemble-SelfSupervisedBinomial.txt ├── output-PAC2-Ensemble-SelfSupervisedNormal.txt ├── output-PAC2-Ensemble-Supervised.txt ├── output-PAC2-Variational-SelfSupervisedBinomial.txt ├── output-PAC2-Variational-SelfSupervisedNormal.txt └── output-PAC2-Variational-Supervised.txt └── scripts ├── PAC2-Ensemble-SelfSupervisedBinomial.py ├── PAC2-Ensemble-SelfSupervisedNormal.py ├── PAC2-Ensemble-Supervised.py ├── PAC2-Variational-SelfSupervisedBinomial.py ├── PAC2-Variational-SelfSupervisedNormal.py └── PAC2-Variational-Supervised.py /.gitignore: -------------------------------------------------------------------------------- 1 | # Byte-compiled / optimized / DLL files 2 | __pycache__/ 3 | *.py[cod] 4 | *$py.class 5 | 6 | # C extensions 7 | *.so 8 | 9 | # Distribution / packaging 10 | .Python 11 | build/ 12 | develop-eggs/ 13 | dist/ 14 | downloads/ 15 | eggs/ 16 | .eggs/ 17 | lib/ 18 | lib64/ 19 | parts/ 20 | sdist/ 21 | var/ 22 | wheels/ 23 | pip-wheel-metadata/ 24 | share/python-wheels/ 25 | *.egg-info/ 26 | .installed.cfg 27 | *.egg 28 | MANIFEST 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 | .nox/ 44 | .coverage 45 | .coverage.* 46 | .cache 47 | nosetests.xml 48 | coverage.xml 49 | *.cover 50 | *.py,cover 51 | .hypothesis/ 52 | .pytest_cache/ 53 | 54 | # Translations 55 | *.mo 56 | *.pot 57 | 58 | # Django stuff: 59 | *.log 60 | local_settings.py 61 | db.sqlite3 62 | db.sqlite3-journal 63 | 64 | # Flask stuff: 65 | instance/ 66 | .webassets-cache 67 | 68 | # Scrapy stuff: 69 | .scrapy 70 | 71 | # Sphinx documentation 72 | docs/_build/ 73 | 74 | # PyBuilder 75 | target/ 76 | 77 | # Jupyter Notebook 78 | .ipynb_checkpoints 79 | 80 | # IPython 81 | profile_default/ 82 | ipython_config.py 83 | 84 | # pyenv 85 | .python-version 86 | 87 | # pipenv 88 | # According to pypa/pipenv#598, it is recommended to include Pipfile.lock in version control. 89 | # However, in case of collaboration, if having platform-specific dependencies or dependencies 90 | # having no cross-platform support, pipenv may install dependencies that don't work, or not 91 | # install all needed dependencies. 92 | #Pipfile.lock 93 | 94 | # PEP 582; used by e.g. github.com/David-OConnor/pyflow 95 | __pypackages__/ 96 | 97 | # Celery stuff 98 | celerybeat-schedule 99 | celerybeat.pid 100 | 101 | # SageMath parsed files 102 | *.sage.py 103 | 104 | # Environments 105 | .env 106 | .venv 107 | env/ 108 | venv/ 109 | ENV/ 110 | env.bak/ 111 | venv.bak/ 112 | 113 | # Spyder project settings 114 | .spyderproject 115 | .spyproject 116 | 117 | # Rope project settings 118 | .ropeproject 119 | 120 | # mkdocs documentation 121 | /site 122 | 123 | # mypy 124 | .mypy_cache/ 125 | .dmypy.json 126 | dmypy.json 127 | 128 | # Pyre type checker 129 | .pyre/ 130 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | Apache License 2 | Version 2.0, January 2004 3 | http://www.apache.org/licenses/ 4 | 5 | TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION 6 | 7 | 1. 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R., Learning under Model Misspecification: Applications to Variational 6 | and Ensemble methods. https://arxiv.org/abs/1912.08335 7 | 8 | 9 | ## Dependencies 10 | 11 | The code is written in Python 3 and uses the following libraries: 12 | * [Tensorflow v1.15.0](https://www.tensorflow.org/) 13 | * [Tensorflow-Probability v0.8.0](https://www.tensorflow.org/probability) 14 | * [Numpy v1.18.4](https://numpy.org/) 15 | 16 | ## Directory structure 17 | 18 | This repository has the following directory structure 19 | * *README*: This file. 20 | * *scripts*: Folder containing the python scripts to reproduce the results of the empirical evaluation of the paper. More details below. 21 | * *results*: Foder containing the ouput of the python scripts included in the folder 'scritps'. 22 | * *notebooks*: Folder containing Jupyter notebooks where all the figures and analysis with artificial data sets can be reprodcued. More details below. 23 | 24 | 25 | 26 | ## Reproduce experiments with real data sets 27 | 28 | Execute the following python scrpits, which are grouped by algorithm and by task. Running each script you get back results for each data set and for each method used in the paper. 29 | 30 | * **PAC^2-Varitional** and **PAC^2_T-Variational** learning algorithms: 31 | 32 | - Supervised classification task: [PAC2-Variational-Supervised.py](https://github.com/PGM-Lab/PAC2BAYES/blob/master/scripts/PAC2-Variational-Supervised.py). 33 | ```console 34 | > python ./scripts/PAC2-Variational-Supervised.py 35 | ``` 36 | 37 | - Self-Supervised classification task with Normal likelihood: [PAC2-Variational-SelfSupervisedNormal.py](https://github.com/PGM-Lab/PAC2BAYES/blob/master/scripts/PAC2-Variational-SelfSupervisedNormal.py). 38 | ```console 39 | > python ./scripts/PAC2-Variational-SelfSupervisedNormal.py 40 | ``` 41 | 42 | - Self-Supervised classification task with Binomial likelihood: [PAC2-Variational-SelfSupervisedBinomial.py](https://github.com/PGM-Lab/PAC2BAYES/blob/master/scripts/PAC2-Variational-SelfSupervisedBinomial.py). 43 | ```console 44 | > python ./scripts/PAC2-Variational-SelfSupervisedBinomial.py 45 | ``` 46 | 47 | * **PAC^2-Ensemble** and **PAC^2_T-Ensemble** learning algorithms: 48 | 49 | - Supervised classification task: [PAC2-Ensemble-Supervised.py](https://github.com/PGM-Lab/PAC2BAYES/blob/master/scripts/PAC2-Ensemble-Supervised.py). 50 | ```console 51 | > python ./scripts/PAC2-Ensemble-Supervised.py 52 | ``` 53 | 54 | - Self-Supervised classification task with Normal likelihood: [PAC2-Ensemble-SelfSupervisedNormal.py](https://github.com/PGM-Lab/PAC2BAYES/blob/master/scripts/PAC2-Ensemble-SelfSupervisedNormal.py). 55 | ```console 56 | > python ./scripts/PAC2-Ensemble-SelfSupervisedNormal.py 57 | ``` 58 | 59 | - Self-Supervised classification task with Binomial likelihood: [PAC2-Ensemble-SelfSupervisedBinomial.py](https://github.com/PGM-Lab/PAC2BAYES/blob/master/scripts/PAC2-Ensemble-SelfSupervisedBinomial.py). 60 | ```console 61 | > python ./scripts/PAC2-Ensemble-SelfSupervisedBinomial.py 62 | ``` 63 | 64 | ## Notebooks 65 | 66 | Each of the figures with artificial data illustrating the algorithms can be reproduced using the following notebooks: 67 | 68 | * [First-order vs Second-order bounds](https://github.com/PGM-Lab/PAC2BAYES/blob/master/notebooks/FirstOrdervsSeconOrderBounds.ipynb) [[Open in Google Colab](http://colab.research.google.com/github/PGM-Lab/PAC2BAYES/blob/master/notebooks/FirstOrdervsSeconOrderBounds.ipynb)]. 69 | 70 | * [Bayesian Linear Regression](https://github.com/PGM-Lab/PAC2BAYES/blob/master/notebooks/Bayesian-LinearRegression.ipynb) [[Open in Google Colab](http://colab.research.google.com/github/PGM-Lab/PAC2BAYES/blob/master/notebooks/Bayesian-LinearRegression.ipynb)]. 71 | 72 | * [PAC2-Variational Linear Regression](https://github.com/PGM-Lab/PAC2BAYES/blob/master/notebooks/PAC2-Variational-LinearRegression.ipynb) [[Open in Google Colab](http://colab.research.google.com/github/PGM-Lab/PAC2BAYES/blob/master/notebooks/PAC2-Variational-LinearRegression.ipynb)]. 73 | 74 | * [PAC2-Variational - Sinusoidal Data - Neural Network](https://github.com/PGM-Lab/PAC2BAYES/blob/master/notebooks/PAC2-Variational-SinusoidalData-NeuralNetwork.ipynb) [[Open in Google Colab](http://colab.research.google.com/github/PGM-Lab/PAC2BAYES/blob/master/notebooks/PAC2-Variational-SinusoidalData-NeuralNetwork.ipynb)]. 75 | 76 | * [PAC2-Ensemble - Sinusoidal Data - Neural Network](https://github.com/PGM-Lab/PAC2BAYES/blob/master/notebooks/PAC2-Ensemble-SinusoidalData-NeuralNetwork.ipynb) [[Open in Google Colab](http://colab.research.google.com/github/PGM-Lab/PAC2BAYES/blob/master/notebooks/PAC2-Ensemble-SinusoidalData-NeuralNetwork.ipynb)]. 77 | 78 | * [PAC2-Ensemble - MultiModal Data - Neural Network](https://github.com/PGM-Lab/PAC2BAYES/blob/master/notebooks/PAC2-Ensemble-MultiModalData-NeuralNetwork.ipynb) [[Open in Google Colab](http://colab.research.google.com/github/PGM-Lab/PAC2BAYES/blob/master/notebooks/PAC2-Ensemble-MultiModalData-NeuralNetwork.ipynb)]. 79 | 80 | 81 | 82 | 83 | 84 | 85 | 86 | 87 | -------------------------------------------------------------------------------- /notebooks/Bayesian-LinearRegression.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "markdown", 5 | "metadata": {}, 6 | "source": [ 7 | "## Imports" 8 | ] 9 | }, 10 | { 11 | "cell_type": "code", 12 | "execution_count": 1, 13 | "metadata": { 14 | "scrolled": true 15 | }, 16 | "outputs": [], 17 | "source": [ 18 | "import matplotlib.pyplot as plt\n", 19 | "import numpy as np\n", 20 | "import tensorflow as tf\n", 21 | "import math\n", 22 | "from tensorflow_probability import edward2 as ed\n", 23 | "%matplotlib inline" 24 | ] 25 | }, 26 | { 27 | "cell_type": "markdown", 28 | "metadata": {}, 29 | "source": [ 30 | "# Data Set\n", 31 | "\n", 32 | "In this first part, we present the data set used for this example. By setting the flag ``MODEL_MISSSPECIFICATION`` we can generate the figures under perfect model specification or under model miss-specification. " 33 | ] 34 | }, 35 | { 36 | "cell_type": "code", 37 | "execution_count": 2, 38 | "metadata": {}, 39 | "outputs": [ 40 | { 41 | "data": { 42 | "image/png": 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\n", 43 | "text/plain": [ 44 | "
" 45 | ] 46 | }, 47 | "metadata": { 48 | "needs_background": "light" 49 | }, 50 | "output_type": "display_data" 51 | } 52 | ], 53 | "source": [ 54 | "## Control the presence of model miss-specficication as shown in Figures 2 and 3. \n", 55 | "MODEL_MISSSPECIFICATION = True\n", 56 | "\n", 57 | "if MODEL_MISSSPECIFICATION:\n", 58 | " VAR=5.\n", 59 | "else:\n", 60 | " VAR=1.\n", 61 | "\n", 62 | "\n", 63 | "# Set seeds for reproducibility\n", 64 | "np.random.seed(0)\n", 65 | "tf.set_random_seed(0)\n", 66 | "\n", 67 | "NSAMPLE = 100\n", 68 | "def sampleData(samples, variance):\n", 69 | " x = np.linspace(-10.5, 10.5, samples).reshape(-1, 1)\n", 70 | " r = 1+np.float32(np.random.normal(size=(samples,1),scale=variance))\n", 71 | " y = np.float32(x*1.0+r*1.0)\n", 72 | " return (x,y)\n", 73 | "\n", 74 | "(x_train, y_train) = sampleData(NSAMPLE, VAR)\n", 75 | "plt.scatter(x_train, y_train, marker='+', label='Training data')\n", 76 | "plt.ylim(-20,20)\n", 77 | "plt.xticks(np.arange(-10.5, 10.5, 4))\n", 78 | "plt.legend()\n", 79 | "plt.show()" 80 | ] 81 | }, 82 | { 83 | "cell_type": "markdown", 84 | "metadata": {}, 85 | "source": [ 86 | "# The Bayesian Posterior\n", 87 | "\n", 88 | "We now perform the learning with the Bayesian Posterior computed with the Variational algorithm presented in Section 2.1, using a Multivariate Normal (MVN) distribuiton as approximation family. \n", 89 | "\n", 90 | "We now employ Tensorflow Probability and Edward 2 to define and make varitional inference over a Bayesian Linear regression model. \n", 91 | "\n", 92 | "This algorithm converges to the exact posterior solution." 93 | ] 94 | }, 95 | { 96 | "cell_type": "code", 97 | "execution_count": 3, 98 | "metadata": {}, 99 | "outputs": [ 100 | { 101 | "name": "stderr", 102 | "output_type": "stream", 103 | "text": [ 104 | "/Users/andresmasegosa/Google Drive/papers/2019-denmark-pac-bayes/tfp0.8/lib/python3.6/site-packages/ipykernel_launcher.py:2: UserWarning: tfp.edward2 module is deprecated and will be removed on 2019-12-01. Use https://github.com/google/edward2 library instead.\n", 105 | " \n" 106 | ] 107 | } 108 | ], 109 | "source": [ 110 | "def model(NSAMPLE):\n", 111 | " W = ed.MultivariateNormalTriL(tf.zeros([1,2]), tf.zeros([2, 2]) + tf.eye(2), name=\"W\")\n", 112 | "\n", 113 | " x = ed.Normal(loc=tf.zeros([NSAMPLE, 1]), scale=1.0, name=\"x\")\n", 114 | "\n", 115 | " out = tf.matmul(x, W)[:,0] + tf.matmul(tf.ones(x.shape), W)[:,1]\n", 116 | " out = tf.expand_dims(out,1)\n", 117 | " y = ed.Normal(loc=out, scale=1.0, name=\"y\")\n", 118 | "\n", 119 | " return W, x, y\n", 120 | "\n", 121 | "\n", 122 | "def qmodel():\n", 123 | " qmu0 = tf.Variable(tf.random_normal([1,2], 0.0, 0.05, dtype=tf.float32))\n", 124 | " qR = tf.Variable(tf.random_normal([2, 2], 0.0, stddev=0.05, dtype=tf.float32))\n", 125 | "\n", 126 | " qW = ed.MultivariateNormalTriL(qmu0, qR, name=\"W\")\n", 127 | "\n", 128 | " return qW\n", 129 | "\n", 130 | "\n", 131 | "W,x,y = model(NSAMPLE)\n", 132 | "\n", 133 | "qW = qmodel()\n", 134 | "\n", 135 | "with ed.interception(ed.make_value_setter(W=qW,x=x_train,y=y_train)):\n", 136 | " pW,px,py = model(NSAMPLE)\n", 137 | "\n" 138 | ] 139 | }, 140 | { 141 | "cell_type": "markdown", 142 | "metadata": {}, 143 | "source": [ 144 | "## Defining ${\\cal L}(q)$\n", 145 | "And, now, we define the functional ${\\cal L}(q)$, as defined in Section 2.1." 146 | ] 147 | }, 148 | { 149 | "cell_type": "code", 150 | "execution_count": 4, 151 | "metadata": {}, 152 | "outputs": [], 153 | "source": [ 154 | "datalikelihood = tf.reduce_sum(py.distribution.log_prob(py.value))\n", 155 | "\n", 156 | "KL = tf.reduce_sum(qW.distribution.log_prob(qW.value))- \\\n", 157 | " tf.reduce_sum(pW.distribution.log_prob(pW.value))\n", 158 | "\n", 159 | "elbo = datalikelihood - KL\n", 160 | "\n" 161 | ] 162 | }, 163 | { 164 | "cell_type": "markdown", 165 | "metadata": {}, 166 | "source": [ 167 | "## Optimizing ${\\cal L}(q)$\n", 168 | "\n", 169 | "We perform gradient-based optimization of the above objective. " 170 | ] 171 | }, 172 | { 173 | "cell_type": "code", 174 | "execution_count": 5, 175 | "metadata": {}, 176 | "outputs": [ 177 | { 178 | "name": "stdout", 179 | "output_type": "stream", 180 | "text": [ 181 | ".\n", 182 | "0 epochs\t3619.3044..........\n", 183 | "100 epochs\t1426.6193..........\n", 184 | "200 epochs\t1362.8108..........\n", 185 | "300 epochs\t1360.2006..........\n", 186 | "400 epochs\t1360.3262..........\n", 187 | "500 epochs\t1360.2031..........\n", 188 | "600 epochs\t1359.9584..........\n", 189 | "700 epochs\t1360.0768..........\n", 190 | "800 epochs\t1359.8759..........\n", 191 | "900 epochs\t1359.8707..........\n", 192 | "1000 epochs\t1360.4103" 193 | ] 194 | }, 195 | { 196 | "data": { 197 | "text/plain": [ 198 | "[]" 199 | ] 200 | }, 201 | "execution_count": 5, 202 | "metadata": {}, 203 | "output_type": "execute_result" 204 | }, 205 | { 206 | "data": { 207 | "image/png": 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\n", 208 | "text/plain": [ 209 | "
