experiments/cross_validations.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "sns.set()\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import env\n",
    "from ml_mnist.knn import KNNClassifier\n",
    "from ml_mnist.gp import GPClassifier\n",
    "from ml_mnist.logreg import LogisticRegression\n",
    "from ml_mnist.nn import NNClassifier, RBM\n",
    "from ml_mnist.nn.layers import FullyConnected, Activation\n",
    "from ml_mnist.nn.activations import leaky_relu\n",
    "from ml_mnist.decomposition import PCA\n",
    "\n",
    "from ml_mnist.preprocessing import StandardScaler\n",
    "from ml_mnist.feature_selection import VarianceThreshold\n",
    "from ml_mnist.model_selection import TrainTestSplitter, GridSearchCV\n",
    "from ml_mnist.augmentation import RandomAugmentator\n",
    "from ml_mnist.metrics import (accuracy_score,\n",
    "                               zero_one_loss, \n",
    "                               confusion_matrix, \n",
    "                               plot_confusion_matrix)\n",
    "from ml_mnist.utils import (one_hot, unhot,\n",
    "                             Stopwatch, RNG, \n",
    "                             plot_greyscale_image, plot_rbm_filters)\n",
    "from ml_mnist.utils.dataset import load_mnist\n",
    "from ml_mnist.utils.read_write import load_model\n",
    "\n",
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### load dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(60000, 784)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X, y = load_mnist(mode='train', path='data/')\n",
    "X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Px+jRo3H8+HHRByEiMhVLm09YZ0/4T3/6EzZv3gzg/ppzGRkZ6Nu3LyorK/H666/D39/f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\nMBGRGbEIExGZEYswEZEZsQgTEZnR/wF3SWwjMkrQkwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1fb4757c90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_greyscale_image(X[0], title=\"Label is {0}\".format(y[0]));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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jD9P0g4+Pj2kxZGtZXG05OjoaADBixAgkJSVh6dKlmDp1qstNfhNR2+CIbLr7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\nQ0BxGW0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1f79406ad0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_greyscale_image(X[42], title=\"Label is {0}\".format(y[42]));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# k-NN"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### load small subset of dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def load_small(n_samples=5000):\n",
