EMF_RBM_Energy_Densities_Long.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#  EMF RBM Energy Densities  Long run\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": 1,
   "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": 2,
   "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': 'ignore'}"
      ]
     },
     "execution_count": 2,
     "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": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.datasets import fetch_mldata\n",
    "mnist = fetch_mldata(\"MNIST original\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "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": 5,
   "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": 6,
   "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": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import emf_rbm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "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": 8,
     "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": null,
   "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 = -234.89, time = 25.42s\n",
      "computing TAP Free Energies\n",
      "monitor:  -361.351919679 333.63360437 -27.0747410857\n",
      "[EMF_RBM] Iteration 2, pseudo-likelihood = -202.00, time = 58.09s\n",
      "computing TAP Free Energies\n",
      "monitor:  -348.491569775 280.976056706 -66.142838803\n",
      "[EMF_RBM] Iteration 3, pseudo-likelihood = -162.68, time = 58.07s\n",
      "computing TAP Free Energies\n",
      "monitor:  -339.800065392 252.684885317 -84.8376244858\n",
      "[EMF_RBM] Iteration 4, pseudo-likelihood = -144.45, time = 58.20s\n",
      "computing TAP Free Energies\n",
      "monitor:  -349.045776069 232.857566125 -113.190081158\n",
      "[EMF_RBM] Iteration 5, pseudo-likelihood = -131.48, time = 58.28s\n",
      "computing TAP Free Energies\n",
      "monitor:  -359.614943443 218.365962956 -137.577973637\n",
      "[EMF_RBM] Iteration 6, pseudo-likelihood = -121.53, time = 58.16s\n",
      "computing TAP Free Energies\n",
      "monitor:  -370.305042473 206.932460092 -159.087175463\n",
      "[EMF_RBM] Iteration 7, pseudo-likelihood = -115.95, time = 58.11s\n",
      "computing TAP Free Energies\n",
      "monitor:  -379.127231281 197.579966093 -176.764995632\n",
      "[EMF_RBM] Iteration 8, pseudo-likelihood = -112.00, time = 59.05s\n",
      "computing TAP Free Energies\n",
      "monitor:  -386.40423925 190.017981994 -191.196644349\n",
      "[EMF_RBM] Iteration 9, pseudo-likelihood = -103.94, time = 59.30s\n",
      "computing TAP Free Energies\n",
      "monitor:  -392.95217553 183.976726882 -203.417141548\n",
      "[EMF_RBM] Iteration 10, pseudo-likelihood = -102.77, time = 59.57s\n",
      "computing TAP Free Energies\n",
      "monitor:  -399.159857331 178.95457116 -214.303449284\n",
      "[EMF_RBM] Iteration 11, pseudo-likelihood = -97.97, time = 59.31s\n",
      "computing TAP Free Energies\n",
      "monitor:  -405.099720717 174.639290959 -224.237255536\n",
      "[EMF_RBM] Iteration 12, pseudo-likelihood = -94.69, time = 59.18s\n",
      "computing TAP Free Energies\n",
      "monitor:  -410.830870696 170.842196895 -233.465150545\n",
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      "computing TAP Free Energies\n",
      "monitor:  -416.401324377 167.423953107 -242.176492144\n",
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      "computing TAP Free Energies\n",
      "monitor:  -421.787054327 164.30797728 -250.425364826\n",
      "[EMF_RBM] Iteration 15, pseudo-likelihood = -89.72, time = 59.46s\n",
      "computing TAP Free Energies\n",
      "monitor:  -426.932330754 161.466398824 -258.182499555\n",
      "[EMF_RBM] Iteration 16, pseudo-likelihood = -89.86, time = 59.41s\n",
      "computing TAP Free Energies\n",
      "monitor:  -431.797502408 158.886819539 -265.417060699\n",
      "[EMF_RBM] Iteration 17, pseudo-likelihood = -86.30, time = 59.60s\n",
      "computing TAP Free Energies\n",
      "monitor:  -436.381595095 156.551227633 -272.142217614\n",
      "[EMF_RBM] Iteration 18, pseudo-likelihood = -84.81, time = 59.41s\n",
      "computing TAP Free Energies\n",
      "monitor:  -440.710305557 154.432480692 -278.407719215\n",
      "[EMF_RBM] Iteration 19, pseudo-likelihood = -82.67, time = 59.62s\n",
      "computing TAP Free Energies\n",
      "monitor:  -444.819102662 152.499459689 -284.278084564\n",
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      "computing TAP Free Energies\n",
      "monitor:  -448.742819931 150.722077647 -289.816943997\n",
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      "computing TAP Free Energies\n",
      "monitor:  -452.503657935 149.075464891 -295.070559455\n",
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      "computing TAP Free Energies\n",
      "monitor:  -456.117118234 147.541940954 -300.071406214\n",
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      "computing TAP Free Energies\n",
      "monitor:  -459.595822452 146.109346362 -304.843532637\n",
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      "computing TAP Free Energies\n",
      "monitor:  -462.951533645 144.767936624 -309.407750736\n",
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      "computing TAP Free Energies\n",
      "monitor:  -466.188582896 143.510442942 -313.775014451\n",
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      "computing TAP Free Energies\n",
      "monitor:  -469.311343416 142.330047223 -317.955932383\n",
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      "computing TAP Free Energies\n",
      "monitor:  -472.327404231 141.22008227 -321.964273875\n",
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      "computing TAP Free Energies\n",
      "monitor:  -475.241883797 140.174203907 -325.811107547\n",
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      "computing TAP Free Energies\n",
      "monitor:  -478.061152971 139.186848533 -329.50801635\n",
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      "computing TAP Free Energies\n",
      "monitor:  -480.792107888 138.252121849 -333.067567285\n",
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      "computing TAP Free Energies\n",
      "monitor:  -483.437700382 137.365183294 -336.497340802\n",
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      "computing TAP Free Energies\n",
      "monitor:  -486.003197363 136.521763311 -339.80668293\n",
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      "computing TAP Free Energies\n",
      "monitor:  -488.494287629 135.717948624 -343.005059822\n",