" 210 | ] 211 | }, 212 | "metadata": { 213 | "needs_background": "light" 214 | }, 215 | "output_type": "display_data" 216 | } 217 | ], 218 | "source": [ 219 | "num_epochs=1000\n", 220 | "verbose=True\n", 221 | "sess = tf.Session()\n", 222 | "optimizer = tf.train.AdamOptimizer(0.01)\n", 223 | "t = []\n", 224 | "train = optimizer.minimize(-elbo)\n", 225 | "init = tf.global_variables_initializer()\n", 226 | "sess.run(init)\n", 227 | "\n", 228 | "for i in range(num_epochs+1):\n", 229 | " t.append(sess.run(elbo))\n", 230 | " sess.run(train)\n", 231 | " if verbose:\n", 232 | " if i % 10 == 0: print(\".\", end=\"\", flush=True)\n", 233 | " if i % 100 == 0:\n", 234 | " str_elbo = str(-t[-1])\n", 235 | " print(\"\\n\" + str(i) + \" epochs\\t\" + str_elbo, end=\"\", flush=True)\n", 236 | "\n", 237 | "plt.plot(t)" 238 | ] 239 | }, 240 | { 241 | "cell_type": "markdown", 242 | "metadata": {}, 243 | "source": [ 244 | "## Evaluating the Bayesian posterior\n", 245 | "Once the model is learned, we evaluate how it makes predictions by ploting its associated epistemic and aleatoric uncertainty" 246 | ] 247 | }, 248 | { 249 | "cell_type": "code", 250 | "execution_count": 6, 251 | "metadata": {}, 252 | "outputs": [ 253 | { 254 | "data": { 255 | "image/png": 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Oi6TNYqM5tIsqk42FH1ST/2Idt31Qg9klac6M5vC9i6gsmsfd23/lm2sdgBYHjUYzbRjRklavIDiURRAWp2oZdTZCV6OKOrJ39BcEHyClpMHdQ0a+mStdTaS+eYE7jlSz5HQdVruL9qQITt45j+KbZ+CYncrskDhuicjw6Ri8Cag4CCGeBzYCdVLKRcZrCcBOIBcoBe6VUjYHaowajWYa4Fk2cruUNeC0KedycwkgoOkyOO2q5pHLMerDD2cxtLrtFNtbuNTTRMSJcubsL6PwvUpCuxy0R4VwYX0exWtz6MzPZFZYPOutsSSZwhBCgCV8HBc9PIG2HF4AfgZ420XfBN6WUv5ACPFN4/k/BGBsGo1mijBkGO22G/uWjHpalUXQVqVqGnXW91kHnqUil28S1LrdTi47Wrlob4Yz5czeV8bHDpQT0WrDHm7hyqosim+eQXNBFrPC41ljjSPFHK4EYYIIqDhIKfcKIXIHvPxxoMh4/EtgN1ocNBqNz5CYpYNw2a2Widqr+8phu53Q1aQsiVGEnY4Eh3RT4mij2N5M56UKZu8r40P7y4ip78JpNVG2IoPitTOoL8whNyqRQmssaeaICRUEbwJtOQxGqpSy2nhcA6QOtpEQYhuwDSAnJ2eChqaZ6kzaMEvNsOx8eBUIwX1Pv0u8u4lf3JcLNafh8jtG9nKrsiCgL0zVB7ilpNLZQbGjhYbyKnL3XmH1/nISKttwmwQVS9M4fN9iqlfPIDs2mcXWWNLNkZgCJAjeBKM49CKllEKIQUsRSil3ADsACgsLJ7ZcoUajCX68I43snWBrZ6bjEtnOMrhYC90txnKR9GnFUyklda5uLjpauFpzlax9V1i8r5yUy2pJ62p+Mnu2raDypjwyElOYa41lvSUqKATBm2AUh1ohRLqUsloIkQ7UBXpAmqlPsJd3nowE5DP0TPJSgq1VWQTttdBaAd3N/O9lHeAIUbkJPqbFZaPY0UJpYw3J+y8zZ38ZNxu5CPV58Rx4YCllN+eRkpHObGssN1uiMIvg7dQcjOLwB+BB4AfG798HdjgajSYo6RUCd1/2stMGLptqjFN3vrcCKrYOv1Q77XI7KHa0cqWtnqgDxczZX87yE9UqFyEjmiObFlKybibxuZnMssay0hKNJYgFwRshJ7iBRL+TC/EyyvmcBNQC3wFeA14BcoAyVChr03DHKSwslEeOHPHvYDXTAm0xjJ+BVtiqvATAx5+plH1F7pw9Kvy0s0EJQXOpylY2Oqf5ukmOXboocbRxqasR06Fi5uwtZcaRq1jtLjoSwym+eQZX1uYSOTeHOaHx5FiisfpDEMwWiMuFJZvGfAghxFEpZeFg7wU6WmmonO9bJ3QgGo0mePEucifdgAC3Q4Wcttcon0LdefWalMq/YDL7VBRc0k2Fs4Pinibsx4qZua+UDxm5CN0xoVxYn8eldTMIXTSTWaHxfMwajVWYfXb+3pIc1jCwRqq2oVEpkDDLd+cYeMpAWg6+QlsOGk3wMVorrN/2AwVBSmUh9LQqi8DeAfXn+5aL7J0+H7+UkhpXF8X2ZtpOXyZnzxVmD8hFuLR2BmL5bGaHJ5BrjSHUl4IAfaIQk6HELzwekhdAWAyERiuhMI/9Hj9oLQeNRqMZFE9LTbdDdU/rauwTA3uHKnzntPmlr3Kjq4diezMNF0vI2HuZAiMXwWExcXpRCnW3zca5cg55UYl8yBJDmMkP06jJogTAGq4a+qTkq8fWCAiLBZO1f1MhP6AtB41GE1A2P30QpORQaSMAN+bGEyp7eOHePFXCortZJaa116DCTt0+F4UOt4NiRwvVZeUk7rnInP1lJFT05SJcWjuDdzOTiQ2J5eHFc4nwtSB4rCRrmCqJkbIAIpMgPEFZD5FJ6rf39j45rbYcNBpNMCIlJunCKu1EYCNedDDT0UCMuxWulBkF7uzK+exjQbBJF5cdrZRXVxG99zyz95Wx7FL/XIT2tfMobhAkuyKIaXYggf85rnJ0x93BTQgwW1XNpqhUNfknz4OIRIjNAnMIIACpfCgTjBYHjUYzsXj7E5w9vPyJFOhp4cnfnSPVWc3Dy5KMrmojT3EaaUlsp3RT5myntKEGy/6zzN5XxkfO1PXLRWi+ZR6ZGZkst8YSbQrhNzUVxt7XL7g34tLclhCITFF+A5MF0happaLIZEAqh7OHAK3uaHHQaDT+x+ND8GQku+zQVq16IjSXgtvJbPsFBG5wRPr01G4puerq5HJrPe53z5C3r5SiAbkIDbfMIzUvh4UhccSaQvrtP9aeDED/VqIms/IZhERCwkzlXA6NVktG1ghADL5cpGsraTSaKYVnUnSojma9PZbtHdDVDG2VyjowahndtyJ91KcY2DXN8/ye5Vk0uHu41NlI93tnyNl7hTVeuQgnN86j9pY5JM7LY3ZIHDeYw8Z1qUONY9NNC9VykdkK8bkQlaZEITxeTfomi3ovCNHioLkuOjFMM5Bh/ydcDjUhOrrU44Zi9byzXpWxcPb0CYaPl0y6hYN60cHu/ZdJ21PM8gG5CFdvmU3skjnMDo1n2SgFYaQWQ48MwSmstJjiIWMZWMKUTyE8vk8oJkGWtBYHjUYzdjz+A7dRmkK6oKVchZl21qms5Y46QPqlhMWmFdl0uZ3sOHmBsIoKCo5VX5OLULVuFhEr5jE7IpGFniY5vkSY2HRDHoRE8MzBajotaWy5ayUkzlZLSeZQ5Vz2nDfICuwNhRYHzZDoYnSagXjCTt8vbUIg+eTT+xG4+a8Hl6q+CN3NUH9BLSHZ2vvKX/tYFBzSRYm9jeriy0TvOsen95SS2NTd2xehfN1MQm/MZ2ZUEvP80STHc+dvDVNO5NhsCIvl3NGzdJqiIH2pEW3k2X5yCII3Whw0Gs3IMJzKZpxE0U0U3aS4uol3NUGVA5rL1HKRrb0vs9eHuKSbSmcHFeVlhO46w6x9pcw1chEql6Ry9lMFmG5eSF5cKkX+apJjtqplorBY5S9InquWjCKSwGThR4/MUe9PQjEYiE6C01wXbTFMczxzhNOm/Ai2dp78z9dJctWxfXU62NvV+66hO6eNKdIHVcKi1tVFaU0VYvcpcveWkOrJRViQROnaPOQti8hJTifTX01yzBaQQEQCRKcrSyEySQlFRFKfD8ETmTSJhEEnwWk0mpHjEQMh1IRva1PLRZ310NMGbVXMdBRjlQ7oHl+Uz1A0uXooaazGsecU2fuusMorF+H9B5bhKFpIdmYWq/zVE0GY1I81DNIWKyshJkNFG1nClFXkEQRvMZhEwnA9tOWg0Wj6Rw257KoUtq1diUHtaeVUtnd4FcIb2ZLRwBDPzLhwYHALosPt4EpbHV37TpG29xLZXrkIV9bm0rN+IRl5uWRbonzfE0EIQBj1i4waRrGZqrBd2iJ13eaQviJ3k8xCGAptOWg0msHpXTLq6St33VKurIXWSiUS7TX9k7l8SI/bSUlXE23vnSZxz0UWHK7qzUU4vXE+nUULSF0wmyXWGP/0RBBCTfqh0SorOWmuEoa4bGUtmKzKenC7p6yFMBRaHDSa6UZvxVOnsgDar4K9C7qboO2qKnLn7FEWBKJvnzEwWHaxU7q53NNM09GzRO0+x8yDFb25CBc35NFWtICEJfNYEBpLyDAlsMfqxwCM5DOLKmwXkwmRiaqmUXi8EXpqJKZ5RMAU/HkJvkaLg0YzlfGuYwR9CWpNl5Vz2d4FdWeVEHj6IvQTgtGJwlATtkTSIro5cvQI4bvPkPduGbNaerCHWyhZlUVz0XxiCxcwOzzB9z0RwPANmNSSkcmqyldYQiB5vvIhWMOVYHj8CBotDhrNlMbjI3DZVbRRV6NqmFN5RPVK8IiBdPt86UhKSb2zi8riy8x/7xS5+0qJqevEaTVRviKDhqJ5RN24kLyoJOaNogT2kKUqvAWpN3LIBOFx6ndUqpGYZlFVT4VQwuDZXtOPoBUHIUQp0A64AOdQThONRmPgbSW4XYYo2JQz2eWAhovKf2DvUM+R/cVAyjEv1XhP2D0mJ8+8c4Ds45dYefIqy71yES5uWUHY2sXkxaUw0+SHmkKe0tbWCGUNRKWo0NPoNCPSyKvaqRaEYQlacTBYL6VsCPQgNJqgR0plGVjDlJXQUqHqGLns6rfbpcJR/RSdaMdFZ2c9mR+cZ/kHVcyqaANULsKx7aux3rKE3OR0cgZUPB0L1/gxbshV12cNV+GmYXGQNNtokpOiBMPTOU0LwogJdnHQaDSD0a+mkeFcbqtSE2RLuSp2192kGsm4h05O8zCipZoB2KWL0sZauvecoGjPRTKMXITy7BhOPFiIaf0SZmRms9wcOuQxxkTv8pfAhVlZBcKklozicpQ4WEKN8FM9xY2VYP7kJPBXIYQEnpZS7vB+UwixDdgGkJOTE4DhaYKFQGZwT/i5vZeMPMtD7VdVa8nKQ6p8hb2jL1vZxyUsnNJNRXsjbfs+IG73eWZ55SKc3ryU9/OysCSmsXX5LJ+eF+jLRQiJBEsomzZkqSWjpDmqnEVIVP+KpyZtJYyHYBaHm6WUVUKIFOBNIcR5KeVez5uGWOwAlQQXqEFqAsO0KOlhWAeeYnc7P7tMhZi2lKuJsOGi4WBuU9VQr4k0GjnDNbRxS8nV7laa3ztFxO6z5Byq7M1FOH/nAlwblpAxfzaLzOEs9nmBO68oI7dTLRNFp6key26XEgWzVS0bmS1TJjktGAhacZBSVhm/64QQvwNWAnuH30sTLHhP3v6ayM9Wt7H56YMBqRrr94q1vdVMwSwdhEqbCjm1dUD1CQiL5cXdJwmVNjatyPLNOb2QUtLg6KLuyGlCdp0m+71ysjoddEeHcGXDLOzrF5K8NJ98qx8K3HmWjcwWlaEcY9QzMllVclp4gpGH4OVDmGTlsCcDQSkOQohIwCSlbDce3wZ8N8DD0gQBAyfls9VtgRyOb/EsGZnM4OjmoecPEOnuwFFZQrjo5Jc7OwiRNrYsTwN7F6Gyx+dDuG1pMlWnznPxR7vIfreUhS092MMslN+YTff6hSTesIi5odH+qXgqTCr3wByqitxFJqlCd54oI0sYm585BJSyc/sa359/FEwHyzUoxQFIBX5n/ANagJeklH8O7JA0I2Hg5L34ib/Q3uPs954vv1D56TGcrW4jPz1mQr+onnON+5o8FgJC5R2016ilkvKDLLWdIMrdTpOpXhUFdavQz7E4j4ejy2Wnsvgy7rc/IGPfZfKNXISKFZl0FOUTv2YxMyPjfV/x1FPWWwh1zZHJavkoNltlLRuCACjB1NFGE0pQioOU8gqwNNDj0AQfg03KnseTCo+VYGtTBe6kSwlDS4VaW++s4+8KBBDDb460ANf6BcaDXbqoKCvD8c5xUvYU9/ZFqFqaRsX9K4lau5Sc2CT/VTy1hPYlp1kjVH/lmEwIi+kvCABSsnnHe0DgG09NpwZYQSkOmsnLcJO3v75AgfxijujcXiWwNz91ACt2Xty6XJXAbihWZSy6GlWegr2Ta5LTBjCc83g4nNJNVe1Vut4+TuKeC8wy+iJUL0jmzPabiVxfQGZSGtk+r3hqWAgmixKFmAwVcmoJM/oihKr8DEtY/74IvftrayEQaHHQTEomxZ2ap5Kn2wWOTjCHkuBuIM7VDJeaVOayo1NNnG7XkIIw1uUiUJFG1c0NtO8+Tszuc+ScqVV9EWbGc+4zqwhZX0B2Zhbpvq5n5O1UNlmVVRCVopaP4meoaCthHrrS6QBB8Nky3jgJlnFMBFocNH7B+0szlb9AQ+J2KUvA2QPSzXefexW7sBJXc4Yw7LzyZxC4xzXxD7WvlJKGjlaa9h8nYtdZMk5Uk+l005IRzcXNyzDfWkBWXh7Jo6hnNGJMZnXtljC1XBSdqh6nLlLLSOYQo8Dd8NbAdJh8gx0tDhqNL/GUwm4uVQXunDboaiDbWUKY7KFWqOgqQfiYDj/cUlJLdyf1732AdddpMg9VkGx30ZEQzpWN+XDrUjLnz2We2Q/1jKCviF1IpBKA2Cz1E5GkBCM0xicO5WARi2AZhz/R4qDRjAePGLgcyqnc2aDKVlw9oXwJRoG7zyyLA+A3Rx3A+JaKvOlw2Kg5egrzO6dIP1jKHCMXoXzDHNwbFpNekM8c72JzvpfW0wMAACAASURBVMZsVT9J85Q/IS5HfR5xOX2O51Ekpk0nh2+wo8VhBOh/UE0vnkY5njV1ezvUX1QTZNNlVdyup81olIPPCt15h686cfHK7/eSfbyYpSermG3kIlTdOAPH+kWkrlzMrNAIn5z3GoQwGuVYlaUQl6NyETxiEBqjxMFs1YlpkxwtDhrNSPA4jF02ZQ10NSoBaCpRoiClshQQw9YzGqvF4MKNrL1K/uFzLDtVSXJTDw6LieobsrCtX0jCmgLyIqLHeHGD028JS5jUhB+brXwHIVGqc1pkkip0J919Re7GUXl1qGi3zU8f1DdnE4wWh2HQJu40xnPH71k2srVDT4uyDDoblDjYO5RfoTeRDUbbOW04XNJNTXkF3e8c57bdF0ioaMVlEhTPS6LlwZuJW1dAdky837KV3ZhoN8Wq1pmRScqHEJ2mxMBsVSGonuQ0pl8bzamOFgeNxhuPKHQ1qWxdeye0VUJbNXTUqqqnji6j/7Lv6z1KKamrq+WDV/Yy71gpM8pUAlzNgmSKH13H+6kZhETGce8KP1QiNlkAyX8dqabTFMXRpkRKZDqnjybQbormuc8V9K9p5MflIm+LQd+cBQYtDsMwnWKapy3e/gOXA5zdSgCunlATYdtVtZTU2aiazA+TjzD2IUiaWppp3n2UyN3nSDtdw20SKrNiuLR1NRG3LiMtI5M0IZgzjvMMGekkTOraYrIgNIpL1hhqLBnsd9uxYSXBnIT0OJcngf9Af199gxYHzfRjYDtNR6f63VyquqY5uqG9WjXKwWt5yeXb3gitHe007jtO6O7TpB2/SqLTTV1KJHtvW8Cp2XnY45LJjouAGsmmTD9UPjWZVS5CSBQkzFSZyxGJfOfRUDCHsvmZ90FKfh2gInf65iywaHEYAcH+T6m/PCPAu3Oas0fdLTu61PJR3RnlO+huUa8J0wA/gu/o7Omm7r0PsOw6RdqhcmJtqi9C2cZFWG4t4EB3GGZhxtnS7bNVfI/FUNncg0Tw7PEOLDjZeueHVTtNKZVPwRLeV89oEkYaaR+hb9HioJnaeJaAHN1qmaijTjmVuwynclu1cjZ71/ORvhWGHoed2qNn4J0PSDtYQp6Ri1C1YS5sWEJ6QT4zjeQ0jydhPJVWe/ctnAFC4BRW2kyxVEgblTKZlNBZWHFA9koIHRDh5CUGwTKpBss4phtaHCYx+k5pCHonebf66WlTrTStEXD1uOq1DCoUtbedpm/9CA63i5qT53G9c4KU/ZeZYeQi1KzOxbV+Makrl5Ab4r/ktC5TlCpmF5nClo8tg+R5PPTyecIx87NH1quNplgJbL0M5Vu0OIwS/Y8XpHiS06Cvt3JXo1pCarqsWmtawpXV4OO+yh5c0k1N8RXsbx0nae9Fso2+CDWF2dSuX0TSTQXkhEeO6FijthhMFnYeLqfTFMX7Tcm4MFN8LJpqSwLPPbQarOF0ikoEUjmfNZrroMVhEqPvlFA+BLdDiYHbofwGLeVKIDob1HKSvV1ZCPYun59eSkltZSXdbx0jbs95MstbcZsEtUvSqf/UGhLWLScrJtbn5wWMu34BoVGQOIcKq6DYOp99bhth2JlnzUYiVL0jIQLePW2imJbfAz+gxWGE6CWcIMJ72cjeAa1VKgfB2QOtleo1p80veQjq9JLGujra3jlK9O5zpBU3AlC3IJkrj95C7PoVpCUm+ik5TXg5kI1+CJEpkDyPr312GUQm9f5vvjxBYjBZvwuTddwThRaHKcC0+Od2G0tB0og2ctmVZdBWBS1lRgVUu3Im+0kUmpubadlzjPBdZ0g9XUOShMa8eK58ZjVRG1aQnJFOir/W8E0WFUkUkaiEL3uVcrBHpytfiqfW0RTzI2gCh5B++iKNFyHE7cD/BczAs1LKHwy1bWFhoTxy5MiEjMsfdxv6DmYY3G5AqogiW5vKWG6vUWLQ1ahCT502v2Ust3W207TvBCG7TpN6vAqz001rejSNRXMJ37CC1JkzfN9b2YMQKvHMZIWkuap2UUymCrWNy1HNckzmgInBQGt6VV4CEPz/x5N13P5ACHFUSlk42HtBaTkIIczA/wM+DFQCh4UQf5BSng3syDR+x3uCd3QpB7LbBbWnVVtNu1G6wjsfYWBbyXHS5ZWLkHqonFwjF6H8zsVYby0gbf5sYk3Dd04bcyiqEKofgjlE1TGKyVSd08LjlbVkjQDEiEUh2G88gn1805nrioMQ4kvAi1LK5gkYj4eVwCUp5RVjDL8GPg4EXBz8YTFMez+GZ2J3u4zwUrvqiVB/QZWvsISp5SMp+0caefIRfCAMNqeDmqOn4Z2TpB24Qq5XLoJpw1LSChaQ569GOZ6JPjRG5R1kLFdZ23G56rmnc5pn2WiQ/gij/d/xxf/aZA2ImKzjnmhGYjmkou7cjwHPA3+R/l+LygQqvJ5XAqu8NxBCbAO2AeTk+KEI2TRkQr4snn8d77t9l10tF3U1qcqnrRXqcXeTijLysWXgweF2UXPqAq53TpC8/xIzmvtyEeT6JaSsXDzqXATvvgvezwe1IIQJLCGqr3JMFsRlKyFImKmsI5NFbTPQQhiFxRCsNx7BPj7NCMRBSvm/hBDfAm4DPgP8TAjxCvCclPKyvwc4zLh2ADtA+RzGepxA/lNOmzsY7ztd6VYWgsnct2zUXqucyvYO5Ufw1DzyWAk+FIbeXIS3j5O4t5js2g6Vi7Aim7oNi0i+aRk54X5slCPMKvTUZFHO5JBIo2FOmiqBLd2GJWHq22cYhppkR7u9LyyIycZkHfdEMSKfg5RSCiFqgBrACcQDrwoh3pRSfsMP46oCvG+1sozXNH7Ar3dxnoleCDXhdTYoZ7K9XZWu6GpUzx3dfktOc/fmIhwlfs+FfrkIDZ9cTcItvstF8FgI/SwGa5jyIUSlKgdzTAZEpUGI4T8IiepbWvK2rMbBUDce1xOPiWLa3BhNYkbic/g74AGgAXgW+LqU0iGEMAHFgD/E4TAwRwiRhxKF+4BP+vIEwWTWTtkvhtulfmxtapnIEgql+3sthp2HywHYvCLT56eWUlJfV0v7O8eI2X2OdCMXodbIRYjxZy4CIDHhEmblTI5OV8KYtthwNlvBHMJ9Tx8A4Nfbb+rbcZTjGe0kqydlzUgZieWQANwtpSzzflFK6RZCbPTHoKSUTiHEF4G/oEJZn5dSnvHHuTQ+nDA8VoKnzHVLubIU7O2qnabLoXwLblXPyMToLIXrRQB5+iK07DlG5K6zpJ6uIcUrFyFywwpSMtL9Jgiqh3IUhMVy7605yocQn6cijZw2iEjot8Qmhf/LWAT75B/s45vOBG2ew2gYT56DvoPqY9SfhXemstuloofaq5UAuOyqyJ2tw8hBcPeWwR7otM2MCweuH/Y5lDi0dLTTuP84obtOk378ar9chNANy0mbOQOzPyZiT/kKk1ktFYVEqlaasdkqUS8iSb1nMqKcjJpGOs5eEyxMujwHTWAY8eTkdquJ0WlTk19PKzRdUf6Dzoa+4naObp+Ma7AIILvLxo3dDVjfOUX6oXLiBvRFSF8w57q5CKPGY3GYzKqIX1gMRCara01boiwDS1ifM9njXNZoJiHT3nKY7ozYWvDORfAkoTWXqsmvrVpVPnXZwdEz4nOPNFHMs11ZcxvxVeUsuVjOwhNVRHQ76Y4OoeammQgjFyHMEjLi848Yj6PYGq6WjSISlSik5Pc52q2RKoPZm0HyEbzRVqsm0GjLQTN2vJvl2NqVKNjaoPasCj11dPs10qjH5aDQ0op85wNu23OJ2DYb9jAL1TfOwLl+MWmrlpAXEuaXc/e20oxMUcIQHq/CTiOSlEiYQ9TnM1QJbF3jSDOJ0ZbDNGXIde9tN6pJzeXsq3ra3axKYbdXq+qnLod6zU/YpYuqi5dVo5y9xcTUqr4I5xakcmX5TG75xC3ERUb57fxYw5SFFJMJsZkQkcT2/75Mjwjnhc/drKKN9HKRZgqgLQfNdVA3CMJT8RSgpQKc3XD1hHrf0aN8C+O0EIZaSnJIN9UVFdjePkbi7ovkVahchOoladRuWU180TIWRcex2G9VT81q0g+NhvhcJQ6ZK4wcBAttpgZcWJRwaDTTAC0O0xSPhbD56YOEunv41UPL1ORf/YHqidDdrKKOnD2A8MuykUu6qa6toWvXMeJ2XyDHyEWoWZDMxe1riV6/nIykFP+EnprMRhlsi7q2pDnKjxAeryKP3E4IjWHzjvcAeL+0HdB+As30QYvDdGJg6KmzmzhXI2muaiiXylrobjYa5XiLwfiXHj0WQ2VLF05HB6/vOMzcYyXMKW5ESGjIi+fi1lWEb1hORmYmaT4IPb3GShGmvkzk8Hi1bBSRBOFxEJWiQk4tRi0lQzjPVreRnx4z7rFoNJMNLQ7TBSmNlpmdyqHsckDDRZ6+sRW6u6H6pHrfD0XupJR0OjqIO1/M+iOXWXShAYtLUpcSQfHm5Vg3FJA1K48k4ft1fImpL4oocY4SvYiEvuQ0a7iyHmBQB3J+egw7H1mtLQbNtEOLQ5Dhs0nI20pwOVSlU1ubWjKytUNPm/IpeEpcDNxvnEgpaejpoOG9k4TtPsP9hyqw2lw0x4VxcN0s0u+6kYwFc0jxQxlsj8VQ0uyknliuHnPRJSJ5/OF1apksJFKVx75O+Wvv0iragtBMN7Q4TFYGi6GXsu/1nlYlCl2NShDaqpQ4OLr7i4GPabR3UXfsDNZ3TpN1sJRkoy9CWdEsXBuWcEjEESasrF00yiY4w9E7yZt4+ehVSjusRMSlcUxaKHOnsigkGbcwQVhc32c28Pd18FgQY0FbHZrJiBYHHzHeCWDUhQD7lcE2aho5e4ylo3ZorVIC0V6teiRIemsa+ZpWZw9XT1/A9M5JsvaXsKBF9UWoXJWDbcMiklcuYnaoCj2d58sTe3wIZqvyF0QkUmYJpT0xjn/8zEc5+p9nmCFCeOaRNcb2IxMCXZxOo9HiMPnozVR2AhZw2ZQgtFaqH3unaqfpdvb1VvYD7W47v/3rYbJPFLPigyoW1HbispioKMykrCif+DVLyYuM9U+kkdmIMgqLU41yLKF8680aqs0xHKhW/9KXX7zE2Vob+elhQdNjeTKLzWQeu2ZsaHEYJ76aAK57t+oRBadN3TE7OlUdo9YK5VeoPQtuBzjt6n0/hJ52uR2Ul5fheucD0vZe4sHyVtwCri5Np2LLDUSvKyA7Nsn3Re48y0Yms6pdFJWqktOi0pT/QJgos5zFIax04erdJz89dlo2sdFofIEWh2DGs3TkdqulIpNFFbiTbtVb2eNcdjkG9FZWj8fc5N6LbreT8tqr2HepbOX5F1UuwuWZ8bz98UWUzJ3JjJR0zJjYFJcy9msdiCEIvzlaQYcpms+snauii5Lnqd/hCV5RRiZ+9eh6ILjucKfC8tRUsn40o0OLwxAEqnnKzkdWKzFwu40lIalKVnQ1qbpGjZego05t7HKM61xDYZMuyprq6N5zgsQ9F5lzpg6TW9KQG8fpBwt5PyeL8JgU6lrshAJmfGwpWEJV3SKThXqznYsh+TBjkUpSC41W/oWh6hlNUvSkqwk2tDgEC263mvCcdrVk1NWkLIC6s6qukaOLX+8/hxkXm1ZkDXuoUTW5N3BIF2XtjXTsP0ncngvMOl6N2emmJT2Kc/csQWxYStbsmSwyhbBowHnGY5kAfZVNLaFgjYDoNB5/qxGbCOXt2jhaCaP+t3W4aOrfNW0QgnFyDcYxjZSpYP1oxoYWhwGM1Ywe05fGOxehu1mVvO6sVw7murNq2aS9Rr0vJWb6nMu+mJid0k15dwst758mZtc5ZhyuxGpz0ZEQzvmPzse1YTEZ+XNYaIkY8zmGRZiUz8AarvIO4rJV1nJYDCXWU0gELTQDAifWKVnlVC/baIIVLQ4TjScXASNj2dGlwk09kUa2dpWP4LQb/gbXoJZAfYeN5KjQQU8xaJN7A5d0U2Fro+nYOSJ3n2XGwXJmGrkIl4tm0rN+IakF+eRbI68baTRQmEYkWJ4y2Car6poWlQrRacqHEBKpwlKFiZe33wzoyXIiGMlnrD//6UfQiYMQ4gngYaDeeOlxKeUbE3V+v5jR3lnHtjYVceQJP20pV691txjbejuWBz9cfYcNu9NNVUv3iCZkt5RUOTuoO3WBsN1nyN1fRq6Ri1C2KouOogXEr1zEnLBYP7XTNEpYhESpx7FZqpRFZKJ6zdNqE6akdTAcetlGE6wEnTgY/LuU8oeBHsS46I00MjqndTWpchV155Q49LSoJDWn7bolK7wtAY/F4LEihj695KalCVwtvsypX+wjd18J2UYuQtmKDJqL5hG9ejF50YlYx1nTaDDLRmLi3htmKEsgNktN/jNuVkIYmaSWkWDIEhYe9GTpP/SSlmY4glUcAs6YfQhup/IV2NpVTH5LuRKBllJlHXTWq7vnMZawSI4KZdOK7EEtBiklta5uKsrLMO86xYx9JRSWq74IlUtSKb5vOeFrl5AXl8pMk+//9G5pQiCxiTDqzamQNBuiMyA6VYWfhsao30L0F4NpZi0Mhp6QNcFG0HWCM5aVtgJtwBHg76WU17QdE0JsA7YB5OTkrCgrK5vAUdI/B0EIJQq2duVYtoSqJjnmEBV6KgTYOvjN4RLAB