    "    X, y = load_mnist(mode='train', path='data/')\n",
    "    X_scaled = X / 255.\n",
    "    X_scaled = VarianceThreshold(0.1).fit_transform(X_scaled)\n",
    "    X_scaled = StandardScaler(copy=False).fit_transform(X_scaled)\n",
    "    tts = TrainTestSplitter(shuffle=True, random_seed=1337)\n",
    "    indices, _ = tts.split(y, train_ratio=n_samples/60000., stratify=True)\n",
    "    return X_scaled[indices], y[indices] # 5000 -> 4994 training samples"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Approach #1: remove (almost) constant features + standartize + (non-kernelized) k-NN"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Scale data to [0, 1] range"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0 1.0\n",
      "(60000, 784)\n"
     ]
    }
   ],
   "source": [
    "X_scaled = X / 255.\n",
    "print X_scaled.min(), X_scaled.max()\n",
    "print X_scaled.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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THxERyaPNLHUgIiJqi9jzIyIiWaio48fkR0RE8lDTUgfR5FdfX4+9e/ciOzsb5eXlAACt\nVougoCA8//zzsLGxsUiQREREchJNfjExMfDy8sJrr70GV1dX6PV6XL16FVlZWVi6dCnWrVtnqTiJ\niKiVU1HHTzz5lZeXY+PGjU3e8/Lygr+/PyIiIhQNjIiI1KXNzPYUBAGHDh1qUsezrq4OBw4cgK2t\nreLBERERKUG057d+/XokJycjKSkJtbW1AAAHBwcEBAQgMTHRIgESEZE6qKjjJ578OnfujLVr1za7\nLzQ0FAcOHFAkKCIiUh81DXuKJr/du3e3uO/GjRuyB0NERGQJosnvo48+QmBgINzc3B7Y98cffygW\nFBERqY+KOn7iyW/Tpk1ISkpCbGzsAxNcsrKyFA2MiIjURU2L3EVne/r6+iItLQ3t2j2YI9esWaNY\nUEREREoyWt6sQ4cOzb7fv39/2YMhIiL1UlHHj7U9iYhIHmqa7clHGhERkdUxO/mtXLlSxjCIiEjt\nBMH8zdJEhz3vVnW5n16vx8mTJxUJiIiI1ElNw56iyc/f3x9arbbJe4IgQK/XGx5xREREpDaiyW/R\nokWoqqrC3LlzH9gXGhqqWFBERKQ+Kur4id/ze/XVV9G9e/dmhz+ffvppxYIiIiL1EQTB7M3SjC51\nmDhxYrPv854fERGpFQtbExGRLNQ07MnC1kREJIs2M9uTha2JiKgtEk1+LGxNRERSqajjx8LWREQk\nDzU90oiFrYmISBYqyn0sbE1ERNZHNPlVVFRg/fr1WL58OY4dO9Zk36pVqxQNjIiI1EVNi9xFk9+i\nRYvg6emJwMBApKamIjU11bDvwoULigdHRESkBNHkV19fjylTpiAkJAQ7duxAYWEhUlJSANx5sgMR\nEdFdanqkkWjya9euHQ4ePIjGxkZoNBqsX78ely5dwooVK1BTU2OpGImISAUEjWD2ZmmiyS8hIQFH\njhzB7du373yzRoOkpCT4+/sb3iMiIgLaUM+vS5cuSExMfGCt3/jx46HRcKIoERGpEwtbExGRLNpM\nbU8WtiYioraIha2JiEgWKur4sbA1ERHJo80MewIsbE1ERNKoKPexticREVkf0Z7ftWvXkJGRAQ8P\nD0yYMAFbtmzBqVOn4O3tjRkzZsDFxcVScRIRUWunoq6faM8vJiYGdXV1+OmnnzB79mzcvHkTs2fP\nRrdu3RATE2OpGImIyMqtXbsW4eHhePnll5Gfn9/s97z77ruIjIyUdDzRnt/t27cxZ84c6PV6jBs3\nzlDYul+/fpztSURETSg14SU3NxfFxcVIT09HQUEBli1bhvT09CbfU1BQgJMnT6J9+/aSjina82to\naEBJSQkEQcDy5csN7587dw719fVm/AhERNRWKVXeLCcnB8HBwQAAHx8fVFVVPVBfOikpCQsXLpQc\nq9FHGq1fvx4AEBQUBAA4dOgQFi9ejNjYWMknISKitk+pwtY6na7JHBNnZ2fodDrD68zMTAQEBKBL\nly6SYxUd9vTz84Ofn1+T98aMGYMxY8YgNDQUBw4ckHwiIiIiOdz7SL0bN27gyy+/xIcffojLly9L\nftwea3sSEZEslJrsqdVqm/T0ysrK4O7uDgA4duwYKioq8Morr+D27du4dOkSEhMTsWTJEtFjsrYn\nERG1aoGBgUhJScGkSZNw9uxZeHh4wN7eHgAwduxYjB07FgBQUlKCpUuXGk18AGt7EhGRTJSa7enn\n54fevXsjPDwcNjY2iIuLQ2ZmJhwdHQ0TYUwl6I0MkNbW1sLOzu6B5/fl5eVJKnFWV1VhVmBERCQ/\n20dcFTv28cTtZrcdtGSajJEYx9qeREQkCzUVtmZtTyIisjpGe35ERERSqKjjZ3rPT2rdNCIiotbK\n6MNstVot2rdvb1g4WF5ejpEjR0IQBBw+fNgiQRIRUeunpnt+osnvgw8+wNatWxEZGYkxY8YAACZP\nnozPPvvMIsEREZGKqGgWiWioQUFB2LZtG86dO4d58+bh8uXLqsrsRERkOYIgmL1ZmtEJL7a2tpg3\nbx6KioqwatUqXLt2DcCd8mZOTk6KB0hERCQ3ybM9vb29sXnzZly9ehUAEBERwcLWRERkoKaBQRa2\nJiIiq8PC1kREJAs1zQlhYWsiIpKFinKf8XV+aWlpaNfuwW9bs2aNYkEREZEKqSj7sbA1ERFZHdb2\nJCIiWQga9fT8VLQen4iISB6iye/IkSOGr69fv47Vq1cjMjISq1evRmVlpeLBERGRegiC+ZuliSa/\nbdu2Gb5evXo1PDw8sHLlSjzxxBOIjY1VPDgiIlKPNlXe7C6dTod3330XAODj44P/+Z//USwoIiJS\nHxVN9hRPfteuXTMMfdra2uLcuXPw9fXF+fPnUVNTY5EAiYiI5Caa/Pr06YNvvvkGAODm5obr168D\nAFJTU/HGG28oHx0REamHirp+gv7uU2pNFBoaKqmwdV1VhTmHJyIiBdg+4qrYsc9s/tTstn1mvixj\nJMaxsDUREclCTev8WNiaiIhkoaJRTxa2JiIimago+4mu82NhayIiaotY2JqIiGShoo4fa3sSEZH1\n4VMdiIhIFm1mtufNmzdx8uRJjBgxAlVVVdi8eTMKCgrg7e2NGTNmwMXFxVJxEhFRK/cwanSaS3TY\nc968edDpdACAv//973B0dMScOXPw6KOPYvHixRYJkIiIVEL4E5uFifb8qqurERYWBgAoKyszFLbu\n27cv9u/fr3x0REREChDt+Xl5eSEhIQH5+fkYNGgQDh48CJ1Ohy+++ALu7u6WipGIiFRATY80Eq3t\n2dDQgD179uC7775DSUkJ9Ho93NzcMHToUEyYMAFardboCVjbk4io9VCytudvOz83u23PqJdkjMQ4\nFrYmIrIiSia/f+/aa3bbJyJflDES41jYmoiI5KGileMsbE1ERLJQ01IHFrYmIiKrI5r8WNiaiIik\najM9P4CFrYmIqO1hbU8iIpKHejp+TH5ERCQPNRW2Fp2YGhcXh/z8fEvFQkREaiYI5m8WJtrzO336\nNBoaGvDBBx8gIiICAwcOtFRcREREihFNfk5OTkhISEBRURF27tyJ+Ph49OvXD76+vnBxcUFISIil\n4iQiolZORZM9xZPf3Wmr3t7eePvtt1FfX4/c3Fzk5+ejqKiIyY+IiFRJNPk5Ozs3ed2+fXs888wz\neOaZZ1jejIiImlDTOj/RCS/Jyckt7ouIiJA9GCIiUjGNYP5mYSxsTUREslBTz4+FrYmIyOqwsDUR\nEclDPR0/4w+zra2thZ2dHTSaprcH8/LyJNX35MNsiYhaDyUfZlv85Vdmt+0x4TkZIzGOha2JiEgW\nbeaeHxERkVRqqu0pmvxu3ryJ9PR0ODs748UXX8Qnn3yC/Px8eHl5ISoqCh07drRUnERE1NqpqOcn\nus5v0aJFaGxsRGFhIV555RWUlJTgueeegyAIiI2NtVSMRESkAoIgmL1ZmmjP79atW3j99dcBACEh\nIYiJiQEADBkyBFFRUcpHR0REpADR5NfQ0IDi4mJUVlaiqqoKp0+fxpNPPomCggLU19dbKkYiIrJy\na9euRV5enmHksW/fvoZ9x44dw8aNG2FjYwNvb2/Ex8cbPZ5o8ps/fz4WLFgANzc37Nq1C6tXr8b5\n8+fh7u6OlStX/ukfhoiI2hCFRi9zc3NRXFyM9PR0FBQUYNmyZUhPTzfsf/vtt7Fz5054eHjgzTff\nxA8//IChQ4eKHlM0+fn7+2Pv3r2G19u3bzd8HRoaigMHDpj7sxARURuj1GzPnJwcBAcHAwB8fHxQ\nVVWFmpoaODg4AAD27t1rmIDp4uKC69evGz0ma3sSEZE8FJq4otPp0KdPH8NrZ2dn6HQ6Q/K7m/jK\nysqQnZ2Nt956y+gxWduTiIhkYalZm80VJquoqMAbb7yBlStXwsnJyegxWNuTiIhaNa1WC51OZ3hd\nVlYGd3d3w+vq6mpMnz4dCxcuREBAgKRjiq7z8/X1RVpaGtq1ezBHrlmzRmrcREREZgsMDDR0uM6e\nPQsPDw/Y29sb9icmJmLatGkIDAyUfEyjha3/LBa2JiJqPZQsbH358Ldmt/UcFSy6f8OGDThx4gRs\nbGwQFxeHX3/9FY6OjhgyZAgGDhyIJ598Enq9HoIgIDQ0FGFhYaLHY/IjIrIiSia/K/86bHbbLiNH\nyRiJcSxsTURE8lBPaU/x5NfY2IiDBw/ixx9/REVFBfR6Pbp27YoRI0Zg2LBhloqRiIhUQE2PNBKd\n8LJy5UpcvHgRkyZNwpNPPom//vWveOqpp7Br1y4kJSVZKkYiIiJZiSa/oqIizJ49G35+fpg1axbO\nnDmD0NBQ/OMf/8Dx48ctFSMREZGsRJOfXq/Hjz/+iBs3buDLL7+ERnPn23/44Ydmlz8QEZEV0wjm\nbxYmmsFWrVqFd955B8XFxejZsyf+/ve/AwDy8vKwfPlyiwRIRETqoKZ7fmYvdZBa2JpLHYiIWg8l\nlzpc/fGI2W09hlh2EiULWxMRkSzU1PNjYWsiIrI6LGxNRERWx+g9v9raWtjZ2Rlmet6Vl5eH/v37\nGz0B7/kREbUeSt7zK8s5anZbbUCQjJEYZ3S9QocOHZp9X0riIyIi69Fm7vkRERFJxuRHRETWRngI\ni9XNJZr86uvrsXfvXmRnZ6O8vBzAnSfqBgUF4fnnn4eNjY1FgiQiIpKT6ISX+fPnw8vLCyNGjICr\nqyv0ej2uXr2KrKwsVFVVYd26dUZPwAkvRESth5ITXnS52Wa3dfN/RsZIjBPt+ZWXl2Pjxo1N3vPy\n8oK/vz8iIiIUDYyIiFRGRff8RAtbC4KArKws1NfXG96rq6vDgQMHHlj3R0RE1k0QBLM3i8cqNuxZ\nWlqK5ORk5Obmora2Fnq9Hg4ODggICMAbb7yBLl26GD0Bhz2JiFoPJYc9K06Z/6g71wGDZIzEONFh\nz/z8fBw7dgy3bt3C8OHDsWLFCnTs2BEAEBUVhZ07d1okSCIiav3UNNtTdNhz69atyMzMRE5ODp56\n6ilER0fj5s2bAO4864+IiEiNRJOfjY0NOnXqBI1Gg0mTJmH69OmIjo5GZWWlqlbyExER3Ut02HPA\ngAGYMWMGkpOT0aFDBwQHB8POzg5Tp07F9evXLRUjERGpgYo6RaLJLyYmBsePH4ednZ3hvaCgIPj5\n+eHrr79WPDgiIlIRFSU/s5/kLhVnexIRtR5Kzva8lv+T2W2d+z4lYyTGsbYnERHJo63M9iQiImqL\nzE5+K1eulDEMIiIiyxEd9qytrW32fb1ej5MnTyoSEBERqZMgqGcwUTT5+fv7Q6vVNnlPEATo9XrD\nI46IiIgAqGq2p2jyW7RoEaqqqjB37twH9oWGhioWFBERqY+aip+I9lFfffVVdO/eHTU1NQ/s69On\nj2JBERGRCmkE8zdLhyq289tvv0VycjJGjRqFxYsXo7q62rCvpKRE8eCIiIiUIJr8tmzZgszMTGRn\nZ2PAgAEsbE1ERG2C6D2/u4WtAWDy5MlwdXVFdHQ0Nm/erKqxXSIiUp6a8gILWxMRkTzaSvJjYWsi\nIpJMRev8FC9snbvuI7Pb9p/J5RRERPfTHT9ldlvP0aNljKSpm0XnzG7r6O0rYyTGqSdNExERyYTJ\nj4iIrI5o8quoqMD69euxfPlyHDt2rMm+VatWKRoYERGpjCCYv1mYaPJbtGgRPD09ERgYiNTUVKSm\nphr2XbhwQfHgiIhIPQRBMHuzNNHkV19fjylTpiAkJAQ7duxAYWEhUlJSAHCROxER3UfQmL9ZmOgZ\n27Vrh6+//hqNjY3QaDRYv349Ll26hBUrVjRb75OIiKyXoBHM3ixNNPmtXbsWR48eNTzXT6PRICkp\nCf7+/oYyZ0RERGojmvzy8/Nx7NixBwpbjx8/Hp07d7ZIgERERHITTX5bt25tsbC1mmq4ERGRBaho\ntqfZha2JiIjupaZOEQtbExGRPFRU25OFrYmISB4PYdamuRQvbF1