EMF_RBM_Energy_Densities.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#  EMF RBM Energy Densities\n",
    "\n",
    "Look at different ways of computing the\n",
    "\n",
    "- energy density\n",
    "- free energy density\n",
    "- entropy density\n",
    "\n",
    "We can\n",
    "\n",
    "- use the TAP S and MF Energy *U_naive   \n",
    "    - which takes an equlibration step first  \n",
    "    - S(mv, mh), U_naive(mv, mh)\n",
    "- use a simple h = means_hiddens() step\n",
    "    - S(v, h), E_MF(v, h)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-11-08T23:33:50.367876",
     "start_time": "2016-11-08T23:33:50.361534"
    },
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import h5py\n",
    "\n",
    "import matplotlib\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline \n",
    "\n",
    "from sklearn import linear_model, datasets, metrics, preprocessing \n",
    "from sklearn.cross_validation import train_test_split\n",
    "from sklearn.metrics import accuracy_score\n",
    "\n",
    "import psutil"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-11-08T23:33:50.512461",
     "start_time": "2016-11-08T23:33:50.507597"
    },
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'divide': 'warn', 'invalid': 'warn', 'over': 'warn', 'under': 'warn'}"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.datasets import fetch_mldata\n",
    "from sklearn.utils.validation import assert_all_finite\n",
    "from scipy.sparse import csc_matrix, csr_matrix, lil_matrix\n",
    "from sklearn.preprocessing import Binarizer\n",
    "np.seterr(all='warn')"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-11-08T23:33:53.684714",
     "start_time": "2016-11-08T23:33:51.186577"
    },
    "collapsed": false,
    "scrolled": true
   },
   "source": [
    "hf =  h5py.File('mnist.h5','r')\n",
    "print('List of arrays in this file: \\n', hf.keys())\n",
    "X = np.array(hf.get('HDF5.name___X'))\n",
    "y = np.array(hf.get('HDF5.name___y'))\n",
    "\n",
    "print X.shape, y.shape\n",
    "hf.close()\n",
    "np.linalg.norm(X, ord=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## MNIST data\n",
    "\n",
    "http://scikit-learn.org/stable/auto_examples/neural_networks/plot_mnist_filters.html\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.datasets import fetch_mldata\n",
    "mnist = fetch_mldata(\"MNIST original\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "Xall, y = mnist.data / 255., mnist.target\n",
    "X_train, X_test = Xall[:60000], Xall[60000:]\n",
    "y_train, y_test = y[:60000], y[60000:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import binarize\n",
    "X = binarize(X_train, threshold=0.1, copy=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### Helper methods for simple case"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-11-08T22:38:39.742812",
     "start_time": "2016-11-08T22:38:39.737075"
    },
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.utils.fixes import expit    \n",
    "from sklearn.utils.extmath import safe_sparse_dot\n",
    "\n",
    "def sig_means(x, b, W):\n",
    "    a = safe_sparse_dot(x, W.T) + b\n",
    "    return expit(a, out=a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-10-20T17:56:14.156132",
     "start_time": "2016-10-20T17:56:14.153682"
    }
   },
   "source": [
    "### Baseline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import emf_rbm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-11-08T22:42:32.963306",
     "start_time": "2016-11-08T22:42:32.959982"
    },
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "sswap(total=0, used=0, free=0, percent=0.0, sin=0, sout=0)"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "psutil.swap_memory()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### mean Entropy, Energy, and Free Energy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-11-08T22:55:48.509468",
     "start_time": "2016-11-08T22:45:04.953105"
    },
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[EMF_RBM] Iteration 1, pseudo-likelihood = -233.51, time = 23.45s\n",
      "computing TAP Free Energies\n",
      "monitor:  -361.590476288 333.987235796 -26.9541948016\n",
      "[EMF_RBM] Iteration 2, pseudo-likelihood = -199.81, time = 53.50s\n",
      "computing TAP Free Energies\n",
      "monitor:  -347.1014084 281.540042684 -64.1845633544\n",
      "[EMF_RBM] Iteration 3, pseudo-likelihood = -161.95, time = 53.19s\n",
      "computing TAP Free Energies\n",
      "monitor:  -340.751219697 253.508561995 -84.9607242813\n",