9E99N2t37M8iwZ3D6U1VbD7FNl7r5Bm9EWonpdE1S2zsBQtJS8lg1iTP/orG0tGwsSzhxpoN8XwlU9sgJT5yioKi1VLZeaQ61oJmsCgLYbpS9B1ghNCvAWkDfLWPwG/AL6HWnH/HvBvwEMDN5RS7gB2gGoT6rfBDoU0chHsHcpSaLwMLWXQXqv6AzSXAoZo+KEM9oaCZEqaanj/t6+TtfcyK87U9+YiHH1gGaxfQk5WDitMYb4vYeHJwA6LUY7k6FQwWTgR2ohdhEL6UrWcZI0cc6E7jUYTWILOcvBGCJELvC6lXDTcdn7vIe19t+voVnfBnQ0qH6G7WT1uLlVlsAcRg4Fr8plx4cDoLYgWl43L7fXY3j1N+p5L5Jyo6c1FuHJzLo4Ni8icNZNM8/UjjUaNx1FtCYHodKO2USxkLO/rqhYS2fdZaRHQaIKeoLMchkMIkS6lrDae3gWcDuR4eiueSqPqaXuNet50RYWgup0qHNVp77+Pj/jVsSs0ynYKWxpI21PMksNVvbkIpz86l86ifNLyZ7PEGoPFH5FGoCb98HhlKcRkqjaaljAlkiGRaptpZBnoZRjNdCDoxAH4VyFEAWpZqRR4JCCjkFKVp7C1q+S0xkvKmdzdbJTG7gKXc0RF7obLOxiMDreDSz1NtB2/wKw/neETJ2qI7HLQExXCxVvyaCmaR0LBfOaHxhHqh+5pgLIGwuPV46S5Kh8hLFb9mEMmZeipntQ1mpETdOIgpfx0AE7a99hpU1aC2wkNxUbIaZuKOnI7+0pge2c3+4Aut4PL9hYaz1wifvcFcveXEddqoyfEzNHFKVy8YQats/N4uGA+kSbfd0/DEqIsImu4KmERNwPiZ6g8hIgEEOY+QYBJJQq+Qod+aqYTQScOAUG6+3oftJSrQnfCpEpYuOzKgvBB9zRvi+E3Rytw4GLp4hhqi68Qu/s8s/eXsdjIRTi1MJlTK7I4n5VJtIxmVkwMURLfCoMwqXpOJqtaKopKVUtH8blK/MJi1TaTXAj0pK7RjB4tDo4eJQbdzaoMdluVKmPhcvilUY5NuihxtFHRfoXZx0tI+2ktC41chKrFKZy8dwnmmxcxMz6VpeZwXj1WCfgm/LUXYYKQCMNCyFHWQdJcZTWYzGrZCCa9KPganc2smU5ocWi8BOUHVaIa+KUMtl26KHW0U1F7leY/HmPFkat8tVSVy7g8M553Ni0k9WOF5KZkcJMlCtM4JuUh/Rpmq5r4Q6IgKkVZByFRylowWVRuBkxJQdCTukYzerQ42DtUKKqPcUg3ZY42SpvrsOw/x+y9Jaw3chEqM6PZeccczizKISU1kyRXOOsyZwx6nHFZDJ5J31P1NDpN5WBEpSlnszl4Kp1Opol7MoxRoxkvWhy8GG8ZbKd0U+5sp6S9AQ6cZ+a+UtZ79UU4+ol8WovmkzYzF9fpdhZjZlOBb5aLvHMp7NLKs8c7aDYn8vVPrOmLMIpI7BOMIBGFicTfk/pkEjiN5npocRgnLumm0tnB5a4mnIcvkLuvhHWH+nIRTv3NHGpvmUPSglnMC40nxihhcY4uH49E0C3CKXPHUE0iaaEzaDPFQcoC5Vvot2nwCIN2Fms0wYkWB0bfOc1TAvtSTzPdH1wid+8V1rxXSViH3chFyKVi3Sxils5lblg8SwcpYTFuB7PZoiKKLGEQl8OmOxZBVCr7/9iAMMXw488WTlsLYaLRAqeZimhxGCFuKal2dXLJ3kLb2Svk7LnCygPlRDb34AizcGVVJiVr8wgrnMfsiETy/VXCwmxVS0PR6aqfclQyxOep16zhtJoOK0GYJMIQKGexnsA1muHR4sDQGcyqBHYXxY5Wmi6VkrX3CgX7y4j19EVYns7ldbnIVfOYHZPMhyzRvi1h4anRZEz8RKcp30HSHAiLU+JgCeuXnLZz+xrfnV8zIiZC4BwOB5WVlfT09Pj82JqpT1hYGFlZWVitI8+T0uIwAImk1tnFZUcrNZWVZOy5RP7+chK9chGOblpE95q55CWkss4aO2wJizE5uU0WlZgXnaZKdcRkqv7KcTmqhlNEosrB8KN1MNF31hNtMUy2JaDKykqio6PJzc31vUWqmdJIKWlsbKSyspK8vLwR76fFAePDc/eQtdDK1ZqrFP/6fWbvK2eNV1+EvZ9bTvPaucxISWelNY4of5WwsISpMthmK6Tkq5DTkAgjyigcQtzKUpgCmctTDX8KTE9PjxYGzZgQQpCYmEh9ff31N/Zi2otDRXcd79WcIundy8zeX86q03W9fREOfmop1WtnkZGdxSJrHAnmsBEfd0RObiGMmkVGCYu4HGUlRCUrIQiL7UtO82wv/VsOe7LeWY+UyZwQp4VBM1bG8r8zvcXh3DmiP//P3L3/RL9chIp1eSTNnMEcaxw3miNG/cF693oeFGFSk35YrAozjU5Txe2iM65fwmIalcbWaDSBY3qLQ2QkEWdLOPU3cyhZm0vkglzmhsSz3BKFeZyO5f69ngWbVmT1ZSTHzVA/YbHKfxASCUglDBDQVpqT+c56NEzV6/InZrOZxYsX43Q6WbBgAb/85S+JiIi4/o6DsHXrVjZu3Mg999zD5z73Ob761a+Sn58/6La7d+8mJCSENWtUsMVTTz1FREQEDzzwwJivRXN9prc45ORQvft5wssPcIc1hpBx9kYYuJS082gVDR12QmLSjCWjDGUxJMw0eiWIPsHwLhuurYIJZaoLoa8IDw/nxIkTANx///089dRTfPWrX+193+l0YrGMfkp59tlnh31/9+7dREVF9YrD9u3bR30OzeiZ3uIAzIhMg5B4nx7TJkMw46LWkoEjzsoXPrnRyElIA6RRKnuAEAWZIOiJMoj58pfBmKR9RkEB/PjHI9587dq1nDx5kt27d/Otb32L+Ph4zp8/z7lz5/jmN7/J7t27sdlsfOELX+CRRx5BSsmXvvQl3nzzTbKzswkJCek9VlFRET/84Q8pLCzkz3/+M48//jgul4ukpCSee+45nnrqKcxmMy+++CI//elPefvtt4mKimLjxo088MADHDp0CIDS0lLuvPNOTp06xdGjR/nqV79KR0cHSUlJvPDCC6Snp/e7hq1btxIeHs7x48epq6vj+eef51e/+hUHDx5k1apVvPDCCwD89a9/5Tvf+Q42m41Zs2bxH//xH0RFRfHd736XP/7xj3R3d7NmzRqefvpphBAUFRWxatUqdu3aRUtLC8899xxr164d/99ogpn24jBuTGYjF8HEppV5gOC7J6Iw4eJr2z5lRBmF9UUXBXDJSNOfqe589xdOp5M//elP3H777QAcO3aM06dPk5eXx44dO4iNjeXw4cPYbDZuuukmbrvtNo4fP86FCxc4e/YstbW15Ofn89BDD/U7bn19PQ8//DB79+4lLy+PpqYmEhIS2L59O1FRUXzta18D4O233wZg/vz52O12SkpKyMvLY+fOnWzevBmHw8GXvvQlfv/735OcnMzOnTv5p3/6J55//vlrrqW5uZmDBw/yhz/8gY997GO8++67PPvss9xwww2cOHGCrKwsnnzySd566y0iIyP5l3/5F370ox/x7W9/my9+8Yt8+9vfBuDTn/40r7/+OnfeeWfvZ3To0CHeeOMN/vmf/5m33nrLb38Pf6HFYSx4Jndp+AnCYsEcqnwHUalcOtOOCbeqhDpwnwAJg574phCjuMP3Jd3d3RQUFADKcvjsZz/LgQMHWLlyZW/8/F//+ldOnjzJq6++CkBrayvFxcXs3buXLVu2YDabycjIYMOGDdcc/7333mPdunW9x0pISLjumO6991527tzJN7/5TXbu3MnOnTu5cOECp0+f5sMf/jAALpfrGqvBw5133okQgsWLF5OamsrixYsBWLhwIaWlpVRWVnL27FluuukmAOx2O6tXq+/Qrl27+Nd//Ve6urpoampi4cKFveJw9913A7BixQpKS0uv/+EGIQERByHEJuAJYAGwUkp5xOu9fwQ+C7iAx6SUfwnEGAfFE3pqtkJolOqHEJ8HsZmqk5wRffSr7eF922uClunifPcV3j4HbyIjI3sfSyn56U9/ykc+8pF+27zxxht+GdPmzZvZtGkTd999N0II5syZw6lTp1i4cCEHDx687v6hoSqi0GQy9T72PHc6nZjNZj784Q/z8ssv99uvp6eHz3/+8xw5coTs7GyeeOKJftnrnmOZzWacTt83DZsIfFjrYVScBu4G9nq/KITIB+4DFgK3Az8XYpxeYl9gMitHcng8xGbBjDWQdQPMulWVsohKUyIRnqAsCeHfXITRsPnpg2x++iDvlzTxNP/DBwAAGdtJREFUfklT73ONxh985CMf4Re/+AUOh2qadfHiRTo7O1m3bh07d+7E5XJRXV3Nrl27rtn3xhtvZO/evZSUlADQ1KSW+6Kjo2lvbx/0fLNmzcJsNvO9732PzZs3AzBv3jzq6+t7xcHhcHDmzJkxXc+NN97Iu+++y6VLlwDo7Ozk4sWLvUKQlJRER0dHr6U0lQiI5SClPAeDJmZ8HPi1lNIGlAghLgErgYmdzYTocxiHxqqkNJNVFbsLj4PYbJAutZSk8w4mPdpi8B2f+9znKC0tZfny5UgpSU5O5rXXXuOuu+7inXfeIT8/n5ycnN6lGW+Sk5PZsWMHd999N263m5SUFN58803uvPNO7rnnHn7/+9/z05/+9Jr9Nm/ezNe//vVeUQkJCeHVV1/lscceo7W1FafTyZe//GUWLlw46utJTk7mhRdeYMuWLdhsNgCefPJJ5s6dy8MPP8yiRYtIS0vjhhtuGPWxgx0hvUMoJ/rkQuwGvuZZVhJC/Ax4T0r5ovH8OeBPUsprZFkIsQ3YBpCTk7OirKxsbIMofw8uG3cxwqRKYVvCIGkeuOzKUohOU++FxYHboawDt1tlNk8S9NLJ5ObcuXMsWLAg0MPQTGIG+x8SQhyVUhYOtr3fLAchxFtA2iBv/ZOU8vfjPb6UcgewA6CwsHB8CmcyG30RsiEkGiKTIH4GKg8hRP2YzMo6MBsf2SQSBo1GoxktfhMHKeWHxrBbFeBdvjTLeM1/WCMgY5nyGUQkqAik8DhlKcCUCT/VFoNGoxkNwRbK+gfgJSHEj4AMYA5wyK9nTJoLibP76h0ZOQv9mOTCoNFoNKMlIGsjQoi7hBCVwGrgf4QQfwGQUp4BXgHOAn8GviCldPl1MNYw5UPw9EbQy0UajUYTsGil3wG/G+K97wPfn9ABactgxGjHtkYzPdC3yRqNRqO5Bi0OmhGhk+mmN42NjRQUFFBQUEBaWhqZmZm9z+12+7D7HjlyhMcee+y65/BUXfU1RUVFHDlyZNhtfvzjH9PV1eWX809Wgs0hrdFofIQvlwATExN7S2c88cQT/QrhwfDlugsLCyksHDSUvh8HDhwY9zjHyo9//GM+9alPjbk/xVREWw6aEbHzkdXsfGQ1q/ISWJWX0PtcM33ZunUr27dvZ9WqVXzjG9/g0KFDrF69mmXLlrFmzRouXLgAqH4MGzduBJSwPPTQQxQVFTFz5kx+8pOf9B4vKiqqd/uioiLuuece5s+fz/33348nWfeNN95g/vz5rFixgscee6z3uN50d3dz3333sWDBAu666y66u7t733v00UcpLCxk4cKFfOc73wHgJz/5CVevXmX9+vWsX79+yO2mG9py0GimGBNZiryyspIDBw5gNptpa2tj3759WCwW3nrrLR5//HH++7//+5p9zp8/z65du2hvb2fevHk8+uijWK3WftscP36cM2fOkJGRwU033cS7775LYWEhjzzySG9J7y1btgw6pl/84hdERERw7tw5Tp48yfLly3vf+/73v09CQgIul4tbb72VkydP8thjj/GjH/2IXbt2kZSUNOR2S5Ys8eEnF/xocdCMiomwFnRE1ORh06ZNmM2qDllraysPPvggxcXFCCF6i+8N5I477iA0NJTQ0FBSUlKora0lKyur3zYrV67sfa2goIDS0lKioqKYOXNmb0nvLVu2sGPHjmuOv3fv3l4fx5IlS/pN6q+88go7duzA6XRSXV3N2bNnB530R7rdVEaLg0YzxZjIUuTe5bq/9a1vsX79en73u99RWlpKUVHRoPt4l8YeqqT1SLYZLSUlJfzwhz/k8OHDxMfHs3Xr1n5ltke73VRH+xw0QYOOiJrctLa2kpmZCdDbYtOXzJs3jytXrvQ2z9m5c+eg261bt46XXnoJgNOnT3Py5EkA2traiIyMJDY2ltraWv70pz/17uNdFny47aYT2nLQaKYoE70s941vfIMHH3yQJ598kjvuuMPnxw8PD+fnP/85t99+O5GRkUOWyX700Uf5zGc+w4IFC1iwYAErVqwAYOnSpSxbtoz58+eTnZ3d290NYNu2bdx+++1kZGSwa9euIbebTgS0ZLevKCwslNeLY9ZMHrTP4Vp0yW5FR0cHUVFRSCn5whe+wJw5c/jKV74S6GFNCkZbslsvK40Dveyh0UwszzzzDAUFBSxcuJDW1lYeeeSRQA9pyqKXlTRBh7YYNEPxla98RVsKE4QWhzEwkXHkGo1GEwj0spJGo9ForkFbDmNgIuPINRqNJhBoy0Gj0Wg016Ath3GgLQZNwNj1f3x7vPX/OKLNXnvtNe666y7OnTvH/PnzASgtLWXjxo2cPn161KdtaWnhpZde4vOf//yo9w1GXnvtNebOnUt+fv6w2z311FNERETwwAMPDLnNiRMnuHr1Kh/96Ed9PcwRoS0HjUYzYl5++WVuvvlmXn75ZZ8cr6WlhZ///Oej2scXpTT8gdPp5LXXXuPs2bPX3Xb79u3DCgMocXjjjTd8NbxRE6ge0puEEGeEEG4hRKHX67lCiG4hxAnj56lAjE+j0VxLR0cH+/fv///t3X1UVXW6wPHvI2JYjjgSmqUjTulM8nIQBd+uGjEBzSJT8S5p6VzNhY7efMEmM0eXvTrhy5pMm/GlUFYzphTmy2R5k4Wkk5qAAqI1mktaWqYoE45OVwV+949zOBc4h5cj4OHA81mLJZv923v/Hs/hPOzf3vv5kZKSwtatW522KS8vZ/78+YSHhxMSEsL69evt20ZFRREWFkZwcDA7d+4E4IUXXuDMmTOEhoYyf/58jDHMnz+foKAggoOD7SUysrKyGDFiBKNHj6Z///4sWbKEVatW2Y+7aNEi3nzzzWp9KSoqIigoyL68cuVKXnrpJcA6AdCCBQuIiIigX79+HDhwwN7/5557jqCgIEJCQlizZg0Aubm5jBo1ioEDBxITE8OFCxfs+0lKSmLQoEEsW7aMXbt2MX/+fEJDQzlz5gxvv/024eHhWCwW4uPj7RMKvfTSS6xcubLWvty8eZMlS5aQlpZGaGgoaWlp9O3bl+LiYgAqKip46KGH7MvNwV3DSoXAOGC9k3VnjDGhd7g/Sql67Ny5k9jYWPr164efnx+5ubn20hSVUlJS8PX1JTs7mxs3bjB8+HCio6Pp1asX27dvp3Pnzly+fJkhQ4YwevRokpOTKSwstE8ktG3bNvLy8sjPz+fy5cuEh4czcuRIAI4ePUphYSF9+vShqKiIcePGkZSUREVFBVu3buXIkSMuxVNWVsaRI0f4+OOPefnll8nIyGDDhg0UFRWRl5dH+/btKSkp4datW8yePZudO3fi7+9PWloaixYtYuPGjQDcvHnTPtPc6dOniYuLY/z48QB06dKFadOmAbB48WJSUlKYPXt2g/ryyiuvkJOTw1tvvQVYS51v3ryZpKQkMjIysFgs+Pv7uxSzK9ySHIwxXwKIiDsOr5S6DVu2bGHu3LkAJCQksGXLFofk8Omnn1JQUEB6ejpgLcZ3+vRpevbsye9//3v2799Pu3bt+Pbbb7l48aLDMf7+97/z1FNP4eXlRffu3Rk1ahTZ2dl07tyZiIgIe7nugIAA/Pz8OHbsGBcvXmTAgAH4+fm5FM+4ceMAGDhwoL2YX0ZGBjNmzLDPate1a1cKCwspLCzkscceA6xnFz169LDvZ8KECbUeo7CwkMWLF/PDDz9w7do1YmJiGtyXmqZOncqTTz5JUlISGzdu5Omnn3YpXle1xAvSfUTkGHAVWGyMOeDuDinV1pWUlJCZmcnx48cREcrLyxERVqxYUa2dMYY1a9Y4fAimpqZSXFxMbm4u3t7eBAQEuFwGu2p5cIDExERSU1P5/vvvmTp1qkP79u3bU1FRYV+uebzKsuD1lQQ3xhAYGMihQ85L5dTsV1VTpkxhx44dWCwWUlNTycrKctquIX3p1asX3bt3JzMzkyNHjrB58+Zaj9sUmu2ag4hkiEihk68n69jsAvAzY8wA4FngPRHpXMv+p4tIjojkNOe4m1IK0tPT+c1vfsM333xDUVER586do0+fPvax+koxMTGsXbvWPtHPqVOnuH79OqWlpXTr1g1vb2/27dvHN998A1QvlQ0wYsQI0tLSKC8vp7i4mP379xMREeG0T2PHjmXPnj1kZ2c7/Yu8e/fuXLp0iStXrnDjxg0++uijeuN87LHHWL9+vf0DuqSkhF/84hcUFxfbk8OtW7c4ceKE0+1rxvOvf/2LHj16cOvWLZc/zGvuC6wJcdKkSdUmWWouzXbmYIz51W1scwO4Yfs+V0TOAP0Ah5KrxpgNwAawVmVtXG+V8jANvPW0qWzZsoUFCxZU+1l8fLzDzxMTEykqKiIsLAxjDP7+/uzYsYOJEyfyxBNPEBwczKBBg+y3wfr5+TF8+HCCgoJ4/PHHWb58OYcOHcJisSAiLF++nPvuu4+vvvrKoU8dOnQgMjKSLl26OP2g9Pb2ZsmSJURERPDAAw/Yj1mXxMRETp06RUhICN7e3kybNo1Zs2aRnp7OnDlzKC0tpaysjKSkJAIDAx22T0hIYNq0aaxevZr09HReffVVBg8ejL+/P4MHD3b4sK9LZGQkycnJhIaGsnDhQiZMmMDo0aN5+umnm31ICdxcsltEsoDnjDE5tmV/oMQYUy4iPwcOAMHGmJK69qMlu1VrpyW7HVVUVBAWFsYHH3xA37593d2dOyInJ4d58+Y5nLE1hEeU7BaRsSJyHhgK7BaR/7GtGgkUiEgekA7MqC8xKKXanpMnT/LQQw8RFRXVZhJDcnIy8fHxvP56Ez8AWQud7EcpD6BnDqqxPOLMQSmlVMumyUEppZQDTQ5KKaUcaHJQSinloCU+Ia2Uqsef81yrZFqf/w6tv2S2l5cXwcHB9uWEhAReeOGFWtvXV5Y6KyuLDh06MGzYMNc77ERiYiLPPvtsveWy3WXVqlVMnz6du+++u852DYmjoaXBG0OTg1KqQTp27GgvkNcQM2bMqHN9VlYWnTp1arLk8M477zTJfppDeXk5q1atYtKkSfUmh4bEsWPHDuLi4po1OeiwklKqUQICAnj++ecJDg4mIiKCr7/+Gqhelnr16tX079+fkJAQEhISKCoqYt26dbzxxhuEhoZy4MABiouLiY+PJzw8nPDwcD7//HP7fiZPnsyIESPo3bs3H374of14sbGx9lIdjzzyiL066p49ewgLC8NisRAVFeXQ59TUVGbNmmVfjouLs9c96tSpE4sWLcJisTBkyBB7gcCLFy8yduxYLBYLFouFgwcPAvDXv/6ViIgIQkND+e1vf0t5ebl9P7/73e+wWCwsXbqU7777jsjISCIjIwGYOXMmgwYNIjAwkBdffNHel6pxOOvLwYMHHUqDh4WF2bc/ffp0teXbpclBKdUgP/74I6GhofavyrkWAHx9fTl+/DizZs0iKSnJYdvk5GSOHTtGQUEB69atIyAggBkzZjBv3jzy8vIYMWIEc+fOZd68eWRnZ7Nt2zYSExPt2585c4bMzEx27drFpEmTiIyM5Pjx43Ts2JHdu3dXO1ZxcTHTpk1j27Zt5Ofn88EHH7gU5/Xr1xkyZAj5+fmMHDmSt99+G4A5c+YwatQo8vPzOXr0KIGBgXz55ZekpaXx+eefk5eXh5eXl72G0vXr1xk8eDD5+fksWbKE+++/n3379rFv3z4Ali5dSk5ODgUFBXz22WcUFBQ0qC/Dhg1j9OjRrFixgry8PB588EF8fX3tZ3WbNm1qkvIaOqzUBk1Yby0gptOcKlfUNaz01FNP2f+dN2+ew/qQkBAmTpzImDFjGDNmjNN9ZGRkVJtF7erVq1y7dg2Axx9/HG9vb4KDgykvLyc2NhaA4OBghxLXhw8fZuTIkfby3l27dnUpzg4dOhAXFwdYS2jv3bsXgMzMTN59913Aev3F19eXv/zlL+Tm5hIeHg5YE2i3bt3sbeLj42s9zvvvv8+GDRsoKyvjwoULnDx5kpCQkAb1pabExEQ2bdrEH//4R9LS0lye28IZTQ5KqUarOjeLs3ladu/ezf79+/nb3/7G0qVLOX78uEObiooKDh8+jI+Pj8O6ypLW7dq1w9vb236Mdu3a3da0oXWV8666/4aU8548ebLTkhY+Pj61Vk49e/YsK1euJDs7m5/+9KdMmTLFaQnzhvYlPj6el19+mUcffZSBAwe6PLeFMzqs1IZMWH+ICesP8cXZEr44W2JfVqqxKoeY0tLSGDq0+hlpRUUF586dIzIykmXLllFaWsq1a9ccSlJHR0fbp+UEXLr4XdWQIUPYv38/Z8+eBaxlt2sKCAggLy/P3reG/KUdFRXF2rVrAesF5tLSUqKiokhPT+fSpUv2Y1WWI6+parxXr17lnnvuwdfXl4sXL/LJJ5+4FGPN/zsfHx9iYmKYOXNmk1Vs1TMHpTxQQ249bWqV1xwqxcbGkpycDMA///lPQkJCuOuuu9iyZUu17crLy5k0aRKlpaUYY5gzZw5dunThiSeeYPz48ezcuZM1a9awevVqnnnmGUJCQigrK2PkyJGsW+f6NPL+/v5s2LCBcePGUVFRQbdu3RyGY4YPH06fPn3o378/Dz/8cIMu4L755ptMnz6dlJQUvLy8WLt2LUOHDuW1114jOjqaiooKvL29+dOf/kTv3r0dtp8+fTqxsbH2aw8DBgzgl7/8Jb169WL48OEuxVizNPiDDz7IxIkT2b59O9HR0S7tqzZaeK8N0msOnqclF94LCAggJyeHe++9191dadNWrlxJaWkpr776qtP1rhbe0zMHpZTycGPHjrXf0dVUNDm0QXrGoJpSzbuF1J23ffv2Jt+nXpBWykO0hiFg5R63897R5KCUB/Dx8eHKlSuaIJTLjDFcuXLF6S3CddFhJaU8QM+ePTl//jzFxcXu7oryQD4+PvTs2dOlbTQ5KOUBvL297U/8KnUnuGVYSURWiMhXIlIgIttFpEuVdQtF5GsR+YeIxLijf0op1da565rDXiDIGBMCnAIWAohIfyABCARigT+LiPPnz5VSSjUbtyQHY8ynxpjKIiGHgcrBsCeBrcaYG8aYs8DXQIQ7+qiUUm1ZS7jmMBWorP37ANZkUem87WcORGQ6MN22eE1E/tGIPtwLXG7E9p6iLcTZFmIEjbO1cVecjnU+bJotOYhIBnCfk1WLjDE7bW0WAWXAZlf3b4zZAGxoVCdtRCSntkfIW5O2EGdbiBE0ztamJcbZbMnBGPOrutaLyBQgDogy/3/z9rdAryrNetp+ppRS6g5y191KscDzwGhjzL+rrNoFJIjIXSLSB+gLNH7WCqWUUi5x1zWHt4C7gL22iSwOG2NmGGNOiMj7wEmsw03PGGPK70B/mmR4ygO0hTjbQoygcbY2LS7OVlGyWymlVNPS2kpKKaUcaHJQSinloE0kBxH5TxE5ISIVIjKoxrp6y3WISKqInBWRPNtXqLN2LY2IzLaVKTkhIstraVMkIsdtcXncdHp1lWKp0c4j4xSRjSJySUQKa1n/iIiUVnlvLrnTfWwK9b0+rSjOuSJSaPudTHKyvsXE2RIegrsTCoFxwPqqP6xRruN+IENE+tVyEXy+MSa92XvaREQkEusT5xZjzA0R6VZH80hjjKc+aLQXWGiMKRORZVhLsSyopa0nxpmK9QaOd+toc8AYE3dnutOs6nt9PDpOEQkCpmGt+nAT2CMiHxljvq7RtEXE2SbOHIwxXxpjnD1B3ZrLdcwEko0xNwCMMZfc3J9mUUcpllbBGLMfKHF3P1STeBj4whjzb9t79jOsf7S2SG0iOdThAeBcleVay3UAS21DF2+IyF3N37VG6weMEJEvROQzEQmvpZ0BPhWRXFtJEk82FfiklnWtKc6ahopIvoh8IiKB7u7MbWrI6+PpcRZi/Z30E5G7gV9T/aHfSi0izlYzrNSQch2NsBD4HuiA9X7kBcArjdxno9UVM9bXtiswBAgH3heRnxvHe5f/wxjzrW3Yaa+IfGX7a7XFaKJSLC0+ztt0FOhtjLkmIr8GdmB9eNTT1Pf6eHycxpgvbUOfnwLXgTyg5hB2i4mz1SSH+sp11KJB5TqMMRds394QkU3Ac7dxrCZXV8wiMhP40JYMjohIBdbiXtWmEjPGfGv795KIbMc6rNaiPjRvsxRLzX20+DhvhzHmapXvPxaRP4vIvZ52baW+16cVxZkCpACIyB+wjlZUXd9i4mzrw0oNKtchIj1s/wowBuvpYUu3A4gEEJF+WM96qr3BROQeEflJ5fdANJ4Rm53UXoqlahuPj7M2InKf7X2JiERg/Z2+4t5euaYhr09riBOg8sYQEfkZ1usN79VY32LibDVnDnURkbHAGsAf2C0iecaYmLrKdYjIx0CiMeY7YLOI+AOC9VRwhlsCcc1GYKPtFsibwGRjjBGR+4F3jDG/BroD223vxfbAe8aYPW7r8e1xWoqltcQpIluAR4B7ReQ88CLgDWCMWQeMB2aKSBnwI5BQ29lTC+b09RGRGdCq4gTYJiJ+wC2snzc/tNQ4tXyGUkopB219WEkppZQTmhyUUko50OSglFLKgSYHpZRSDjQ5KKWUcqDJQSmllANNDkoppRxoclCqGYhIuK1Qo4/tCeATtpLNSnkEfQhOqWYiIq8BPkBH4Lwx5nU3d0mpBtPkoFQzEZEOQDbwv8CwWiaRUqpF0mElpZqPH9AJ+AnWMwilPIaeOSjVTERkF7AV6AP0MMbMcnOXlGqwNlGVVak7TUT+C7hljHlPRLyAgyLyqDEm0919U6oh9MxBKaWUA73moJRSyoEmB6WUUg40OSillHKgyUEppZQDTQ5KKaUcaHJQSinlQJODUkopB/8HZ5SIRw6M3TwAAAAASUVORK5CYII=\n", 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" 258 | ] 259 | }, 260 | "metadata": { 261 | "needs_background": "light" 262 | }, 263 | "output_type": "display_data" 264 | } 265 | ], 266 | "source": [ 267 | "NSAMPLETEST = 10000\n", 268 | "(x_test, y_test) = sampleData(NSAMPLETEST, VAR)\n", 269 | "\n", 270 | "\n", 271 | "with ed.interception(ed.make_value_setter(W=qW,x=x_test)):\n", 272 | " pW,px,py = model(NSAMPLETEST)\n", 273 | "\n", 274 | "#plt.figure(figsize=(8, 8))\n", 275 | "y_pred_list = []\n", 276 | "y_pred_noise = []\n", 277 | "\n", 278 | "for i in range(100):\n", 279 | " [mean, noise] = sess.run([py.distribution.mean(), py])\n", 280 | " y_pred_list.append(mean)\n", 281 | " y_pred_noise.append(noise)\n", 282 | "\n", 283 | "y_preds = np.concatenate(y_pred_list, axis=1)\n", 284 | "y_preds_noise = np.concatenate(y_pred_noise, axis=1)\n", 285 | "\n", 286 | "y_mean = np.mean(y_preds, axis=1)\n", 287 | "y_sigma = np.std(y_preds, axis=1)\n", 288 | "\n", 289 | "y_sigma_noise = np.std(y_preds_noise, axis=1)\n", 290 | "\n", 291 | "plt.plot(x_test, y_mean, 'r-', label='Predictive mean');\n", 292 | "plt.scatter(x_train, y_train, marker='+', label='Training data')\n", 293 | "plt.fill_between(x_test.ravel(),\n", 294 | " y_mean + 2 * y_sigma_noise,\n", 295 | " y_mean - 2 * y_sigma_noise,\n", 296 | " alpha=0.5, label='Aleatory uncertainty')\n", 297 | "\n", 298 | "plt.fill_between(x_test.ravel(),\n", 299 | " y_mean + 2 * y_sigma,\n", 300 | " y_mean - 2 * y_sigma,\n", 301 | " alpha=0.5, label='Epistemic uncertainty')\n", 302 | "\n", 303 | "\n", 304 | "plt.ylabel('y')\n", 305 | "plt.xlabel('x')\n", 306 | "\n", 307 | "plt.ylim(-20,20)\n", 308 | "plt.xticks(np.arange(-10.5, 10.5, 4))\n", 309 | "plt.legend();\n", 310 | "\n", 311 | "plt.title('Bayesian Posterior Predictive')\n", 312 | "plt.show()" 313 | ] 314 | }, 315 | { 316 | "cell_type": "markdown", 317 | "metadata": {}, 318 | "source": [ 319 | "We also compute the *log-likelihood of the predicitive posterior* over the independent test data set." 320 | ] 321 | }, 322 | { 323 | "cell_type": "code", 324 | "execution_count": 7, 325 | "metadata": {}, 326 | "outputs": [ 327 | { 328 | "name": "stdout", 329 | "output_type": "stream", 330 | "text": [ 331 | "WARNING:tensorflow:From /Users/andresmasegosa/Google Drive/papers/2019-denmark-pac-bayes/tfp0.8/lib/python3.6/site-packages/tensorflow_core/python/ops/math_ops.py:2509: where (from tensorflow.python.ops.array_ops) is deprecated and will be removed in a future version.