XVaHk4YmIyAS2j7gqduxbV383\nu629h5eMkRinnj4qERGRTESHPa9du4aMjAx4eHhgwoQJ2LJlC06dOgVvb2/MmDEDLi4uloqTiIha\nOTVNeBHt+cXExKCurg4//fQTZs+ejZs3b2L27Nno1q0bYmJiLBUjERGpgYrKm4n2/G7fvo05c+ZA\nr9dj3Li65FyvAAANcElEQVRxhsLW/fr1Q1ZWlkUCJCIidWgzPb+GhgaUlJRAEAQsX77c8P65c+dQ\nX1+veHBERKQiKur5GR32XL9+PYA7SxwA4NChQ1i8eDH+9re/KR8dERGRAkSTX3l5OfLy8jB48GBD\nbc8xY8bgyy+/xHvvvWepGImIyMqtXbsW4eHhePnll5Gfn99kX3Z2NsLCwhAeHo60tDRJxzO7tief\n50dERPdS6pFGubm5KC4uRnp6OtasWYP4+Pgm++Pj45GSkoJPP/0U//u//4uCggKjsYomv7u1PTUa\nDSZPnozp06cjOjoalZWVqrqxSUREFqBQYeucnBwEBwcDAHx8fFBVVWV4puylS5fQqVMneHh4QBAE\nDBs2DMeOHTMaqmjyu1vb8+7z/IKDgzF37lxMnToVFy9elPKrICIiKyEIGrM3MTqdrsm6cmdnZ+h0\numb3ubi4oKyszGisrO1JRETysNCIoNhtN6m35ESTHwAMGjTogfc6duyISZMmSTqBknXkiIio9VDq\n816r1Rp6egBQVlYGd3d3w77y8nLDvqtXr0Kr1Ro9Jmt7EhFRqxYYGGgorHL27Fl4eHjA3t4eANC1\na1fU1NTg8uXLaGhowPfff48hQ4YYPabiT3UgIiL6szZs2IATJ07AxsYGcXFx+PXXX+Ho6Ijg4GCc\nPHkS77zzDgBg3LhxmDp1qtHjMfkREZHV4bAnERFZHSY/IiKyOkx+RERkdR5a8hOr02bMuXPnMHr0\naOzevdvk865btw7h4eEICwvDP//5T8nt/vOf/+Ctt95CZGQkJk+ejO+//97kc9++fRujR4/Gvn37\nJLc5ceIEAgICEBUVhcjISKxZs8akc+7fvx8TJkzAiy++iCNHjkhq8/nnnyMyMtJwzgEDBkg+361b\ntzB37lxERUXh5Zdfxo8//ii5rV6vR1xcHMLDwxEVFYWioiJJ7e6/HkpLSxEZGYmIiAjMnz+/xSeQ\nNHcd7dixA3369DEUdpB6zitXrmDatGmIjIzEa6+9hoqKCsltf/75Z7zyyiuIiorC9OnTce3aNclt\n7zp69Ch8fX1Ninnp0qUIDQ1FVFQUoqKiRK+P+9s2NDRg4cKFCAsLw7Rp0wxlD6W0ffPNNw3X1vjx\n4xEXFye5bW5uruF3NXPmzBbPe3+7wsJCREREIDIyEnFxcWhsbGzxnPd/Rki9nu5v++233wKQfk01\nd16p19T9bU+fPi35mrJWRtf5KeHeOm0FBQVYtmwZ0tPTJbWtra1FUlISAgMDTT7v8ePHceHCBaSn\np+P69et4/vnnMXr0aElt//Wvf6Fv376Ijo7G5cuXMW3aNAwfPtyk86elpaFTp04mxz1w4EAkJyeb\n3O769etITU3Fvn37UFNTg/feew/Dhg0z2u6ll17CSy+9BODOf6tvvvlG8jkzMzPx2GOPYf78+Sgr\nK8Orr76KgwcPSmp7+PBhVFdXIz09Hb///jvi4+OxZcsW0TbNXQ/JycmIjIzEmDFjsHHjRuzduxfh\n4eFG2+3btw9VVVVG1wi1dM5JkyYhJCQEu3fvxocffohFixZJartjxw6sX78eXbt2RUpKCjIyMjBj\nxgxJbQGgrq4OW7duFY27pbZ/+9vfjF4TzbXds2cPXF1d8e677yIjIwMnT57EiBEjJLW991qOjY1F\nWFiY5PMmJiZiw4YN6NGjB7Zs2YL09HRMnz7daLt33nkHM2fOxJAhQ5CamoqDBw/iv/7rvx44Z3Of\nEYMHD0ZERATGjh3b4vXUUtvq6mpJ11RL5w0LC8Ozzz4rek0117Z///6Srilr9lB6fmJ12oyxs7PD\nli1b4ObmZvJ5/f39DX94jzzyCGprayVXA3j22WcRHR0NALh8+TK6dOli0rkLCwtRVFQkKfncz9wJ\nudnZ2QgMDESHDh3g5uaGVatWmXyM1NRUzJo1S/L3u7i4GP6VeePGjSZlh4y5ePEi+vXrBwDw8vLC\npUuXjP7szV0PJ06cMHwQjxgxAtnZ2ZLajR07FnPnzjUaZ3Nt3377bYwdOxbAnd/BjRs3JLf97//+\nb3Tt2hV6vR5lZWXw8PCQ3BYANm/ejMjISLRv396kmKVqru13332H0NBQAEBYWFizic/YeYuKilBd\nXY2+fftKbuvm5obKykoAd64vZ2dnSe2Ki4sN53nmmWdaHJG4/zPi1q1byM3NxciRIwG0fD0