EMF_RBM_Energy_Densities_3.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": 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": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import rbm_datasets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "train_x, train_t, test_x, test_t  = rbm_datasets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(50000, 32, 32, 3)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_x.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "Found array with dim 4. Estimator expected <= 2.",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-6-ff74ef5758c3>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0msklearn\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpreprocessing\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mbinarize\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mX\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mbinarize\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtrain_x\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mthreshold\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0.01\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcopy\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m/home/ec2-user/src/anaconda2/lib/python2.7/site-packages/sklearn/preprocessing/data.pyc\u001b[0m in \u001b[0;36mbinarize\u001b[0;34m(X, threshold, copy)\u001b[0m\n\u001b[1;32m   1402\u001b[0m     :class:`sklearn.pipeline.Pipeline`)\n\u001b[1;32m   1403\u001b[0m     \"\"\"\n\u001b[0;32m-> 1404\u001b[0;31m     \u001b[0mX\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcheck_array\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maccept_sparse\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'csr'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'csc'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcopy\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mcopy\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1405\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0msparse\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0missparse\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1406\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mthreshold\u001b[0m \u001b[0;34m<\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/home/ec2-user/src/anaconda2/lib/python2.7/site-packages/sklearn/utils/validation.pyc\u001b[0m in \u001b[0;36mcheck_array\u001b[0;34m(array, accept_sparse, dtype, order, copy, force_all_finite, ensure_2d, allow_nd, ensure_min_samples, ensure_min_features, warn_on_dtype, estimator)\u001b[0m\n\u001b[1;32m    394\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mallow_nd\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0marray\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mndim\u001b[0m \u001b[0;34m>=\u001b[0m \u001b[0;36m3\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    395\u001b[0m             raise ValueError(\"Found array with dim %d. %s expected <= 2.\"\n\u001b[0;32m--> 396\u001b[0;31m                              % (array.ndim, estimator_name))\n\u001b[0m\u001b[1;32m    397\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mforce_all_finite\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    398\u001b[0m             \u001b[0m_assert_all_finite\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mValueError\u001b[0m: Found array with dim 4. Estimator expected <= 2."
     ]
    }
   ],
   "source": [
    "from sklearn.preprocessing import binarize\n",
    "X = binarize(train_x, threshold=0.01, copy=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
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   "outputs": [],
   "source": []
  },
  {
   "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": 14,
   "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": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import emf_rbm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "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": 16,
     "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": 17,
   "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 = -250.48, time = 9.95s\n",
      "computing TAP Free Energies\n",
      "monitor:  -314.171713225 417.643157365 103.479902116\n",
      "[EMF_RBM] Iteration 2, pseudo-likelihood = -242.32, time = 24.28s\n",
      "computing TAP Free Energies\n",
      "monitor:  -311.883392684 415.497312213 103.670005269\n",
      "[EMF_RBM] Iteration 3, pseudo-likelihood = -227.67, time = 24.57s\n",
      "computing TAP Free Energies\n",
      "monitor:  -301.33418311 393.456914109 92.8084122982\n",
      "[EMF_RBM] Iteration 4, pseudo-likelihood = -216.42, time = 24.69s\n",
      "computing TAP Free Energies\n",
      "monitor:  -290.875488216 364.169795189 74.4673250356\n",
      "[EMF_RBM] Iteration 5, pseudo-likelihood = -200.88, time = 24.54s\n",
      "computing TAP Free Energies\n",
      "monitor:  -284.760235952 344.120048601 61.2078356171\n",
      "[EMF_RBM] Iteration 6, pseudo-likelihood = -194.78, time = 24.65s\n",
      "computing TAP Free Energies\n",
      "monitor:  -282.499515775 325.535774554 45.3502290321\n",
      "[EMF_RBM] Iteration 7, pseudo-likelihood = -191.02, time = 24.49s\n",
      "computing TAP Free Energies\n",
      "monitor:  -280.215966561 313.642803487 36.125496138\n",
      "[EMF_RBM] Iteration 8, pseudo-likelihood = -180.73, time = 24.59s\n",
      "computing TAP Free Energies\n",
      "monitor:  -279.6040162 304.442445632 27.9673683129\n",
      "[EMF_RBM] Iteration 9, pseudo-likelihood = -179.30, time = 24.57s\n",
      "computing TAP Free Energies\n",
      "monitor:  -280.603247614 296.28797873 19.2710032221\n",
      "[EMF_RBM] Iteration 10, pseudo-likelihood = -172.90, time = 24.50s\n",
      "computing TAP Free Energies\n",
      "monitor:  -282.434813449 289.037387623 10.6457809873\n",
      "[EMF_RBM] Iteration 11, pseudo-likelihood = -164.91, time = 24.51s\n",
      "computing TAP Free Energies\n",
      "monitor:  -284.661342773 282.531813554 2.3619789671\n",
      "[EMF_RBM] Iteration 12, pseudo-likelihood = -163.70, time = 24.42s\n",
      "computing TAP Free Energies\n",
      "monitor:  -286.963826764 276.673346036 -5.37925079806\n",
      "[EMF_RBM] Iteration 13, pseudo-likelihood = -160.30, time = 24.47s\n",
      "computing TAP Free Energies\n",
      "monitor:  -289.09725549 271.518093724 -12.2673037094\n",
      "[EMF_RBM] Iteration 14, pseudo-likelihood = -154.05, time = 24.59s\n",
      "computing TAP Free Energies\n",
      "monitor:  -291.25342753 266.847542098 -18.7048455648\n",
      "[EMF_RBM] Iteration 15, pseudo-likelihood = -154.32, time = 24.63s\n",
      "computing TAP Free Energies\n",
      "monitor:  -293.514494111 262.548066852 -24.8871998373\n",
      "[EMF_RBM] Iteration 16, pseudo-likelihood = -153.30, time = 24.40s\n",
      "computing TAP Free Energies\n",
      "monitor:  -295.9067065 258.52126202 -30.9423605908\n",
      "[EMF_RBM] Iteration 17, pseudo-likelihood = -145.64, time = 24.66s\n",
      "computing TAP Free Energies\n",
      "monitor:  -298.457760173 254.682440633 -36.9903665944\n",
      "[EMF_RBM] Iteration 18, pseudo-likelihood = -143.61, time = 24.42s\n",
      "computing TAP Free Energies\n",
      "monitor:  -301.08142442 251.036940684 -42.9407483302\n",
      "[EMF_RBM] Iteration 19, pseudo-likelihood = -136.67, time = 24.57s\n",
      "computing TAP Free Energies\n",
      "monitor:  -303.685638259 247.587972656 -48.6953440545\n",
      "[EMF_RBM] Iteration 20, pseudo-likelihood = -137.09, time = 24.53s\n",
      "computing TAP Free Energies\n",
      "monitor:  -306.236360724 244.319693669 -54.2339859531\n"
     ]
    }
   ],
   "source": [
    "rbm = emf_rbm.EMF_RBM(verbose=True, monitor=True)\n",
    "rbm= rbm.fit(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-11-08T22:57:27.868434",
     "start_time": "2016-11-08T22:57:27.697130"
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    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f2741c4c890>]"
      ]
     },
     "execution_count": 18,
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    {
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grfd+pwWOzrnzgOeB6t77bc6554E0733vYufEAxuB3vmXT0qrIQOY1L17d5KT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\nH+mnIUt5oQY/AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2741cf1410>"
      ]
     },
     "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
}