      "[EMF_RBM] Iteration 4, pseudo-likelihood = -143.83, time = 53.14s\n",
      "computing TAP Free Energies\n",
      "monitor:  -349.615439283 233.776341949 -112.80351918\n",
      "[EMF_RBM] Iteration 5, pseudo-likelihood = -133.14, time = 53.17s\n",
      "computing TAP Free Energies\n",
      "monitor:  -360.027094493 218.87089056 -137.450810833\n",
      "[EMF_RBM] Iteration 6, pseudo-likelihood = -121.99, time = 53.18s\n",
      "computing TAP Free Energies\n",
      "monitor:  -370.436213399 207.845811892 -158.268702403\n",
      "[EMF_RBM] Iteration 7, pseudo-likelihood = -114.35, time = 53.06s\n",
      "computing TAP Free Energies\n",
      "monitor:  -380.389411213 198.811182541 -176.737491108\n",
      "[EMF_RBM] Iteration 8, pseudo-likelihood = -111.12, time = 53.07s\n",
      "computing TAP Free Energies\n",
      "monitor:  -389.176217312 191.335239037 -192.573345657\n",
      "[EMF_RBM] Iteration 9, pseudo-likelihood = -105.72, time = 53.20s\n",
      "computing TAP Free Energies\n",
      "monitor:  -396.991812367 185.315178082 -206.02367808\n",
      "[EMF_RBM] Iteration 10, pseudo-likelihood = -101.68, time = 53.08s\n",
      "computing TAP Free Energies\n",
      "monitor:  -404.306817343 180.30525679 -217.988028961\n",
      "[EMF_RBM] Iteration 11, pseudo-likelihood = -99.13, time = 53.02s\n",
      "computing TAP Free Energies\n",
      "monitor:  -411.135558263 175.931319824 -228.862119135\n",
      "[EMF_RBM] Iteration 12, pseudo-likelihood = -95.51, time = 53.11s\n",
      "computing TAP Free Energies\n",
      "monitor:  -417.571740128 172.063612853 -238.862995624\n",
      "[EMF_RBM] Iteration 13, pseudo-likelihood = -95.84, time = 52.93s\n",
      "computing TAP Free Energies\n",
      "monitor:  -423.684477649 168.614864158 -248.143484082\n",
      "[EMF_RBM] Iteration 14, pseudo-likelihood = -91.27, time = 53.20s\n",
      "computing TAP Free Energies\n",
      "monitor:  -429.440924214 165.500843371 -256.755163458\n",
      "[EMF_RBM] Iteration 15, pseudo-likelihood = -88.36, time = 53.04s\n",
      "computing TAP Free Energies\n",
      "monitor:  -434.809092564 162.66365222 -264.723311234\n",
      "[EMF_RBM] Iteration 16, pseudo-likelihood = -88.89, time = 52.99s\n",
      "computing TAP Free Energies\n",
      "monitor:  -439.798974252 160.068257798 -272.091046366\n",
      "[EMF_RBM] Iteration 17, pseudo-likelihood = -85.74, time = 52.96s\n",
      "computing TAP Free Energies\n",
      "monitor:  -444.443367405 157.691093477 -278.912231222\n",
      "[EMF_RBM] Iteration 18, pseudo-likelihood = -84.75, time = 53.12s\n",
      "computing TAP Free Energies\n",
      "monitor:  -448.783535686 155.511022318 -285.246764136\n",
      "[EMF_RBM] Iteration 19, pseudo-likelihood = -80.58, time = 53.05s\n",
      "computing TAP Free Energies\n",
      "monitor:  -452.854372009 153.507891957 -291.147579929\n",
      "[EMF_RBM] Iteration 20, pseudo-likelihood = -82.22, time = 53.26s\n",
      "computing TAP Free Energies\n",
      "monitor:  -456.691781558 151.662994952 -296.667508653\n"
     ]
    }
   ],
   "source": [
    "rbm = emf_rbm.EMF_RBM(verbose=True, monitor=True)\n",
    "rbm= rbm.fit(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-11-08T22:57:27.868434",
     "start_time": "2016-11-08T22:57:27.697130"
    },
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f54ee4699d0>]"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAhkAAAFkCAYAAACNTikJAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f54ee1be310>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(rbm.entropies-rbm.entropies[0], color='red')\n",
    "plt.plot(rbm.mean_field_energies-rbm.mean_field_energies[0], color='blue')\n",
    "plt.plot(rbm.free_energies-rbm.free_energies[0], color='green')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f54ee33ea10>]"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAhUAAAFkCAYAAACXcsmHAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f54ee19a790>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(rbm.entropies-rbm.entropies[0], rbm.mean_field_energies-rbm.mean_field_energies[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f54ee8e1510>]"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAhUAAAFkCAYAAACXcsmHAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nB4NlgAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f54ee488910>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(rbm.entropies-rbm.entropies[0], rbm.free_energies-rbm.free_energies[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [default]",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}