117a2\nthajR4+WdE0113b58uUYN24cAPFrqrm2Uq8pa/ZQkp9YnTZjNBoNbG1tzTqvRqNBhw4dAAAZGRkY\nNmyYyQW6w8PDERMTg9jYWJParVu3DkuWLDGpzV0FBQWYNWsWpkyZ0uIfXnNKSkpQW1uLN954AxER\nEcjJyTHpvPn5+ejSpQtcXaVXbQgJCUFpaSnGjBmDqKgok37mJ554AkePHkVjYyMKCwtx5coVo8M1\nzV0PtbW1hkTg6urapPqDWLu714YxLbXVaDRobGzEJ598gueee05yW+DOsOW4ceNQUVGBCRMmSG5b\nVFSECxcuYMyYMaL/UGjpvB9//DFeffVVLFy4ENevX5fctqSkBEeOHEFkZCQWLlyIqqoqk84LADt3\n7kRERIRJMS9evBhz5sxBSEgIfv75Z7z44ouS2vXs2dNwqyInJ6fFIcR7PyM+//xzDB8+XNL1dH/b\nu58vDg4OLf58UtpKvabubwtIu6asWauY8GLppYbffvstvvjiC6xYscLktunp6UhLSzPpYb779u2D\nv78/PD09AZj28/bo0QNz5sxBWloaEhMTsWzZMjQ0NEhqq9frcf36daSlpWHt2rUmJ+yMjAy88MIL\nJrXZv38/OnfujEOHDmH79u0m9TaHDRuG3r17Y8qUKfj888+h1Wr/9LVhyWursbERixYtwuDBgzF4\n8GCT2gYFBSErKwve3t5Gh3rvlZSUZPY/qiZMmICFCxdix44d6NWrFzZt2iS5rV6vh4+PD3bt2oXH\nH38cmzdvNunc9fX1OHXqFAYOHGhSu9WrVxuGLf38/PDJJ59Iardo0SJ89dVXiI6Oxu3bt41eF99+\n+y327t2LFStWNPleKdfTn/l8ub+tKdfU/W3NvaasxUNJfmJ12pR29OhRbN26Ff/4xz/QsWNHye3O\nnDmDK1euAAB8fX3xxx9/GIZfjDly5Ai++eYbTJ48GRkZGXj//fcl98I8PDwQEhICAOjevTvc3Nxw\n9epVSW3d3Nzg5+cHQRDQvXt3ODg4SI4ZuDN86OfnJ/n7AeDUqVMICgoCcOf3VFpaalICWrBgAT79\n9FMsWLAAN2/eNKnXeZeDgwPq6uoASK/zdy9zH9e1dOlSeHt7Y/bs2Sa1O3TokOHrMWPG4NSpU5La\nXb16FUVFRViwYAEmT56M8vJyREZGSj7v4MGDDZNkRo0ahd9++01yWzc3N/j7+wMAhgwZIun5affK\nzc01DHGb4vz583jyyScB3Bm+lDpZztPTEx988AG2bduGxx9/HF27dm3xe+//jDDlemrp80XKNdVc\nW6nX1P1tzb2mrMlDSX5iddqUVF1djfXr12Pz5s1wdHQ0qe3Jkyexfft2AHeGbWtrayXfz9q4cSMy\nMjLw2WefISwsDLNmzUJAQICktgcOHEBKSgoAoKKiApWVlZLH7wMDA3H8+HHo9Xpcu3YNt27dkhxz\nWVkZHBwc0K6daXOievTogdOnTwO4MzRmb28vOZmcO3cOy5cvBwB88803JvcK7goICDBcX1lZWYZk\nLJVerze5x7h//37Y2tpizpw5JrUD7txXPXfuHADgl19+gbe3t6R2Hh4eyMrKQnp6Oj777DO4u7tj\n165dks87b948nD9/HsCdZNSzZ0/JbYcOHYoffvgBwJ2/Yakx35Wfn290dmpz3N3dDYk2Pz8fXl5e\nktpt2rTJEO+XX37Z4j3K5j4jpF5PYp8vxq6p5tpKvaaaa2vuNWVNHlp5s/vrtPXq1UtSu7y8PCxf\nvhyVlZWwsbGBk5MTPv74Yzg5ORltu2fPHqSkpODRRx+FXq+HIAhYt24dOnfubLTt7du3ERsbi9LS\nUty+fRtz5841a/JKSkoKunXrhokTJ0r6/pqaGixcuBA3btyAXq/H7NmzTfow37NnDzIyMiAIAmbN\nmiV5hurZs2eRnJyMrVu3Sj4XcGepQ2xsLCoqKvDHH3/grbfekpzE9Ho9YmNjUVBQgPbt22PDhg1G\nE31z18O2bduwZMkS1NXVwdPTE2vXroWNjY3Rdk8//TROnjyJixcvokePHnj66aexcuVKSedsbGyE\nnZ0dHBwcIAgCHn/88Wan8DfXNj4+HgkJCWjfvj3s7Oywbt26Zv+RYuzaHzVqFA4fPiz59zRv3jy8\n//77cHBwgIODAxISEiSfd9u2bYiPj0d5eTkcHByQlJRkUsybNm3CU089ZRjVkBrzqlWrsG7dOrRv\n3x6dOnVCQkLCAyM4Lf2O16xZg4aGBgwaNAiLFy9u9pzNfUYkJSVh2bJlotdTS227du2KM2fOGL2m\n7m0L3PlbKC0thaOjo9Frqrnzzps3D++8847Ra8qasbYnERFZnVYx4YWIiMiSmPyIiMjqMPkREZHV\nYfIjIiKrw+RHRERWh8mPiIisDpMfERFZHSY/IiKyOv8PJlbV4u+NUHoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1f7743d950>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.heatmap(X_scaled[100:124, 