\n", 332 | "Instructions for updating:\n", 333 | "Use tf.where in 2.0, which has the same broadcast rule as np.where\n", 334 | "\n", 335 | "Negative Log-likelihood of the posterior predictive distribution: -130971.31\n" 336 | ] 337 | } 338 | ], 339 | "source": [ 340 | "y_pred_list = []\n", 341 | "for i in range(100):\n", 342 | " y_pred_list.append(sess.run(py.distribution.log_prob(y_test)))\n", 343 | "\n", 344 | "y_preds = tf.concat(y_pred_list, axis=1)\n", 345 | "\n", 346 | "score = tf.reduce_sum(tf.math.reduce_logsumexp(y_preds,axis=1)-tf.log(100.))\n", 347 | "\n", 348 | "score = sess.run(score)\n", 349 | "\n", 350 | "print(\"\\nNegative Log-likelihood of the posterior predictive distribution: \"+str(score))" 351 | ] 352 | }, 353 | { 354 | "cell_type": "markdown", 355 | "metadata": {}, 356 | "source": [ 357 | "And we also plot the posterior distribution $\\rho(\\theta|D)$ or $\\rho_h(\\theta|D)$" 358 | ] 359 | }, 360 | { 361 | "cell_type": "code", 362 | "execution_count": 8, 363 | "metadata": {}, 364 | "outputs": [ 365 | { 366 | "data": { 367 | "image/png": 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\n", 368 | "text/plain": [ 369 | "
" 370 | ] 371 | }, 372 | "metadata": { 373 | "needs_background": "light" 374 | }, 375 | "output_type": "display_data" 376 | } 377 | ], 378 | "source": [ 379 | "N = 2000\n", 380 | "frame=2\n", 381 | "X = np.linspace(1.-frame, 1+frame, N)\n", 382 | "Y = np.linspace(1.-frame, 1.+frame, N)\n", 383 | "X, Y = np.meshgrid(X, Y)\n", 384 | "\n", 385 | "\n", 386 | "\n", 387 | "# Pack X and Y into a single 3-dimensional array\n", 388 | "pos = np.empty(X.shape + (2,))\n", 389 | "pos[:, :, 0] = X\n", 390 | "pos[:, :, 1] = Y\n", 391 | "Z = sess.run(tf.squeeze(qW.distribution.log_prob(tf.expand_dims(np.float32(pos),2))))\n", 392 | "\n", 393 | "\n", 394 | "# Create a surface plot and projected filled contour plot under it.\n", 395 | "plt.contourf(X, Y, np.exp(Z-np.max(Z)))\n", 396 | "plt.ylabel(r'$\\theta_0$')\n", 397 | "plt.xlabel(r'$\\theta_1$')\n", 398 | "\n", 399 | "plt.title('Bayesian Posterior')\n", 400 | "\n", 401 | "plt.show()" 402 | ] 403 | }, 404 | { 405 | "cell_type": "code", 406 | "execution_count": null, 407 | "metadata": {}, 408 | "outputs": [], 409 | "source": [] 410 | } 411 | ], 412 | "metadata": { 413 | "kernelspec": { 414 | "display_name": "Python 3", 415 | "language": "python", 416 | "name": "python3" 417 | }, 418 | "language_info": { 419 | "codemirror_mode": { 420 | "name": "ipython", 421 | "version": 3 422 | }, 423 | "file_extension": ".py", 424 | "mimetype": "text/x-python", 425 | "name": "python", 426 | "nbconvert_exporter": "python", 427 | "pygments_lexer": "ipython3", 428 | "version": "3.6.6" 429 | } 430 | }, 431 | "nbformat": 4, 432 | "nbformat_minor": 2 433 | } 434 | -------------------------------------------------------------------------------- /results/output-PAC2-Ensemble-SelfSupervisedBinomial.txt: -------------------------------------------------------------------------------- 1 | -1072927.046875 2 | -971425.859375 3 | -1072292.3203125 4 | -909174.8203125 5 | -973392.375 6 | -3060388.53125 7 | -2685734.21875 8 | -3060205.5625 9 | -2528124.421875 10 | -2764825.15625 11 | -------------------------------------------------------------------------------- /results/output-PAC2-Ensemble-SelfSupervisedNormal.txt: -------------------------------------------------------------------------------- 1 | -4188668544.0 2 | -3668283744.0 3 | -4188668608.0 4 | -3354778816.0 5 | -3770238016.0 6 | -6458923456.0 7 | -5276280160.0 8 | -6458387072.0 9 | -4879477408.0 10 | -5790183872.0 11 | -------------------------------------------------------------------------------- /results/output-PAC2-Ensemble-Supervised.txt: -------------------------------------------------------------------------------- 1 | -4237.10888671875 2 | -3708.306884765625 3 | -4143.0458984375 4 | -3478.138214111328 5 | -4074.097930908203 6 | -18346.316284179688 7 | -17616.094482421875 8 | -17984.421752929688 9 | -17587.974243164062 10 | -18065.897827148438 11 | -------------------------------------------------------------------------------- /results/output-PAC2-Variational-SelfSupervisedBinomial.txt: -------------------------------------------------------------------------------- 1 | -1047369.4921875 2 | -1032353.3671875 3 | -999141.0078125 4 | -1007490.7109375 5 | -3084409.0625 6 | -2965045.21875 7 | -2789976.9375 8 | -2886265.3125 9 | -------------------------------------------------------------------------------- /results/output-PAC2-Variational-SelfSupervisedNormal.txt: -------------------------------------------------------------------------------- 1 | -4202852800.0 2 | -4142325856.0 3 | -3966816640.0 4 | -4096042368.0 5 | -6491180032.0 6 | -6328674240.0 7 | -5875705920.0 8 | -6078520256.0 9 | -------------------------------------------------------------------------------- /results/output-PAC2-Variational-Supervised.txt: -------------------------------------------------------------------------------- 1 | -4124.8343505859375 2 | -3598.2618713378906 3 | -3558.934844970703 4 | -3610.3741149902344 5 | -18268.12060546875 6 | -19309.876220703125 7 | -19156.56396484375 8 | -18685.65283203125 9 | -------------------------------------------------------------------------------- /scripts/PAC2-Ensemble-SelfSupervisedBinomial.py: -------------------------------------------------------------------------------- 1 | import matplotlib.pyplot as plt 2 | import numpy as np 3 | import tensorflow as tf 4 | from tensorflow_probability import edward2 as ed 5 | import tensorflow_probability as tfp 6 | 7 | 8 | 9 | def PAC2Ensemble(dataSource=tf.keras.datasets.fashion_mnist, NPixels=28, algorithm=0, num_ensemble_models=20, batch_size=100, num_epochs=50, num_hidden_units=20): 10 | """ Run experiments for Ensemble, PAC^2-Ensemble and PAC^2_T-Ensemble algorithms for the self-supervised classification task with a Categorical data model. 11 | Args: 12 | dataSource: The data set used in the evaluation. 13 | NPixels: The size of the images: NPixels\times NPixels. 14 | algorithm: Integer indicating the algorithm to be run. 15 | 0- Ensemble Learning [As derived for a first-order PAC-Bayes bound. No change in performance when using several models.] 16 | 1- PAC^2-Ensemble Learning 17 | 2- PAC^2_T-Ensemble Learning 18 | num_ensemble_models: Number of models in the ensemble. 19 | batch_size: Size of the batch. 20 | num_epochs: Number of epochs. 21 | num_hidden_units: Number of hidden units in the MLP. 22 | Returns: 23 | NLL: The negative log-likelihood over the test data set. 24 | :param algorithm: 25 | :param algorithm: 26 | """ 27 | 28 | np.random.seed(1) 29 | tf.set_random_seed(1) 30 | 31 | K=num_ensemble_models 32 | 33 | sess = tf.Session() 34 | 35 | 36 | (x_train, y_train), (x_test, y_test) = dataSource.load_data() 37 | 38 | if (dataSource.__name__.__contains__('cifar')): 39 | x_train=sess.run(tf.cast(tf.squeeze(tf.image.rgb_to_grayscale(x_train)),dtype=tf.float32)) 40 | x_test=sess.run(tf.cast(tf.squeeze(tf.image.rgb_to_grayscale(x_test)),dtype=tf.float32)) 41 | 42 | x_train = (x_train < 128).astype(np.int32) 43 | x_test = (x_test < 128 ).astype(np.int32) 44 | 45 | NPixels = np.int(NPixels/2) 46 | 47 | y_train = x_train[:, NPixels:] 48 | x_train = x_train[:, 0:NPixels] 49 | 50 | y_test = x_test[:, NPixels:] 51 | x_test = x_test[:, 0:NPixels] 52 | 53 | NPixels= NPixels * NPixels * 2 54 | 55 | 56 | 57 | 58 | 59 | 60 | N = x_train.shape[0] 61 | M = batch_size 62 | 63 | x_batch = tf.placeholder(dtype=tf.float32, name="x_batch", shape=[None, NPixels]) 64 | y_batch = tf.placeholder(dtype=tf.float32, name="y_batch", shape=[None, NPixels]) 65 | 66 | 67 | def model(NHIDDEN, x): 68 | W = tf.Variable(tf.random_normal([NPixels, NHIDDEN], 0.0, 0.1, dtype=tf.float32, seed=1)) 69 | b = tf.Variable(tf.random_normal([1, NHIDDEN], 0.0, 0.1, dtype=tf.float32, seed=1)) 70 | 71 | W_out = tf.Variable(tf.random_normal([NHIDDEN, 2 * NPixels], 0.0, 0.1, dtype=tf.float32, seed=1)) 72 | b_out = tf.Variable(tf.random_normal([1, 2 * NPixels], 0.0, 0.1, dtype=tf.float32, seed=1)) 73 | 74 | hidden_layer = tf.nn.tanh(tf.matmul(x, W) + b) 75 | out = tf.matmul(hidden_layer, W_out) + b_out 76 | y = ed.Categorical(logits=tf.reshape(out, [tf.shape(x_batch)[0], NPixels, 2]), name="y") 77 | 78 | ###Prior 79 | normal = tf.distributions.Normal(0., 1.) 80 | logpiror = tf.math.reduce_sum(normal.log_prob(W)) + \ 81 | tf.math.reduce_sum(normal.log_prob(b)) + \ 82 | tf.math.reduce_sum(normal.log_prob(W_out)) + \ 83 | tf.math.reduce_sum(normal.log_prob(b_out)) 84 | 85 | return x, y, logpiror 86 | 87 | t = [] 88 | tpy = [] 89 | logprior = tf.constant(0.) 90 | for i in range(K): 91 | px,py, logp = model(num_hidden_units, x_batch) 92 | t.append(tf.expand_dims(tf.reduce_sum(py.distribution.log_prob(y_batch),axis=1),1)) 93 | tpy.append(py) 94 | logprior = logprior + logp 95 | 96 | probs = tf.math.softmax(tf.Variable(tf.ones([K], dtype=tf.float32), trainable=False, name='probs')) 97 | 98 | 99 | ensemble = tf.concat(t,1) 100 | 101 | if K>1: 102 | max = tf.stop_gradient(tf.math.reduce_max(ensemble,axis=1)) 103 | logmean = tf.stop_gradient(tf.math.reduce_logsumexp(ensemble + tf.reshape(tf.tile(tf.log(probs), [batch_size]), [batch_size, K]), axis=1) - tf.log(K + 0.0)) 104 | varlist = [] 105 | 106 | ##### 107 | inc = logmean-max 108 | if (algorithm==2): 109 | hmax = 2*tf.stop_gradient(inc/tf.math.pow(1-tf.math.exp(inc),2) + tf.math.pow(tf.math.exp(inc)*(1-tf.math.exp(inc)),-1)) 110 | else: 111 | hmax = 1. 112 | ##### 113 | 114 | 115 | for i in range(K): 116 | vari = 0.5*(tf.reduce_mean(tf.exp(2*ensemble[:,i]-2*max)*hmax,axis=0)) 117 | for j in range(K): 118 | vari = vari - 0.5*tf.reduce_sum(tf.reduce_mean(tf.exp(ensemble[:,i] + ensemble[:,j] - 2*max)*hmax,axis=0))*probs[j] 119 | varlist.append(vari) 120 | 121 | 122 | 123 | var=tf.stack(varlist,0) 124 | else: 125 | var=tf.constant(0.) 126 | 127 | dataenergy = tf.reduce_mean(ensemble,axis=0) 128 | 129 | if (algorithm==1 or algorithm==2): 130 | elboEnsemble = dataenergy + var 131 | elbo = tf.reduce_sum(tf.math.multiply(elboEnsemble, probs)) 132 | elbo = elbo + 2 * tf.reduce_sum(tf.math.multiply(probs, tf.log(probs)))/N + logprior/N 133 | elif (algorithm == 0): 134 | elboEnsemble = dataenergy 135 | elbo = tf.reduce_sum(tf.math.multiply(elboEnsemble,probs)) 136 | elbo = elbo + tf.reduce_sum(tf.math.multiply(probs,tf.log(probs)))/N + logprior/N 137 | 138 | 139 | verbose=True 140 | sess = tf.Session() 141 | optimizer = tf.train.AdamOptimizer(0.001) 142 | t = [] 143 | train = optimizer.minimize(-elbo) 144 | init = tf.global_variables_initializer() 145 | sess.run(init) 146 | 147 | 148 | 149 | 150 | for i in range(num_epochs+1): 151 | perm = np.random.permutation(N) 152 | x_train = np.take(x_train, perm, axis=0) 153 | y_train = np.take(y_train, perm, axis=0) 154 | 155 | x_batches = np.array_split(x_train, N / M) 156 | y_batches = np.array_split(y_train, N / M) 157 | 158 | for j in range(N // M): 159 | batch_x = np.reshape(x_batches[j], [x_batches[j].shape[0], -1]).astype(np.float32) 160 | batch_y = np.reshape(y_batches[j],[y_batches[j].shape[0],-1]).astype(np.float32) 161 | 162 | value, _ = sess.run([elbo, train],feed_dict={x_batch: batch_x, y_batch: batch_y}) 163 | t.append(value) 164 | if verbose: 165 | if j % 1000 == 0: print(".", end="", flush=True) 166 | if i%50==0 and j % 1000 == 0: 167 | print("\nEpoch: " + str(i)) 168 | str_elbo = str(-t[-1]) 169 | print("\n" + str(j) + " epochs\t" + str_elbo, end="", flush=True) 170 | print("\n" + str(j) + " data\t" + str(sess.run(dataenergy,feed_dict={x_batch: batch_x, y_batch: batch_y})), end="", flush=True) 171 | if K>1: print("\n" + str(j) + " var\t" + str(sess.run(var,feed_dict={x_batch: batch_x, y_batch: batch_y})), end="", flush=True) 172 | if K>1: print("\n" + str(i) + " hmax\t" + str(sess.run(tf.reduce_mean(hmax),feed_dict={x_batch: batch_x, y_batch: batch_y})), end="", flush=True) 173 | 174 | 175 | 176 | 177 | M=1000 178 | N=x_test.shape[0] 179 | x_batches = np.array_split(x_test, N / M) 180 | y_batches = np.array_split(y_test, N / M) 181 | 182 | NLL = 0 183 | 184 | for j in range(N // M): 185 | batch_x = np.reshape(x_batches[j], [x_batches[j].shape[0], -1]).astype(np.float32) 186 | batch_y = np.reshape(y_batches[j], [y_batches[j].shape[0], -1]).astype(np.float32) 187 | y_pred_list = [] 188 | for i in range(K): 189 | y_pred_list.append(tf.expand_dims(tf.reduce_sum(tpy[i].distribution.log_prob(y_batch), axis=1), 1)) 190 | y_preds = tf.concat(y_pred_list, axis=1) 191 | score = tf.reduce_sum(tf.math.reduce_logsumexp(y_preds, axis=1) - tf.log(K + 0.0)) 192 | score = sess.run(score,feed_dict={x_batch: batch_x, y_batch: batch_y}) 193 | NLL = NLL + score 194 | if verbose: 195 | if j % 1 == 0: print(".", end="", flush=True) 196 | if j % 1 == 0: 197 | str_elbo = str(score) 198 | print("\n" + str(j) + " epochs\t" + str_elbo, end="", flush=True) 199 | 200 | print("\nNLL: "+str(NLL)) 201 | 202 | return NLL 203 | 204 | 205 | 206 | iter=100 207 | batch=100 208 | text_file = open("./results/output-PAC2-Ensemble-SelfSupervisedBinomial.txt", "w") 209 | 210 | text_file.write(str(PAC2Ensemble(dataSource= tf.keras.datasets.fashion_mnist, NPixels=28, algorithm=0, num_ensemble_models=1, batch_size=batch, num_epochs=iter, num_hidden_units= 20)) + "\n") 211 | text_file.flush() 212 | text_file.write(str(PAC2Ensemble(dataSource= tf.keras.datasets.fashion_mnist, NPixels=28, algorithm=1, num_ensemble_models=2, batch_size=batch, num_epochs=iter, num_hidden_units= 20)) + "\n") 213 | text_file.flush() 214 | text_file.write(str(PAC2Ensemble(dataSource= tf.keras.datasets.fashion_mnist, NPixels=28, algorithm=2, num_ensemble_models=2, batch_size=batch, num_epochs=iter, num_hidden_units= 20)) + "\n") 215 | text_file.flush() 216 | text_file.write(str(PAC2Ensemble(dataSource= tf.keras.datasets.fashion_mnist, NPixels=28, algorithm=1, num_ensemble_models=3, batch_size=batch, num_epochs=iter, num_hidden_units= 20)) + "\n") 217 | text_file.flush() 218 | text_file.write(str(PAC2Ensemble(dataSource= tf.keras.datasets.fashion_mnist, NPixels=28, algorithm=2, num_ensemble_models=3, batch_size=batch, num_epochs=iter, num_hidden_units= 20)) + "\n") 219 | text_file.flush() 220 | 221 | 222 | text_file.write(str(PAC2Ensemble(dataSource= tf.keras.datasets.cifar10, NPixels=32, algorithm=0, num_ensemble_models=1, batch_size=batch, num_epochs=iter, num_hidden_units= 20)) + "\n") 223 | text_file.flush() 224 | text_file.write(str(PAC2Ensemble(dataSource= tf.keras.datasets.cifar10, NPixels=32, algorithm=1, num_ensemble_models=2, batch_size=batch, num_epochs=iter, num_hidden_units= 20)) + "\n") 225 | text_file.flush() 226 | text_file.write(str(PAC2Ensemble(dataSource= tf.keras.datasets.cifar10, NPixels=32, algorithm=2, num_ensemble_models=2, batch_size=batch, num_epochs=iter, num_hidden_units= 20)) + "\n") 227 | text_file.flush() 228 | text_file.write(str(PAC2Ensemble(dataSource= tf.keras.datasets.cifar10, NPixels=32, algorithm=1, num_ensemble_models=3, batch_size=batch, num_epochs=iter, num_hidden_units= 20)) + "\n") 229 | text_file.flush() 230 | text_file.write(str(PAC2Ensemble(dataSource= tf.keras.datasets.cifar10, NPixels=32, algorithm=2, num_ensemble_models=3, batch_size=batch, num_epochs=iter, num_hidden_units= 20)) + "\n") 231 | text_file.flush() 232 | 233 | 234 | text_file.close() -------------------------------------------------------------------------------- /scripts/PAC2-Ensemble-SelfSupervisedNormal.py: -------------------------------------------------------------------------------- 1 | import matplotlib.pyplot as plt 2 | import numpy as np 3 | import tensorflow as tf 4 | from tensorflow_probability import edward2 as ed 5 | import tensorflow_probability as tfp 6 | 7 | 8 | 9 | def PAC2Ensemble(dataSource=tf.keras.datasets.fashion_mnist, NPixels=28, algorithm=0, num_ensemble_models=1, batch_size=100, num_epochs=50, num_hidden_units=20): 10 | """ Run experiments for Ensemble, PAC^2-Ensemble and PAC^2_T-Ensemble algorithms for the self-supervised classification task with a Normal data model. 11 | Args: 12 | dataSource: The data set used in the evaluation. 13 | NPixels: The size of the images: NPixels\times NPixels. 14 | algorithm: Integer indicating the algorithm to be run. 15 | 0- Ensemble Learning [As derived for a first-order PAC-Bayes bound. No change in performance when using several models.] 16 | 1- PAC^2-Ensemble Learning 17 | 2- PAC^2_T-Ensemble Learning 18 | num_ensemble_models: Number of models in the ensemble. 19 | batch_size: Size of the batch. 20 | num_epochs: Number of epochs. 21 | num_hidden_units: Number of hidden units in the MLP. 22 | Returns: 23 | NLL: The negative log-likelihood over the test data set. 24 | :param algorithm: 25 | """ 26 | 27 | np.random.seed(1) 28 | tf.set_random_seed(1) 29 | 30 | K= num_ensemble_models 31 | 32 | sess = tf.Session() 33 | 34 | (x_train, y_train), (x_test, y_test) = dataSource.load_data() 35 | if (dataSource.__name__.__contains__('cifar')): 36 | x_train=sess.run(tf.cast(tf.squeeze(tf.image.rgb_to_grayscale(x_train)),dtype=tf.float32)) 37 | x_test=sess.run(tf.cast(tf.squeeze(tf.image.rgb_to_grayscale(x_test)),dtype=tf.float32)) 38 | 39 | NPixels = np.int(NPixels/2) 40 | 41 | y_train = x_train[:, NPixels:] 42 | x_train = x_train[:, 0:NPixels] 43 | 44 | y_test = x_test[:, NPixels:] 45 | x_test = x_test[:, 0:NPixels] 46 | 47 | NPixels= NPixels * NPixels * 2 48 | 49 | x_train, x_test = x_train / 255.0, x_test / 255.0 50 | y_train, y_test = y_train / 255.0, y_test / 255.0 51 | 52 | 53 | N = x_train.shape[0] 54 | M = batch_size 55 | 56 | x_batch = tf.placeholder(dtype=tf.float32, name="x_batch", shape=[None, NPixels]) 57 | y_batch = tf.placeholder(dtype=tf.float32, name="y_batch", shape=[None, NPixels]) 58 | 59 | 60 | def model(NHIDDEN, x): 61 | W = tf.Variable(tf.random_normal([NPixels, NHIDDEN], 0.0, 0.1, dtype=tf.float32, seed=1)) 62 | b = tf.Variable(tf.random_normal([1, NHIDDEN], 0.0, 0.1, dtype=tf.float32, seed=1)) 63 | 64 | W_out = tf.Variable(tf.random_normal([NHIDDEN, NPixels], 0.0, 0.1, dtype=tf.float32, seed=1)) 65 | b_out = tf.Variable(tf.random_normal([1, NPixels], 0.0, 0.1, dtype=tf.float32, seed=1)) 66 | 67 | hidden_layer = tf.nn.tanh(tf.matmul(x, W) + b) 68 | out = tf.matmul(hidden_layer, W_out) + b_out 69 | y = ed.Normal(loc=out, scale=1./255,name="y") 70 | 71 | ###Prior 72 | normal = tf.distributions.Normal(0., 1.) 73 | logpiror = tf.math.reduce_sum(normal.log_prob(W)) + \ 74 | tf.math.reduce_sum(normal.log_prob(b)) + \ 75 | tf.math.reduce_sum(normal.log_prob(W_out)) + \ 76 | tf.math.reduce_sum(normal.log_prob(b_out)) 77 | 78 | return x, y, logpiror 79 | 80 | t = [] 81 | tpy = [] 82 | logprior = tf.constant(0.) 83 | for i in range(K): 84 | px,py, logp = model(num_hidden_units, x_batch) 85 | t.append(tf.expand_dims(tf.reduce_sum(py.distribution.log_prob(y_batch),axis=1),1)) 86 | tpy.append(py) 87 | logprior = logprior + logp 88 | 89 | probs = tf.math.softmax(tf.Variable(tf.ones([K], dtype=tf.float32), trainable=False, name='probs')) 90 | 91 | 92 | ensemble = tf.concat(t,1) 93 | 94 | if K>1: 95 | max = tf.stop_gradient(tf.math.reduce_max(ensemble,axis=1)) 96 | logmean = tf.stop_gradient(tf.math.reduce_logsumexp(ensemble + tf.reshape(tf.tile(tf.log(probs), [batch_size]), [batch_size, K]), axis=1) - tf.log(K + 0.0)) 97 | varlist = [] 98 | 99 | ##### 100 | inc = logmean-max 101 | if (algorithm==2): 102 | hmax = 2*tf.stop_gradient(inc/tf.math.pow(1-tf.math.exp(inc),2) + tf.math.pow(tf.math.exp(inc)*(1-tf.math.exp(inc)),-1)) 103 | else: 104 | hmax = 1. 105 | ##### 106 | 107 | 108 | for i in range(K): 109 | vari = 0.5*(tf.reduce_mean(tf.exp(2*ensemble[:,i]-2*max)*hmax,axis=0)) 110 | for j in range(K): 111 | vari = vari - 0.5*tf.reduce_sum(tf.reduce_mean(tf.exp(ensemble[:,i] + ensemble[:,j] - 2*max)*hmax,axis=0))*probs[j] 112 | varlist.append(vari) 113 | 114 | 115 | 116 | var=tf.stack(varlist,0) 117 | else: 118 | var=tf.constant(0.) 119 | 120 | dataenergy = tf.reduce_mean(ensemble,axis=0) 121 | 122 | if (algorithm==1 or algorithm==2): 123 | elboEnsemble = dataenergy + var 124 | elbo = tf.reduce_sum(tf.math.multiply(elboEnsemble, probs)) 125 | elbo = elbo + 2 * tf.reduce_sum(tf.math.multiply(probs, tf.log(probs)))/N + logprior/N 126 | elif (algorithm == 0): 127 | elboEnsemble = dataenergy 128 | elbo = tf.reduce_sum(tf.math.multiply(elboEnsemble,probs)) 129 | elbo = elbo + tf.reduce_sum(tf.math.multiply(probs,tf.log(probs)))/N + logprior/N 130 | 131 | 132 | verbose=True 133 | sess = tf.Session() 134 | optimizer = tf.train.AdamOptimizer(0.001) 135 | t = [] 136 | train = optimizer.minimize(-elbo) 137 | init = tf.global_variables_initializer() 138 | sess.run(init) 139 | 140 | 141 | 142 | 143 | for i in range(num_epochs+1): 144 | perm = np.random.permutation(N) 145 | x_train = np.take(x_train, perm, axis=0) 146 | y_train = np.take(y_train, perm, axis=0) 147 | 148 | x_batches = np.array_split(x_train, N / M) 149 | y_batches = np.array_split(y_train, N / M) 150 | 151 | for j in range(N // M): 152 | batch_x = np.reshape(x_batches[j], [x_batches[j].shape[0], -1]).astype(np.float32) 153 | batch_y = np.reshape(y_batches[j],[y_batches[j].shape[0],-1]).astype(np.float32) 154 | 155 | value, _ = sess.run([elbo, train],feed_dict={x_batch: batch_x, y_batch: batch_y}) 156 | t.append(value) 157 | if verbose: 158 | if j % 1000 == 0: print(".", end="", flush=True) 159 | if i%50==0 and j % 1000 == 0: 160 | print("\nEpoch: " + str(i)) 161 | str_elbo = str(-t[-1]) 162 | print("\n" + str(j) + " epochs\t" + str_elbo, end="", flush=True) 163 | print("\n" + str(j) + " data\t" + str(sess.run(dataenergy,feed_dict={x_batch: batch_x, y_batch: batch_y})), end="", flush=True) 164 | if K>1: print("\n" + str(j) + " var\t" + str(sess.run(var,feed_dict={x_batch: batch_x, y_batch: batch_y})), end="", flush=True) 165 | if K>1: print("\n" + str(i) + " hmax\t" + str(sess.run(tf.reduce_mean(hmax),feed_dict={x_batch: batch_x, y_batch: batch_y})), end="", flush=True) 166 | 167 | 168 | 169 | 170 | M=1000 171 | N=x_test.shape[0] 172 | x_batches = np.array_split(x_test, N / M) 173 | y_batches = np.array_split(y_test, N / M) 174 | 175 | NLL = 0 176 | 177 | for j in range(N // M): 178 | batch_x = np.reshape(x_batches[j], [x_batches[j].shape[0], -1]).astype(np.float32) 179 | batch_y = np.reshape(y_batches[j], [y_batches[j].shape[0], -1]).astype(np.float32) 180 | y_pred_list = [] 181 | for i in range(K): 182 | y_pred_list.append(tf.expand_dims(tf.reduce_sum(tpy[i].distribution.log_prob(y_batch), axis=1), 1)) 183 | y_preds = tf.concat(y_pred_list, axis=1) 184 | score = tf.reduce_sum(tf.math.reduce_logsumexp(y_preds, axis=1) - tf.log(K + 0.0)) 185 | score = sess.run(score,feed_dict={x_batch: batch_x, y_batch: batch_y}) 186 | NLL = NLL + score 187 | if verbose: 188 | if j % 1 == 0: print(".", end="", flush=True) 189 | if j % 1 == 0: 190 | str_elbo = str(score) 191 | print("\n" + str(j) + " epochs\t" + str_elbo, end="", flush=True) 192 | 193 | print("\nNLL: "+str(NLL)) 194 | 195 | return NLL 196 | 197 | 198 | 199 | iter=100 200 | batch=100 201 | text_file = open("./results/output-PAC2-Ensemble-SelfSupervisedNormal.txt", "w") 202 | 203 | text_file.write(str(PAC2Ensemble(dataSource= tf.keras.datasets.fashion_mnist, NPixels=28, algorithm=0, num_ensemble_models=1, batch_size=batch, num_epochs=iter, num_hidden_units= 20)) + "\n") 204 | text_file.flush() 205 | text_file.write(str(PAC2Ensemble(dataSource= tf.keras.datasets.fashion_mnist, NPixels=28, algorithm=1, num_ensemble_models=2, batch_size=batch, num_epochs=iter, num_hidden_units= 20)) + "\n") 206 | text_file.flush() 207 | text_file.write(str(PAC2Ensemble(dataSource= tf.keras.datasets.fashion_mnist, NPixels=28, algorithm=2, num_ensemble_models=2, batch_size=batch, num_epochs=iter, num_hidden_units= 20)) + "\n") 208 | text_file.flush() 209 | text_file.write(str(PAC2Ensemble(dataSource= tf.keras.datasets.fashion_mnist, NPixels=28, algorithm=1, num_ensemble_models=3, batch_size=batch, num_epochs=iter, num_hidden_units= 20)) + "\n") 210 | text_file.flush() 211 | text_file.write(str(PAC2Ensemble(dataSource= tf.keras.datasets.fashion_mnist, NPixels=28, algorithm=2, num_ensemble_models=3, batch_size=batch, num_epochs=iter, num_hidden_units= 20)) + "\n") 212 | text_file.flush() 213 | 214 | 215 | text_file.write(str(PAC2Ensemble(dataSource= tf.keras.datasets.cifar10, NPixels=32, algorithm=0, num_ensemble_models=1, batch_size=batch, num_epochs=iter, num_hidden_units= 20)) + "\n") 216 | text_file.flush() 217 | text_file.write(str(PAC2Ensemble(dataSource= tf.keras.datasets.cifar10, NPixels=32, algorithm=1, num_ensemble_models=2, batch_size=batch, num_epochs=iter, num_hidden_units= 20)) + "\n") 218 | text_file.flush() 219 | text_file.write(str(PAC2Ensemble(dataSource= tf.keras.datasets.cifar10, NPixels=32, algorithm=2, num_ensemble_models=2, batch_size=batch, num_epochs=iter, num_hidden_units= 20)) + "\n") 220 | text_file.flush() 221 | text_file.write(str(PAC2Ensemble(dataSource= tf.keras.datasets.cifar10, NPixels=32, algorithm=1, num_ensemble_models=3, batch_size=batch, num_epochs=iter, num_hidden_units= 20)) + "\n") 222 | text_file.flush() 223 | text_file.write(str(PAC2Ensemble(dataSource= tf.keras.datasets.cifar10, NPixels=32, algorithm=2, num_ensemble_models=3, batch_size=batch, num_epochs=iter, num_hidden_units= 20)) + "\n") 224 | text_file.flush() 225 | 226 | 227 | text_file.close() -------------------------------------------------------------------------------- /scripts/PAC2-Ensemble-Supervised.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | import tensorflow as tf 3 | from tensorflow_probability import edward2 as ed 4 | import math 5 | 6 | 7 | def PAC2Ensemble(dataSource = tf.keras.datasets.fashion_mnist, NLabels=10, NPixels=28, algorithm=0, num_ensemble_models=1, batch_size=100, num_epochs=50, num_hidden_units = 20): 8 | """ Run experiments for Ensemble, PAC^2-Ensemble and PAC^2_T-Ensemble algorithms for the supervised classification task. 9 | Args: 10 | dataSource: The data set used in the evaluation. 11 | NLabels: The number of labels to predict. 12 | NPixels: The size of the images: NPixels\times NPixels. 13 | algorithm: Integer indicating the algorithm to be run. 14 | 0- Ensemble Learning [As derived for a first-order PAC-Bayes bound. No change in performance when using several models.] 15 | 1- PAC^2-Ensemble Learning 16 | 2- PAC^2_T-Ensemble Learning 17 | num_ensemble_models: Number of models in the ensemble. 18 | batch_size: Size of the batch. 19 | num_epochs: Number of epochs. 20 | num_hidden_units: Number of hidden units in the MLP. 21 | Returns: 22 | NLL: The negative log-likelihood over the test data set. 23 | """ 24 | 25 | np.random.seed(1) 26 | tf.set_random_seed(1) 27 | 28 | K= num_ensemble_models 29 | 30 | sess = tf.Session() 31 | 32 | (x_train, y_train), (x_test, y_test) = dataSource.load_data() 33 | 34 | if (dataSource.__name__.