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      "computing TAP Free Energies\n",
      "monitor:  -490.914969204 134.950359494 -346.099752294\n",
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      "computing TAP Free Energies\n",
      "monitor:  -493.268294804 134.216249553 -349.096423186\n",
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      "computing TAP Free Energies\n",
      "monitor:  -495.557634658 133.513295397 -352.000655945\n",
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      "computing TAP Free Energies\n",
      "monitor:  -497.788116277 132.839371556 -354.819574452\n",
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      "computing TAP Free Energies\n",
      "monitor:  -499.961659193 132.192572292 -357.556879066\n",
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      "computing TAP Free Energies\n",
      "monitor:  -502.080088817 131.571356529 -360.215819323\n",
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      "computing TAP Free Energies\n",
      "monitor:  -504.145804136 130.974473131 -362.799911148\n",
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      "computing TAP Free Energies\n",
      "monitor:  -506.160343687 130.400256629 -365.312265616\n",
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      "computing TAP Free Energies\n",
      "monitor:  -508.126420299 129.847714033 -367.756481064\n",
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      "monitor:  -510.044811272 129.315493676 -370.134630063\n",
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      "computing TAP Free Energies\n",
      "monitor:  -511.917935092 128.802144 -372.450530055\n",
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      "computing TAP Free Energies\n",
      "monitor:  -513.746206558 128.306654455 -374.705535251\n",
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      "computing TAP Free Energies\n",
      "monitor:  -515.530260899 127.828476409 -376.900708542\n",
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      "computing TAP Free Energies\n",
      "monitor:  -517.271429031 127.366674034 -379.038231783\n",
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      "computing TAP Free Energies\n",
      "monitor:  -518.971033152 126.920365399 -381.120248038\n",
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      "computing TAP Free Energies\n",
      "monitor:  -520.629256956 126.488817953 -383.147603972\n",
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      "computing TAP Free Energies\n",
      "monitor:  -522.248419366 126.071259982 -385.123328589\n",
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      "computing TAP Free Energies\n",
      "monitor:  -523.830361175 125.66708859 -387.049775672\n",
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      "computing TAP Free Energies\n",
      "monitor:  -525.37635704 125.275668433 -388.928774701\n",
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      "computing TAP Free Energies\n",
      "monitor:  -526.887613703 124.896548585 -390.76192002\n",
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      "computing TAP Free Energies\n",
      "monitor:  -528.366260503 124.529179894 -392.551829825\n",
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      "computing TAP Free Energies\n",
      "monitor:  -529.81350524 124.172915958 -394.300318214\n",
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      "computing TAP Free Energies\n",
      "monitor:  -531.230084324 123.827400946 -396.008431486\n",
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      "computing TAP Free Energies\n",
      "monitor:  -532.616601341 123.491997842 -397.677387353\n",
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      "computing TAP Free Energies\n",
      "monitor:  -533.974420774 123.166282315 -399.308914045\n",
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      "computing TAP Free Energies\n",
      "monitor:  -560.226750555 117.489009795 -430.197856491\n",
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      "computing TAP Free Energies\n",
      "monitor:  -561.119533603 117.316687571 -431.226172845\n",
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      "computing TAP Free Energies\n",
      "monitor:  -561.997914046 117.147954802 -432.236953957\n",
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      "computing TAP Free Energies\n",
      "monitor:  -562.86281172 116.982603491 -433.231326111\n",
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      "computing TAP Free Energies\n",
      "monitor:  -563.715330092 116.820527087 -434.21048889\n",
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      "computing TAP Free Energies\n",
      "monitor:  -567.007647728 116.203533179 -437.982311048\n",
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      "computing TAP Free Energies\n",
      "monitor:  -567.802641683 116.056772163 -438.890684471\n",
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      "computing TAP Free Energies\n",
      "monitor:  -568.587160029 115.912791304 -439.78618661\n",
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      "computing TAP Free Energies\n",
      "monitor:  -569.361067373 115.771549532 -440.668712034\n",
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      "computing TAP Free Energies\n",
      "monitor:  -570.124886347 115.632945079 -441.53887499\n",
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      "computing TAP Free Energies\n",
      "monitor:  -570.878919556 115.496825971 -442.397139888\n",
      "[EMF_RBM] Iteration 96, pseudo-likelihood = -58.88, time = 59.62s\n",
      "computing TAP Free Energies\n",
      "monitor:  -571.62445412 115.363149233 -443.244823472\n",
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      "computing TAP Free Energies\n",
      "monitor:  -572.361329685 115.231798731 -444.081884564\n",
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     ]
    }
   ],
   "source": [
    "rbm = emf_rbm.EMF_RBM(verbose=True, monitor=True, n_iter=500)\n",
    "rbm= rbm.fit(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "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 0x7f29a8937dd0>]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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54Gu/fUZi50TezH6T4l3FnJpzKrvKdvnts0RERNqrkAgevXq5/bqP/bvmxpDuQ3j7grdZ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\n5mu2lkEmB1jxMAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f298aa621d0>"
      ]
     },
     "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": 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
}