__contains__('cifar')): 35 | x_train=sess.run(tf.cast(tf.squeeze(tf.image.rgb_to_grayscale(x_train)),dtype=tf.float32)) 36 | x_test=sess.run(tf.cast(tf.squeeze(tf.image.rgb_to_grayscale(x_test)),dtype=tf.float32)) 37 | 38 | x_train, x_test = x_train / 255.0, x_test / 255.0 39 | 40 | 41 | N = x_train.shape[0] 42 | M = batch_size 43 | 44 | x_batch = tf.placeholder(dtype=tf.float32, name="x_batch", shape=[None, NPixels*NPixels]) 45 | y_batch = tf.placeholder(dtype=tf.float32, name="y_batch", shape=[None,]) 46 | 47 | 48 | def model(NHIDDEN, x): 49 | W = tf.Variable(tf.random_normal([NPixels*NPixels, NHIDDEN], 0.0, 0.1, dtype=tf.float32, seed=1)) 50 | b = tf.Variable(tf.random_normal([1, NHIDDEN], 0.0, 0.1, dtype=tf.float32, seed=1)) 51 | 52 | W_out = tf.Variable(tf.random_normal([NHIDDEN, NLabels], 0.0, 0.1, dtype=tf.float32, seed=1)) 53 | b_out = tf.Variable(tf.random_normal([1, NLabels], 0.0, 0.1, dtype=tf.float32, seed=1)) 54 | 55 | hidden_layer = tf.nn.tanh(tf.matmul(x, W) + b) 56 | out = tf.matmul(hidden_layer, W_out) + b_out 57 | y = ed.Categorical(logits=out, name="y") 58 | 59 | ###Prior 60 | normal = tf.distributions.Normal(0., 1.) 61 | logpiror = tf.math.reduce_sum(normal.log_prob(W)) + \ 62 | tf.math.reduce_sum(normal.log_prob(b)) + \ 63 | tf.math.reduce_sum(normal.log_prob(W_out)) + \ 64 | tf.math.reduce_sum(normal.log_prob(b_out)) 65 | 66 | return x, y, logpiror 67 | 68 | t = [] 69 | tpy = [] 70 | logprior = tf.constant(0.) 71 | for i in range(K): 72 | px,py, logp = model(num_hidden_units,x_batch) 73 | t.append(tf.expand_dims(py.distribution.log_prob(y_batch),axis=1)) 74 | tpy.append(py) 75 | logprior = logprior + logp 76 | 77 | probs = tf.math.softmax(tf.Variable(tf.ones([K], dtype=tf.float32), trainable=False, name='probs')) 78 | 79 | 80 | ensemble = tf.concat(t,1) 81 | 82 | if K>1: 83 | max = tf.constant(-math.log(0.9999)) 84 | logmean = tf.stop_gradient(tf.math.reduce_logsumexp(ensemble+tf.reshape(tf.tile(tf.log(probs),[batch_size]),[batch_size,K]), axis=1) - tf.log(K + 0.0)) 85 | varlist = [] 86 | 87 | ##### 88 | inc = logmean-max 89 | if (algorithm==2): 90 | hmax = 2*tf.stop_gradient(inc/tf.math.pow(1-tf.math.exp(inc),2) + tf.math.pow(tf.math.exp(inc)*(1-tf.math.exp(inc)),-1)) 91 | else: 92 | hmax = 1. 93 | ##### 94 | 95 | 96 | for i in range(K): 97 | vari = 0.5*(tf.reduce_mean(tf.exp(2*ensemble[:,i]-2*max)*hmax,axis=0)) 98 | for j in range(K): 99 | vari = vari - 0.5*tf.reduce_sum(tf.reduce_mean(tf.exp(ensemble[:,i] + ensemble[:,j] - 2*max)*hmax,axis=0))*probs[j] 100 | varlist.append(vari) 101 | 102 | 103 | 104 | var=tf.stack(varlist,0) 105 | else: 106 | var=tf.constant(0.) 107 | 108 | dataenergy = tf.reduce_mean(ensemble,axis=0) 109 | 110 | if (algorithm==1 or algorithm==2): 111 | elboEnsemble = dataenergy + var 112 | elbo = tf.reduce_sum(tf.math.multiply(elboEnsemble, probs)) 113 | elbo = elbo + 2 * tf.reduce_sum(tf.math.multiply(probs, tf.log(probs)))/N + logprior/N 114 | elif (algorithm==0): 115 | elboEnsemble = dataenergy 116 | elbo = tf.reduce_sum(tf.math.multiply(elboEnsemble,probs)) 117 | elbo = elbo + tf.reduce_sum(tf.math.multiply(probs,tf.log(probs)))/N + logprior/N 118 | 119 | 120 | verbose=True 121 | sess = tf.Session() 122 | optimizer = tf.train.AdamOptimizer(0.001) 123 | t = [] 124 | train = optimizer.minimize(-elbo) 125 | init = tf.global_variables_initializer() 126 | sess.run(init) 127 | 128 | 129 | 130 | 131 | for i in range(num_epochs+1): 132 | perm = np.random.permutation(N) 133 | x_train = np.take(x_train, perm, axis=0) 134 | y_train = np.take(y_train, perm, axis=0) 135 | 136 | x_batches = np.array_split(x_train, N / M) 137 | y_batches = np.array_split(y_train, N / M) 138 | 139 | for j in range(N // M): 140 | batch_x = np.reshape(x_batches[j], [batch_size, -1]).astype(np.float32) 141 | batch_y = np.reshape(y_batches[j],[batch_size,]).astype(np.float32) 142 | 143 | value, _ = sess.run([elbo, train],feed_dict={x_batch: batch_x, y_batch: batch_y}) 144 | t.append(value) 145 | if verbose: 146 | if j % 1000 == 0: print(".", end="", flush=True) 147 | if i%50==0 and j % 1000 == 0: 148 | print("\nEpoch: " + str(i)) 149 | str_elbo = str(-t[-1]) 150 | print("\n" + str(j) + " epochs\t" + str_elbo, end="", flush=True) 151 | print("\n" + str(j) + " data\t" + str(sess.run(dataenergy,feed_dict={x_batch: batch_x, y_batch: batch_y})), end="", flush=True) 152 | if K>1: print("\n" + str(j) + " var\t" + str(sess.run(var,feed_dict={x_batch: batch_x, y_batch: batch_y})), end="", flush=True) 153 | if K>1: print("\n" + str(i) + " hmax\t" + str(sess.run(tf.reduce_mean(hmax),feed_dict={x_batch: batch_x, y_batch: batch_y})), end="", flush=True) 154 | 155 | 156 | M=1000 157 | N=x_test.shape[0] 158 | x_batches = np.array_split(x_test, N / M) 159 | y_batches = np.array_split(y_test, N / M) 160 | 161 | NLL = 0 162 | 163 | for j in range(N // M): 164 | batch_x = np.reshape(x_batches[j], [M, -1]).astype(np.float32) 165 | batch_y = np.reshape(y_batches[j], [M,]).astype(np.float32) 166 | y_pred_list = [] 167 | for i in range(K): 168 | y_pred_list.append(tf.expand_dims(tpy[i].distribution.log_prob(batch_y), axis=1)) 169 | y_preds = tf.concat(y_pred_list, axis=1) 170 | score = tf.reduce_sum(tf.math.reduce_logsumexp(y_preds, axis=1) - tf.log(K + 0.0)) 171 | score = sess.run(score,feed_dict={x_batch: batch_x}) 172 | NLL = NLL + score 173 | if verbose: 174 | if j % 1 == 0: print(".", end="", flush=True) 175 | if j % 1 == 0: 176 | str_elbo = str(score) 177 | print("\n" + str(j) + " epochs\t" + str_elbo, end="", flush=True) 178 | 179 | print("\nNLL: "+str(NLL)) 180 | 181 | return NLL 182 | 183 | 184 | 185 | iter=100 186 | batch=100 187 | text_file = open("./results/output-PAC2-Ensemble-Supervised.txt", "w") 188 | 189 | text_file.write(str(PAC2Ensemble(dataSource= tf.keras.datasets.fashion_mnist, NLabels=10, NPixels=28, algorithm=0, num_ensemble_models=1, batch_size=batch, num_epochs=iter, num_hidden_units= 20)) + "\n") 190 | text_file.flush() 191 | text_file.write(str(PAC2Ensemble(dataSource= tf.keras.datasets.fashion_mnist, NLabels=10, NPixels=28, algorithm=1, num_ensemble_models=2, batch_size=batch, num_epochs=iter, num_hidden_units= 20)) + "\n") 192 | text_file.flush() 193 | text_file.write(str(PAC2Ensemble(dataSource= tf.keras.datasets.fashion_mnist, NLabels=10, NPixels=28, algorithm=2, num_ensemble_models=2, batch_size=batch, num_epochs=iter, num_hidden_units= 20)) + "\n") 194 | text_file.flush() 195 | text_file.write(str(PAC2Ensemble(dataSource= tf.keras.datasets.fashion_mnist, NLabels=10, NPixels=28, algorithm=1, num_ensemble_models=3, batch_size=batch, num_epochs=iter, num_hidden_units= 20)) + "\n") 196 | text_file.flush() 197 | text_file.write(str(PAC2Ensemble(dataSource= tf.keras.datasets.fashion_mnist, NLabels=10, NPixels=28, algorithm=2, num_ensemble_models=3, batch_size=batch, num_epochs=iter, num_hidden_units= 20)) + "\n") 198 | text_file.flush() 199 | 200 | 201 | text_file.write(str(PAC2Ensemble(dataSource= tf.keras.datasets.cifar10, NLabels=10, NPixels=32, algorithm=0, num_ensemble_models=1, batch_size=batch, num_epochs=iter, num_hidden_units= 20)) + "\n") 202 | text_file.flush() 203 | text_file.write(str(PAC2Ensemble(dataSource= tf.keras.datasets.cifar10, NLabels=10, NPixels=32, algorithm=1, num_ensemble_models=2, batch_size=batch, num_epochs=iter, num_hidden_units= 20)) + "\n") 204 | text_file.flush() 205 | text_file.write(str(PAC2Ensemble(dataSource= tf.keras.datasets.cifar10, NLabels=10, NPixels=32, algorithm=2, num_ensemble_models=2, batch_size=batch, num_epochs=iter, num_hidden_units= 20)) + "\n") 206 | text_file.flush() 207 | text_file.write(str(PAC2Ensemble(dataSource= tf.keras.datasets.cifar10, NLabels=10, NPixels=32, algorithm=1, num_ensemble_models=3, batch_size=batch, num_epochs=iter, num_hidden_units= 20)) + "\n") 208 | text_file.flush() 209 | text_file.write(str(PAC2Ensemble(dataSource= tf.keras.datasets.cifar10, NLabels=10, NPixels=32, algorithm=2, num_ensemble_models=3, batch_size=batch, num_epochs=iter, num_hidden_units= 20)) + "\n") 210 | text_file.flush() 211 | 212 | 213 | text_file.close() -------------------------------------------------------------------------------- /scripts/PAC2-Variational-SelfSupervisedBinomial.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | import tensorflow as tf 3 | from tensorflow_probability import edward2 as ed 4 | 5 | 6 | def PAC2VI(dataSource=tf.keras.datasets.fashion_mnist, NPixels=14, algorithm=0, PARTICLES=20, batch_size=100, num_epochs=50, num_hidden_units=20): 7 | """ Run experiments for MAP, Variational, PAC^2-Variational and PAC^2_T-Variational algorithms for the self-supervised classification task with a Categorical data model. 8 | Args: 9 | dataSource: The data set used in the evaluation. 10 | NLabels: The number of labels to predict. 11 | NPixels: The size of the images: NPixels\times NPixels. 12 | algorithm: Integer indicating the algorithm to be run. 13 | 0- MAP Learning 14 | 1- Variational Learning 15 | 2- PAC^2-Variational Learning 16 | 3- PAC^2_T-Variational Learning 17 | PARTICLES: Number of Monte-Carlo samples used to compute the posterior prediction distribution. 18 | batch_size: Size of the batch. 19 | num_epochs: Number of epochs. 20 | num_hidden_units: Number of hidden units in the MLP. 21 | Returns: 22 | NLL: The negative log-likelihood over the test data set. 23 | :param algorithm: 24 | """ 25 | 26 | np.random.seed(1) 27 | tf.set_random_seed(1) 28 | 29 | sess = tf.Session() 30 | 31 | 32 | (x_train, y_train), (x_test, y_test) = dataSource.load_data() 33 | 34 | if (dataSource.__name__.__contains__('cifar')): 35 | x_train=sess.run(tf.cast(tf.squeeze(tf.image.rgb_to_grayscale(x_train)),dtype=tf.float32)) 36 | x_test=sess.run(tf.cast(tf.squeeze(tf.image.rgb_to_grayscale(x_test)),dtype=tf.float32)) 37 | 38 | x_train = (x_train < 128).astype(np.int32) 39 | x_test = (x_test < 128 ).astype(np.int32) 40 | 41 | NPixels = np.int(NPixels/2) 42 | 43 | y_train = x_train[:, NPixels:] 44 | x_train = x_train[:, 0:NPixels] 45 | 46 | y_test = x_test[:, NPixels:] 47 | x_test = x_test[:, 0:NPixels] 48 | 49 | NPixels= NPixels * NPixels * 2 50 | 51 | 52 | N = x_train.shape[0] 53 | M = batch_size 54 | 55 | x_batch = tf.placeholder(dtype=tf.float32, name="x_batch", shape=[None, NPixels]) 56 | y_batch = tf.placeholder(dtype=tf.int32, name="y_batch", shape=[None, NPixels]) 57 | 58 | def model(NHIDDEN, x): 59 | W = ed.Normal(loc=tf.zeros([NPixels, NHIDDEN]), scale=1., name="W") 60 | b = ed.Normal(loc=tf.zeros([1, NHIDDEN]), scale=1., name="b") 61 | 62 | W_out = ed.Normal(loc=tf.zeros([NHIDDEN, 2 * NPixels]), scale=1., name="W_out") 63 | b_out = ed.Normal(loc=tf.zeros([1, 2 * NPixels]), scale=1., name="b_out") 64 | 65 | hidden_layer = tf.nn.relu(tf.matmul(x, W) + b) 66 | out = tf.matmul(hidden_layer, W_out) + b_out 67 | y = ed.Categorical(logits=tf.reshape(out, [tf.shape(x_batch)[0], NPixels, 2]), name="y") 68 | 69 | return W, b, W_out, b_out, x, y 70 | 71 | 72 | 73 | def qmodel(NHIDDEN): 74 | W_loc = tf.Variable(tf.random_normal([NPixels, NHIDDEN], 0.0, 0.1, dtype=tf.float32)) 75 | b_loc = tf.Variable(tf.random_normal([1, NHIDDEN], 0.0, 0.1, dtype=tf.float32)) 76 | 77 | if algorithm==0: 78 | W_scale = 0.000001 79 | b_scale = 0.000001 80 | else: 81 | W_scale = tf.nn.softplus(tf.Variable(tf.random_normal([NPixels, NHIDDEN], -3., stddev=0.1, dtype=tf.float32))) 82 | b_scale = tf.nn.softplus(tf.Variable(tf.random_normal([1, NHIDDEN], -3., stddev=0.1, dtype=tf.float32))) 83 | 84 | qW = ed.Normal(W_loc, scale=W_scale, name="W") 85 | qW_ = ed.Normal(W_loc, scale=W_scale, name="W") 86 | 87 | qb = ed.Normal(b_loc, scale=b_scale, name="b") 88 | qb_ = ed.Normal(b_loc, scale=b_scale, name="b") 89 | 90 | W_out_loc = tf.Variable(tf.random_normal([NHIDDEN, 2 * NPixels], 0.0, 0.1, dtype=tf.float32)) 91 | b_out_loc = tf.Variable(tf.random_normal([1, 2 * NPixels], 0.0, 0.1, dtype=tf.float32)) 92 | if algorithm==0: 93 | W_out_scale = 0.000001 94 | b_out_scale = 0.000001 95 | else: 96 | W_out_scale = tf.nn.softplus(tf.Variable(tf.random_normal([NHIDDEN, 2 * NPixels], -3., stddev=0.1, dtype=tf.float32))) 97 | b_out_scale = tf.nn.softplus(tf.Variable(tf.random_normal([1, 2 * NPixels], -3., stddev=0.1, dtype=tf.float32))) 98 | 99 | 100 | qW_out = ed.Normal(W_out_loc, scale=W_out_scale, name="W_out") 101 | qb_out = ed.Normal(b_out_loc, scale=b_out_scale, name="b_out") 102 | 103 | qW_out_ = ed.Normal(W_out_loc, scale=W_out_scale, name="W_out") 104 | qb_out_ = ed.Normal(b_out_loc, scale=b_out_scale, name="b_out") 105 | 106 | return qW, qW_, qb, qb_, qW_out, qW_out_, qb_out, qb_out_ 107 | 108 | 109 | W,b,W_out,b_out,x,y = model(num_hidden_units, x_batch) 110 | 111 | qW,qW_,qb,qb_,qW_out,qW_out_,qb_out,qb_out_ = qmodel(num_hidden_units) 112 | 113 | with ed.interception(ed.make_value_setter(W=qW,b=qb,W_out=qW_out,b_out=qb_out)): 114 | pW,pb,pW_out,pb_out,px,py = model(num_hidden_units, x) 115 | 116 | with ed.interception(ed.make_value_setter(W=qW_,b=qb_,W_out=qW_out_,b_out=qb_out_)): 117 | pW_,pb_,pW_out_,pb_out_,px_,py_ = model(num_hidden_units, x) 118 | 119 | 120 | pylogprob = tf.expand_dims(tf.reduce_sum(py.distribution.log_prob(y_batch),axis=1),1) 121 | py_logprob = tf.expand_dims(tf.reduce_sum(py_.distribution.log_prob(y_batch),axis=1),1) 122 | 123 | logmax = tf.stop_gradient(tf.math.maximum(pylogprob,py_logprob)+0.1) 124 | logmean_logmax = tf.math.reduce_logsumexp(tf.concat([pylogprob-logmax,py_logprob-logmax], 1),axis=1) - tf.log(2.) 125 | alpha = tf.expand_dims(logmean_logmax,1) 126 | 127 | if (algorithm==3): 128 | hmax = 2*tf.stop_gradient(alpha/tf.math.pow(1-tf.math.exp(alpha),2) + tf.math.pow(tf.math.exp(alpha)*(1-tf.math.exp(alpha)),-1)) 129 | else: 130 | hmax=1. 131 | 132 | var = 0.5*(tf.reduce_mean(tf.exp(2*pylogprob-2*logmax)*hmax) - tf.reduce_mean(tf.exp(pylogprob + py_logprob - 2*logmax)*hmax)) 133 | 134 | 135 | datalikelihood = tf.reduce_mean(pylogprob) 136 | 137 | 138 | logprior = tf.reduce_sum(pW.distribution.log_prob(pW.value)) + \ 139 | tf.reduce_sum(pb.distribution.log_prob(pb.value)) + \ 140 | tf.reduce_sum(pW_out.distribution.log_prob(pW_out.value)) + \ 141 | tf.reduce_sum(pb_out.distribution.log_prob(pb_out.value)) 142 | 143 | 144 | entropy = tf.reduce_sum(qW.distribution.log_prob(qW.value)) + \ 145 | tf.reduce_sum(qb.distribution.log_prob(qb.value)) + \ 146 | tf.reduce_sum(qW_out.distribution.log_prob(qW_out.value)) + \ 147 | tf.reduce_sum(qb_out.distribution.log_prob(qb_out.value)) 148 | 149 | entropy = -entropy 150 | 151 | KL = (- entropy - logprior)/N 152 | 153 | if (algorithm==2 or algorithm==3): 154 | elbo = datalikelihood + var - KL 155 | elif algorithm == 1: 156 | elbo = datalikelihood - KL 157 | elif algorithm == 0: 158 | elbo = datalikelihood + logprior/N 159 | 160 | verbose=True 161 | optimizer = tf.train.AdamOptimizer(0.001) 162 | t = [] 163 | train = optimizer.minimize(-elbo) 164 | init = tf.global_variables_initializer() 165 | sess.run(init) 166 | 167 | 168 | 169 | 170 | for i in range(num_epochs+1): 171 | perm = np.random.permutation(N) 172 | x_train = np.take(x_train, perm, axis=0) 173 | y_train = np.take(y_train, perm, axis=0) 174 | 175 | x_batches = np.array_split(x_train, N / M) 176 | y_batches = np.array_split(y_train, N / M) 177 | 178 | for j in range(N // M): 179 | batch_x = np.reshape(x_batches[j], [x_batches[j].shape[0], -1]).astype(np.float32) 180 | batch_y = np.reshape(y_batches[j],[y_batches[j].shape[0],-1]).astype(np.float32) 181 | 182 | value, _ = sess.run([elbo, train],feed_dict={x_batch: batch_x, y_batch: batch_y}) 183 | t.append(-value) 184 | if verbose: 185 | #if j % 1 == 0: print(".", end="", flush=True) 186 | if i%50==0 and j%1000==0: 187 | #if j >= 5 : 188 | print("\nEpoch: " + str(i)) 189 | str_elbo = str(t[-1]) 190 | print("\n" + str(j) + " epochs\t" + str_elbo, end="", flush=True) 191 | print("\n" + str(j) + " data\t" + str(sess.run(datalikelihood,feed_dict={x_batch: batch_x, y_batch: batch_y})), end="", flush=True) 192 | print("\n" + str(j) + " var\t" + str(sess.run(var,feed_dict={x_batch: batch_x, y_batch: batch_y})), end="", flush=True) 193 | print("\n" + str(j) + " KL\t" + str(sess.run(KL,feed_dict={x_batch: batch_x, y_batch: batch_y})), end="", flush=True) 194 | print("\n" + str(j) + " energy\t" + str(sess.run(logprior,feed_dict={x_batch: batch_x, y_batch: batch_y})), end="", flush=True) 195 | print("\n" + str(j) + " entropy\t" + str(sess.run(entropy,feed_dict={x_batch: batch_x, y_batch: batch_y})), end="", flush=True) 196 | print("\n" + str(j) + " hmax\t" + str(sess.run(tf.reduce_mean(hmax),feed_dict={x_batch: batch_x, y_batch: batch_y})), end="", flush=True) 197 | print("\n" + str(j) + " alpha\t" + str(sess.run(tf.reduce_mean(alpha),feed_dict={x_batch: batch_x, y_batch: batch_y})), end="", flush=True) 198 | print("\n" + str(j) + " logmax\t" + str(sess.run(tf.reduce_mean(logmax),feed_dict={x_batch: batch_x, y_batch: batch_y})), end="", flush=True) 199 | 200 | M=1000 201 | 202 | 203 | N=x_test.shape[0] 204 | x_batches = np.array_split(x_test, N / M) 205 | y_batches = np.array_split(y_test, N / M) 206 | 207 | NLL = 0 208 | 209 | for j in range(N // M): 210 | batch_x = np.reshape(x_batches[j], [x_batches[j].shape[0], -1]).astype(np.float32) 211 | batch_y = np.reshape(y_batches[j], [y_batches[j].shape[0],-1]).astype(np.float32) 212 | y_pred_list = [] 213 | for i in range(PARTICLES): 214 | y_pred_list.append(sess.run(pylogprob,feed_dict={x_batch: batch_x, y_batch: batch_y})) 215 | y_preds = np.concatenate(y_pred_list, axis=1) 216 | score = tf.reduce_sum(tf.math.reduce_logsumexp(y_preds,axis=1)-tf.log(np.float32(PARTICLES))) 217 | score = sess.run(score) 218 | NLL = NLL + score 219 | if verbose: 220 | if j % 1 == 0: print(".", end="", flush=True) 221 | if j % 1 == 0: 222 | str_elbo = str(score) 223 | print("\n" + str(j) + " epochs\t" + str_elbo, end="", flush=True) 224 | 225 | print("\nNLL: "+str(NLL)) 226 | 227 | return NLL 228 | 229 | iter=100 230 | batch=100 231 | text_file = open("./results/output-PAC2-Variational-SelfSupervisedBinomial.txt", "w") 232 | 233 | text_file.write(str(PAC2VI(dataSource= tf.keras.datasets.fashion_mnist, NPixels=28, algorithm=0, PARTICLES=1, batch_size=batch, num_epochs=iter, num_hidden_units= 20)) + "\n") 234 | text_file.flush() 235 | text_file.write(str(PAC2VI(dataSource= tf.keras.datasets.fashion_mnist, NPixels=28, algorithm=1, PARTICLES=20, batch_size=batch, num_epochs=iter, num_hidden_units= 20)) + "\n") 236 | text_file.flush() 237 | text_file.write(str(PAC2VI(dataSource= tf.keras.datasets.fashion_mnist, NPixels=28, algorithm=2, PARTICLES=20, batch_size=batch, num_epochs=iter, num_hidden_units= 20)) + "\n") 238 | text_file.flush() 239 | text_file.write(str(PAC2VI(dataSource= tf.keras.datasets.fashion_mnist, NPixels=28, algorithm=3, PARTICLES=20, batch_size=batch, num_epochs=iter, num_hidden_units= 20)) + "\n") 240 | text_file.flush() 241 | 242 | text_file.write(str(PAC2VI(dataSource= tf.keras.datasets.cifar10, NPixels=32, algorithm=0, PARTICLES=1, batch_size=batch, num_epochs=iter, num_hidden_units= 20)) + "\n") 243 | text_file.flush() 244 | text_file.write(str(PAC2VI(dataSource= tf.keras.datasets.cifar10, NPixels=32, algorithm=1, PARTICLES=20, batch_size=batch, num_epochs=iter, num_hidden_units= 20)) + "\n") 245 | text_file.flush() 246 | text_file.write(str(PAC2VI(dataSource= tf.keras.datasets.cifar10, NPixels=32, algorithm=2, PARTICLES=20, batch_size=batch, num_epochs=iter, num_hidden_units= 20)) + "\n") 247 | text_file.flush() 248 | text_file.write(str(PAC2VI(dataSource= tf.keras.datasets.cifar10, NPixels=32, algorithm=3, PARTICLES=20, batch_size=batch, num_epochs=iter, num_hidden_units= 20)) + "\n") 249 | text_file.flush() 250 | 251 | text_file.close() 252 | -------------------------------------------------------------------------------- /scripts/PAC2-Variational-SelfSupervisedNormal.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | import tensorflow as tf 3 | from tensorflow_probability import edward2 as ed 4 | 5 | 6 | def PAC2VI(dataSource=tf.keras.datasets.fashion_mnist, NPixels=14, algorithm=0, PARTICLES=20, batch_size=100, num_epochs=50, num_hidden_units=20): 7 | """ Run experiments for MAP, Variational, PAC^2-Variational and PAC^2_T-Variational algorithms for the self-supervised classification task with a Normal data model. 8 | Args: 9 | dataSource: The data set used in the evaluation. 10 | NPixels: The size of the images: NPixels\times NPixels. 11 | algorithm: Integer indicating the algorithm to be run. 12 | 0- MAP Learning 13 | 1- Variational Learning 14 | 2- PAC^2-Variational Learning 15 | 3- PAC^2_T-Variational Learning 16 | PARTICLES: Number of Monte-Carlo samples used to compute the posterior prediction distribution. 17 | batch_size: Size of the batch. 18 | num_epochs: Number of epochs. 19 | num_hidden_units: Number of hidden units in the MLP. 20 | Returns: 21 | NLL: The negative log-likelihood over the test data set. 22 | """ 23 | 24 | np.random.seed(1) 25 | tf.set_random_seed(1) 26 | 27 | sess = tf.Session() 28 | 29 | (x_train, y_train), (x_test, y_test) = dataSource.load_data() 30 | if (dataSource.__name__.__contains__('cifar')): 31 | x_train=sess.run(tf.cast(tf.squeeze(tf.image.rgb_to_grayscale(x_train)),dtype=tf.float32)) 32 | x_test=sess.run(tf.cast(tf.squeeze(tf.image.rgb_to_grayscale(x_test)),dtype=tf.float32)) 33 | 34 | NPixels = np.int(NPixels/2) 35 | 36 | y_train = x_train[:, NPixels:] 37 | x_train = x_train[:, 0:NPixels] 38 | 39 | y_test = x_test[:, NPixels:] 40 | x_test = x_test[:, 0:NPixels] 41 | 42 | NPixels= NPixels * NPixels * 2 43 | 44 | x_train, x_test = x_train / 255.0, x_test / 255.0 45 | y_train, y_test = y_train / 255.0, y_test / 255.0 46 | 47 | 48 | 49 | 50 | N = x_train.shape[0] 51 | M = batch_size 52 | 53 | x_batch = tf.placeholder(dtype=tf.float32, name="x_batch", shape=[None, NPixels]) 54 | y_batch = tf.placeholder(dtype=tf.float32, name="y_batch", shape=[None, NPixels]) 55 | 56 | def model(NHIDDEN, x): 57 | W = ed.Normal(loc=tf.zeros([NPixels, NHIDDEN]), scale=1., name="W") 58 | b = ed.Normal(loc=tf.zeros([1, NHIDDEN]), scale=1., name="b") 59 | 60 | W_out = ed.Normal(loc=tf.zeros([NHIDDEN, NPixels]), scale=1., name="W_out") 61 | b_out = ed.Normal(loc=tf.zeros([1, NPixels]), scale=1., name="b_out") 62 | 63 | hidden_layer = tf.nn.relu(tf.matmul(x, W) + b) 64 | out = tf.matmul(hidden_layer, W_out) + b_out 65 | y = ed.Normal(loc=out, scale=1./255,name="y") 66 | 67 | return W, b, W_out, b_out, x, y 68 | 69 | 70 | 71 | def qmodel(NHIDDEN): 72 | W_loc = tf.Variable(tf.random_normal([NPixels, NHIDDEN], 0.0, 0.1, dtype=tf.float32)) 73 | b_loc = tf.Variable(tf.random_normal([1, NHIDDEN], 0.0, 0.1, dtype=tf.float32)) 74 | 75 | if algorithm==0: 76 | W_scale = 0.000001 77 | b_scale = 0.000001 78 | else: 79 | W_scale = tf.nn.softplus(tf.Variable(tf.random_normal([NPixels, NHIDDEN], -3., stddev=0.1, dtype=tf.float32))) 80 | b_scale = tf.nn.softplus(tf.Variable(tf.random_normal([1, NHIDDEN], -3., stddev=0.1, dtype=tf.float32))) 81 | 82 | qW = ed.Normal(W_loc, scale=W_scale, name="W") 83 | qW_ = ed.Normal(W_loc, scale=W_scale, name="W") 84 | 85 | qb = ed.Normal(b_loc, scale=b_scale, name="b") 86 | qb_ = ed.Normal(b_loc, scale=b_scale, name="b") 87 | 88 | W_out_loc = tf.Variable(tf.random_normal([NHIDDEN, NPixels], 0.0, 0.1, dtype=tf.float32)) 89 | b_out_loc = tf.Variable(tf.random_normal([1, NPixels], 0.0, 0.1, dtype=tf.float32)) 90 | if algorithm==0: 91 | W_out_scale = 0.000001 92 | b_out_scale = 0.000001 93 | else: 94 | W_out_scale = tf.nn.softplus(tf.Variable(tf.random_normal([NHIDDEN, NPixels], -3., stddev=0.1, dtype=tf.float32))) 95 | b_out_scale = tf.nn.softplus(tf.Variable(tf.random_normal([1, NPixels], -3., stddev=0.1, dtype=tf.float32))) 96 | 97 | qW_out = ed.Normal(W_out_loc, scale=W_out_scale, name="W_out") 98 | qb_out = ed.Normal(b_out_loc, scale=b_out_scale, name="b_out") 99 | 100 | qW_out_ = ed.Normal(W_out_loc, scale=W_out_scale, name="W_out") 101 | qb_out_ = ed.Normal(b_out_loc, scale=b_out_scale, name="b_out") 102 | 103 | return qW, qW_, qb, qb_, qW_out, qW_out_, qb_out, qb_out_ 104 | 105 | 106 | W,b,W_out,b_out,x,y = model(num_hidden_units, x_batch) 107 | 108 | qW,qW_,qb,qb_,qW_out,qW_out_,qb_out,qb_out_ = qmodel(num_hidden_units) 109 | 110 | with ed.interception(ed.make_value_setter(W=qW,b=qb,W_out=qW_out,b_out=qb_out)): 111 | pW,pb,pW_out,pb_out,px,py = model(num_hidden_units, x) 112 | 113 | with ed.interception(ed.make_value_setter(W=qW_,b=qb_,W_out=qW_out_,b_out=qb_out_)): 114 | pW_,pb_,pW_out_,pb_out_,px_,py_ = model(num_hidden_units, x) 115 | 116 | 117 | pylogprob = tf.expand_dims(tf.reduce_sum(py.distribution.log_prob(y_batch),axis=1),1) 118 | py_logprob = tf.expand_dims(tf.reduce_sum(py_.distribution.log_prob(y_batch),axis=1),1) 119 | 120 | logmax = tf.stop_gradient(tf.math.maximum(pylogprob,py_logprob)+0.1) 121 | logmean_logmax = tf.math.reduce_logsumexp(tf.concat([pylogprob-logmax,py_logprob-logmax], 1),axis=1) - tf.log(2.) 122 | alpha = tf.expand_dims(logmean_logmax,1) 123 | 124 | if (algorithm==3): 125 | hmax = 2*tf.stop_gradient(alpha/tf.math.pow(1-tf.math.exp(alpha),2) + tf.math.pow(tf.math.exp(alpha)*(1-tf.math.exp(alpha)),-1)) 126 | else: 127 | hmax=1. 128 | 129 | var = 0.5*(tf.reduce_mean(tf.exp(2*pylogprob-2*logmax)*hmax) - tf.reduce_mean(tf.exp(pylogprob + py_logprob - 2*logmax)*hmax)) 130 | 131 | 132 | datalikelihood = tf.reduce_mean(pylogprob) 133 | 134 | 135 | logprior = tf.reduce_sum(pW.distribution.log_prob(pW.value)) + \ 136 | tf.reduce_sum(pb.distribution.log_prob(pb.value)) + \ 137 | tf.reduce_sum(pW_out.distribution.log_prob(pW_out.value)) + \ 138 | tf.reduce_sum(pb_out.distribution.log_prob(pb_out.value)) 139 | 140 | 141 | entropy = tf.reduce_sum(qW.distribution.log_prob(qW.value)) + \ 142 | tf.reduce_sum(qb.distribution.log_prob(qb.value)) + \ 143 | tf.reduce_sum(qW_out.distribution.log_prob(qW_out.value)) + \ 144 | tf.reduce_sum(qb_out.distribution.log_prob(qb_out.value)) 145 | 146 | entropy = -entropy 147 | 148 | KL = (- entropy - logprior)/N 149 | 150 | if (algorithm==2 or algorithm==3): 151 | elbo = datalikelihood + var - KL 152 | elif algorithm == 1: 153 | elbo = datalikelihood - KL 154 | elif algorithm == 0: 155 | elbo = datalikelihood + logprior/N 156 | 157 | verbose=True 158 | optimizer = tf.train.AdamOptimizer(0.001) 159 | t = [] 160 | train = optimizer.minimize(-elbo) 161 | init = tf.global_variables_initializer() 162 | sess.run(init) 163 | 164 | 165 | 166 | 167 | for i in range(num_epochs+1): 168 | perm = np.random.permutation(N) 169 | x_train = np.take(x_train, perm, axis=0) 170 | y_train = np.take(y_train, perm, axis=0) 171 | 172 | x_batches = np.array_split(x_train, N / M) 173 | y_batches = np.array_split(y_train, N / M) 174 | 175 | for j in range(N // M): 176 | batch_x = np.reshape(x_batches[j], [x_batches[j].shape[0], -1]).astype(np.float32) 177 | batch_y = np.reshape(y_batches[j],[y_batches[j].shape[0],-1]).astype(np.float32) 178 | 179 | value, _ = sess.run([elbo, train],feed_dict={x_batch: batch_x, y_batch: batch_y}) 180 | t.append(-value) 181 | if verbose: 182 | #if j % 1 == 0: print(".", end="", flush=True) 183 | if i%50==0 and j%1000==0: 184 | #if j >= 5 : 185 | print("\nEpoch: " + str(i)) 186 | str_elbo = str(t[-1]) 187 | print("\n" + str(j) + " epochs\t" + str_elbo, end="", flush=True) 188 | print("\n" + str(j) + " data\t" + str(sess.run(datalikelihood,feed_dict={x_batch: batch_x, y_batch: batch_y})), end="", flush=True) 189 | print("\n" + str(j) + " var\t" + str(sess.run(var,feed_dict={x_batch: batch_x, y_batch: batch_y})), end="", flush=True) 190 | print("\n" + str(j) + " KL\t" + str(sess.run(KL,feed_dict={x_batch: batch_x, y_batch: batch_y})), end="", flush=True) 191 | print("\n" + str(j) + " energy\t" + str(sess.run(logprior,feed_dict={x_batch: batch_x, y_batch: batch_y})), end="", flush=True) 192 | print("\n" + str(j) + " entropy\t" + str(sess.run(entropy,feed_dict={x_batch: batch_x, y_batch: batch_y})), end="", flush=True) 193 | print("\n" + str(j) + " hmax\t" + str(sess.run(tf.reduce_mean(hmax),feed_dict={x_batch: batch_x, y_batch: batch_y})), end="", flush=True) 194 | print("\n" + str(j) + " alpha\t" + str(sess.run(tf.reduce_mean(alpha),feed_dict={x_batch: batch_x, y_batch: batch_y})), end="", flush=True) 195 | print("\n" + str(j) + " logmax\t" + str(sess.run(tf.reduce_mean(logmax),feed_dict={x_batch: batch_x, y_batch: batch_y})), end="", flush=True) 196 | 197 | 198 | 199 | 200 | 201 | M=1000 202 | 203 | 204 | N=x_test.shape[0] 205 | x_batches = np.array_split(x_test, N / M) 206 | y_batches = np.array_split(y_test, N / M) 207 | 208 | NLL = 0 209 | 210 | for j in range(N // M): 211 | batch_x = np.reshape(x_batches[j], [x_batches[j].shape[0], -1]).astype(np.float32) 212 | batch_y = np.reshape(y_batches[j], [y_batches[j].shape[0],-1]).astype(np.float32) 213 | y_pred_list = [] 214 | for i in range(PARTICLES): 215 | y_pred_list.append(sess.run(pylogprob,feed_dict={x_batch: batch_x, y_batch: batch_y})) 216 | y_preds = np.concatenate(y_pred_list, axis=1) 217 | score = tf.reduce_sum(tf.math.reduce_logsumexp(y_preds,axis=1)-tf.log(np.float32(PARTICLES))) 218 | score = sess.run(score) 219 | NLL = NLL + score 220 | if verbose: 221 | if j % 1 == 0: print(".", end="", flush=True) 222 | if j % 1 == 0: 223 | str_elbo = str(score) 224 | print("\n" + str(j) + " epochs\t" + str_elbo, end="", flush=True) 225 | 226 | print("\nNLL: "+str(NLL)) 227 | 228 | return NLL 229 | 230 | 231 | 232 | iter=100 233 | batch=100 234 | text_file = open("./results/output-PAC2-Variational-SelfSupervisedNormal.txt", "w") 235 | 236 | text_file.write(str(PAC2VI(dataSource= tf.keras.datasets.fashion_mnist, NPixels=28, algorithm=0, PARTICLES=1, batch_size=batch, num_epochs=iter, num_hidden_units= 20)) + "\n") 237 | text_file.flush() 238 | text_file.write(str(PAC2VI(dataSource= tf.keras.datasets.fashion_mnist, NPixels=28, algorithm=1, PARTICLES=20, batch_size=batch, num_epochs=iter, num_hidden_units= 20)) + "\n") 239 | text_file.flush() 240 | text_file.write(str(PAC2VI(dataSource= tf.keras.datasets.fashion_mnist, NPixels=28, algorithm=2, PARTICLES=20, batch_size=batch, num_epochs=iter, num_hidden_units= 20)) + "\n") 241 | text_file.flush() 242 | text_file.write(str(PAC2VI(dataSource= tf.keras.datasets.fashion_mnist, NPixels=28, algorithm=3, PARTICLES=20, batch_size=batch, num_epochs=iter, num_hidden_units= 20)) + "\n") 243 | text_file.flush() 244 | 245 | text_file.write(str(PAC2VI(dataSource= tf.keras.datasets.cifar10, NPixels=32, algorithm=0, PARTICLES=1, batch_size=batch, num_epochs=iter, num_hidden_units= 20)) + "\n") 246 | text_file.flush() 247 | text_file.write(str(PAC2VI(dataSource= tf.keras.datasets.cifar10, NPixels=32, algorithm=1, PARTICLES=20, batch_size=batch, num_epochs=iter, num_hidden_units= 20)) + "\n") 248 | text_file.flush() 249 | text_file.write(str(PAC2VI(dataSource= tf.keras.datasets.cifar10, NPixels=32, algorithm=2, PARTICLES=20, batch_size=batch, num_epochs=iter, num_hidden_units= 20)) + "\n") 250 | text_file.flush() 251 | text_file.write(str(PAC2VI(dataSource= tf.keras.datasets.cifar10, NPixels=32, algorithm=3, PARTICLES=20, batch_size=batch, num_epochs=iter, num_hidden_units= 20)) + "\n") 252 | text_file.flush() 253 | 254 | text_file.close() 255 | 256 | -------------------------------------------------------------------------------- /scripts/PAC2-Variational-Supervised.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | import tensorflow as tf 3 | from tensorflow_probability import edward2 as ed 4 | import math 5 | 6 | def PAC2VI(dataSource = tf.keras.datasets.fashion_mnist, NLabels=10, NPixels=28, algorithm=0, PARTICLES=20, batch_size=100, num_epochs=50, num_hidden_units = 20): 7 | """ Run experiments for MAP, Variational, PAC^2-Variational and PAC^2_T-Variational algorithms for the supervised classification task. 8 | Args: 9 | dataSource: The data set used in the evaluation. 10 | NLabels: The number of labels to predict. 11 | NPixels: The size of the images: NPixels\times NPixels. 12 | algorithm: Integer indicating the algorithm to be run. 13 | 0- MAP Learning 14 | 1- Variational Learning 15 | 2- PAC^2-Variational Learning 16 | 3- PAC^2_T-Variational Learning 17 | PARTICLES: Number of Monte-Carlo samples used to compute the posterior prediction distribution. 18 | batch_size: Size of the batch. 19 | num_epochs: Number of epochs. 20 | num_hidden_units: Number of hidden units in the MLP. 21 | Returns: 22 | NLL: The negative log-likelihood over the test data set. 23 | """ 24 | 25 | np.random.seed(1) 26 | tf.set_random_seed(1) 27 | 28 | sess = tf.Session() 29 | 30 | 31 | (x_train, y_train), (x_test, y_test) = dataSource.load_data() 32 | 33 | if (dataSource.__name__.__contains__('cifar')): 34 | x_train=sess.run(tf.cast(tf.squeeze(tf.image.rgb_to_grayscale(x_train)),dtype=tf.float32)) 35 | x_test=sess.run(tf.cast(tf.squeeze(tf.image.rgb_to_grayscale(x_test)),dtype=tf.float32)) 36 | 37 | x_train, x_test = x_train / 255.0, x_test / 255.0 38 | 39 | 40 | 41 | N = x_train.shape[0] 42 | M = batch_size 43 | 44 | 45 | x_batch = tf.placeholder(dtype=tf.float32, name="x_batch", shape=[None, NPixels * NPixels]) 46 | y_batch = tf.placeholder(dtype=tf.float32, name="y_batch", shape=[None,]) 47 | 48 | def model(NHIDDEN, x): 49 | W = ed.Normal(loc=tf.zeros([NPixels * NPixels, NHIDDEN]), scale=1., name="W") 50 | b = ed.Normal(loc=tf.zeros([1, NHIDDEN]), scale=1., name="b") 51 | 52 | W_out = ed.Normal(loc=tf.zeros([NHIDDEN, NLabels]), scale=1., name="W_out") 53 | b_out = ed.Normal(loc=tf.zeros([1, NLabels]), scale=1., name="b_out") 54 | 55 | hidden_layer = tf.nn.relu(tf.matmul(x, W) + b) 56 | out = tf.matmul(hidden_layer, W_out) + b_out 57 | y = ed.Categorical(logits=out, name="y") 58 | 59 | return W, b, W_out, b_out, x, y 60 | 61 | 62 | 63 | def qmodel(NHIDDEN): 64 | W_loc = tf.Variable(tf.random_normal([NPixels * NPixels, NHIDDEN], 0.0, 0.1, dtype=tf.float32)) 65 | b_loc = tf.Variable(tf.random_normal([1, NHIDDEN], 0.0, 0.1, dtype=tf.float32)) 66 | 67 | if algorithm==0: 68 | W_scale = 0.000001 69 | b_scale = 0.000001 70 | else: 71 | W_scale = tf.nn.softplus(tf.Variable(tf.random_normal([NPixels * NPixels, NHIDDEN], -3., stddev=0.1, dtype=tf.float32))) 72 | b_scale = tf.nn.softplus(tf.Variable(tf.random_normal([1, NHIDDEN], -3., stddev=0.1, dtype=tf.float32))) 73 | 74 | qW = ed.Normal(W_loc, scale=W_scale, name="W") 75 | qW_ = ed.Normal(W_loc, scale=W_scale, name="W") 76 | 77 | qb = ed.Normal(b_loc, scale=b_scale, name="b") 78 | qb_ = ed.Normal(b_loc, scale=b_scale, name="b") 79 | 80 | W_out_loc = tf.Variable(tf.random_normal([NHIDDEN, NLabels], 0.0, 0.1, dtype=tf.float32)) 81 | b_out_loc = tf.Variable(tf.random_normal([1, NLabels], 0.0, 0.1, dtype=tf.float32)) 82 | if algorithm==0: 83 | W_out_scale = 0.000001 84 | b_out_scale = 0.000001 85 | else: 86 | W_out_scale = tf.nn.softplus(tf.Variable(tf.random_normal([NHIDDEN, NLabels], -3., stddev=0.1, dtype=tf.float32))) 87 | b_out_scale = tf.nn.softplus(tf.Variable(tf.random_normal([1, NLabels], -3., stddev=0.1, dtype=tf.float32))) 88 | 89 | qW_out = ed.Normal(W_out_loc, scale=W_out_scale, name="W_out") 90 | qb_out = ed.Normal(b_out_loc, scale=b_out_scale, name="b_out") 91 | 92 | qW_out_ = ed.Normal(W_out_loc, scale=W_out_scale, name="W_out") 93 | qb_out_ = ed.Normal(b_out_loc, scale=b_out_scale, name="b_out") 94 | 95 | return qW, qW_, qb, qb_, qW_out, qW_out_, qb_out, qb_out_ 96 | 97 | 98 | W,b,W_out,b_out,x,y = model(num_hidden_units, x_batch) 99 | 100 | qW,qW_,qb,qb_,qW_out,qW_out_,qb_out,qb_out_ = qmodel(num_hidden_units) 101 | 102 | with ed.interception(ed.make_value_setter(W=qW,b=qb,W_out=qW_out,b_out=qb_out)): 103 | pW,pb,pW_out,pb_out,px,py = model(num_hidden_units, x) 104 | 105 | with ed.interception(ed.make_value_setter(W=qW_,b=qb_,W_out=qW_out_,b_out=qb_out_)): 106 | pW_,pb_,pW_out_,pb_out_,px_,py_ = model(num_hidden_units, x) 107 | 108 | 109 | pylogprob = tf.expand_dims(py.distribution.log_prob(y_batch),1) 110 | py_logprob = tf.expand_dims(py_.distribution.log_prob(y_batch),1) 111 | 112 | logmax = tf.stop_gradient(tf.math.maximum(pylogprob,py_logprob)+0.000001) 113 | logmax = tf.constant(-math.log(0.9999)) 114 | logmean_logmax = tf.math.reduce_logsumexp(tf.concat([pylogprob-logmax,py_logprob-logmax], 1),axis=1) - tf.log(2.) 115 | alpha = tf.expand_dims(logmean_logmax,1) 116 | 117 | if (algorithm==3): 118 | hmax = 2*tf.stop_gradient(alpha/tf.math.pow(1-tf.math.exp(alpha),2) + tf.math.pow(tf.math.exp(alpha)*(1-tf.math.exp(alpha)),-1)) 119 | else: 120 | hmax=1. 121 | 122 | var = 0.5*(tf.reduce_mean(tf.exp(2*pylogprob-2*logmax)*hmax) - tf.reduce_mean(tf.exp(pylogprob + py_logprob - 2*logmax)*hmax)) 123 | 124 | 125 | datalikelihood = tf.reduce_mean(py.distribution.log_prob(y_batch)) 126 | 127 | 128 | logprior = tf.reduce_sum(pW.distribution.log_prob(pW.value)) + \ 129 | tf.reduce_sum(pb.distribution.log_prob(pb.value)) + \ 130 | tf.reduce_sum(pW_out.distribution.log_prob(pW_out.value)) + \ 131 | tf.reduce_sum(pb_out.distribution.log_prob(pb_out.value)) 132 | 133 | 134 | entropy = tf.reduce_sum(qW.distribution.log_prob(qW.value)) + \ 135 | tf.reduce_sum(qb.distribution.log_prob(qb.value)) + \ 136 | tf.reduce_sum(qW_out.distribution.log_prob(qW_out.value)) + \ 137 | tf.reduce_sum(qb_out.distribution.log_prob(qb_out.value)) 138 | 139 | entropy = -entropy 140 | 141 | 142 | KL = (- entropy - logprior)/N 143 | 144 | if algorithm==2 or algorithm==3: 145 | elbo = datalikelihood + var - KL 146 | elif algorithm==1: 147 | elbo = datalikelihood - KL 148 | elif algorithm==0: 149 | elbo = datalikelihood + logprior/N 150 | 151 | verbose=True 152 | optimizer = tf.train.AdamOptimizer(0.001) 153 | t = [] 154 | train = optimizer.minimize(-elbo) 155 | init = tf.global_variables_initializer() 156 | sess.run(init) 157 | 158 | 159 | 160 | 161 | for i in range(num_epochs+1): 162 | perm = np.random.permutation(N) 163 | x_train = np.take(x_train, perm, axis=0) 164 | y_train = np.take(y_train, perm, axis=0) 165 | 166 | x_batches = np.array_split(x_train, N / M) 167 | y_batches = np.array_split(y_train, N / M) 168 | 169 | for j in range(N // M): 170 | batch_x = np.reshape(x_batches[j], [x_batches[j].shape[0], -1]).astype(np.float32) 171 | batch_y = np.reshape(y_batches[j],[y_batches[j].shape[0],]).astype(np.float32) 172 | 173 | value, _ = sess.run([elbo, train],feed_dict={x_batch: batch_x, y_batch: batch_y}) 174 | t.append(-value) 175 | if verbose: 176 | if i%50==0 and j%1000==0: 177 | print("\nEpoch: " + str(i)) 178 | str_elbo = str(t[-1]) 179 | print("\n" + str(j) + " epochs\t" + str_elbo, end="", flush=True) 180 | print("\n" + str(j) + " data\t" + str(sess.run(datalikelihood,feed_dict={x_batch: batch_x, y_batch: batch_y})), end="", flush=True) 181 | print("\n" + str(j) + " var\t" + str(sess.run(var,feed_dict={x_batch: batch_x, y_batch: batch_y})), end="", flush=True) 182 | print("\n" + str(j) + " KL\t" + str(sess.run(KL,feed_dict={x_batch: batch_x, y_batch: batch_y})), end="", flush=True) 183 | print("\n" + str(j) + " energy\t" + str(sess.run(logprior,feed_dict={x_batch: batch_x, y_batch: batch_y})), end="", flush=True) 184 | print("\n" + str(j) + " entropy\t" + str(sess.run(entropy,feed_dict={x_batch: batch_x, y_batch: batch_y})), end="", flush=True) 185 | print("\n" + str(j) + " hmax\t" + str(sess.run(tf.reduce_mean(hmax),feed_dict={x_batch: batch_x, y_batch: batch_y})), end="", flush=True) 186 | print("\n" + str(j) + " alpha\t" + str(sess.run(tf.reduce_mean(alpha),feed_dict={x_batch: batch_x, y_batch: batch_y})), end="", flush=True) 187 | print("\n" + str(j) + " logmax\t" + str(sess.run(tf.reduce_mean(logmax),feed_dict={x_batch: batch_x, y_batch: batch_y})), end="", flush=True) 188 | 189 | 190 | 191 | 192 | 193 | M=1000 194 | 195 | N=x_test.shape[0] 196 | x_batches = np.array_split(x_test, N / M) 197 | y_batches = np.array_split(y_test, N / M) 198 | 199 | NLL = 0 200 | 201 | for j in range(N // M): 202 | batch_x = np.reshape(x_batches[j], [x_batches[j].shape[0], -1]).astype(np.float32) 203 | batch_y = np.reshape(y_batches[j], [y_batches[j].shape[0],]).astype(np.float32) 204 | y_pred_list = [] 205 | for i in range(PARTICLES): 206 | y_pred_list.append(sess.run(tf.expand_dims(py.distribution.log_prob(batch_y),axis=1),feed_dict={x_batch: batch_x})) 207 | y_preds = np.concatenate(y_pred_list, axis=1) 208 | score = tf.reduce_sum(tf.math.reduce_logsumexp(y_preds,axis=1)-tf.log(np.float32(PARTICLES))) 209 | score = sess.run(score) 210 | NLL = NLL + score 211 | if verbose: 212 | if j % 1 == 0: print(".", end="", flush=True) 213 | if j % 1 == 0: 214 | str_elbo = str(score) 215 | print("\n" + str(j) + " epochs\t" + str_elbo, end="", flush=True) 216 | 217 | print("\nNLL: "+str(NLL)) 218 | 219 | return NLL 220 | 221 | 222 | 223 | iter=100 224 | batch=100 225 | text_file = open("./results/output-PAC2-Variational-Supervised.txt", "w") 226 | 227 | text_file.write(str(PAC2VI(dataSource= tf.keras.datasets.fashion_mnist, NLabels=10, NPixels=28, algorithm=0, PARTICLES=1, batch_size=batch, num_epochs=iter, num_hidden_units= 20)) + "\n") 228 | text_file.flush() 229 | text_file.write(str(PAC2VI(dataSource= tf.keras.datasets.fashion_mnist, NLabels=10, NPixels=28, algorithm=1, PARTICLES=20, batch_size=batch, num_epochs=iter, num_hidden_units= 20)) + "\n") 230 | text_file.flush() 231 | text_file.write(str(PAC2VI(dataSource= tf.keras.datasets.fashion_mnist, NLabels=10, NPixels=28, algorithm=2, PARTICLES=20, batch_size=batch, num_epochs=iter, num_hidden_units= 20)) + "\n") 232 | text_file.flush() 233 | text_file.write(str(PAC2VI(dataSource= tf.keras.datasets.fashion_mnist, NLabels=10, NPixels=28, algorithm=3, PARTICLES=20, batch_size=batch, num_epochs=iter, num_hidden_units= 20)) + "\n") 234 | text_file.flush() 235 | 236 | text_file.write(str(PAC2VI(dataSource= tf.keras.datasets.cifar10, NLabels=10, NPixels=32, algorithm=0, PARTICLES=1, batch_size=batch, num_epochs=iter, num_hidden_units= 20)) + "\n") 237 | text_file.flush() 238 | text_file.write(str(PAC2VI(dataSource= tf.keras.datasets.cifar10, NLabels=10, NPixels=32, algorithm=1, PARTICLES=20, batch_size=batch, num_epochs=iter, num_hidden_units= 20)) + "\n") 239 | text_file.flush() 240 | text_file.write(str(PAC2VI(dataSource= tf.keras.datasets.cifar10, NLabels=10, NPixels=32, algorithm=2, PARTICLES=20, batch_size=batch, num_epochs=iter, num_hidden_units= 20)) + "\n") 241 | text_file.flush() 242 | text_file.write(str(PAC2VI(dataSource= tf.keras.datasets.cifar10, NLabels=10, NPixels=32, algorithm=3, PARTICLES=20, batch_size=batch, num_epochs=iter, num_hidden_units= 20)) + "\n") 243 | text_file.flush() 244 | 245 | text_file.close() --------------------------------------------------------------------------------