100:124]); # lots of zeros ofc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Remove features with low variance (784 -> 444)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0 1.0\n",
      "(60000, 444)\n"
     ]
    }
   ],
   "source": [
    "X_scaled = VarianceThreshold(0.1).fit_transform(X_scaled)\n",
    "print X_scaled.min(), X_scaled.max()\n",
    "print X_scaled.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Now perform mean-std standartization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-1.27420789208 9.7871062278\n",
      "(60000, 444)\n"
     ]
    }
   ],
   "source": [
    "X_scaled = StandardScaler(copy=False).fit_transform(X_scaled)\n",
    "print X_scaled.min(), X_scaled.max()\n",
    "print X_scaled.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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x6aefIjc3F926dUNcXBzatRO/JQcREbUyDl7wFPdp5s+fD5PJhMuXL+Oll15C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\nOYX/B9xHxfgRtuvMAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1f76fdb9d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.heatmap(X_scaled[100:124, 100:124], cmap='RdYlGn'); # more interesting"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Some benchmarks\n",
    "As you can see, for brute-force algorithm no training time needed at all, but longer prediction, compared to k-d tree. The difference become bigger as number of training samples grows and it should be even bigger when we'll use much less number of features after PCA (now 444)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "KNNClassifier(algorithm='brute', k=5, kd_tree_=None, kernel=None,\n",
       "       kernel_params={}, leaf_size=30, metric=None, p=2.0,\n",
       "       weights='uniform')"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "knn = KNNClassifier(algorithm='brute')\n",
    "knn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Elapsed time: 0.000 sec\n"
     ]
    }
   ],
   "source": [
    "with Stopwatch(verbose=True) as s:\n",
    "    knn.fit(X_scaled[:1000], y[:1000])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Elapsed time: 2.041 sec\n",
      "0.21\n"
     ]
    }
   ],
   "source": [
    "with Stopwatch(True) as s:\n",
    "    y_pred = knn.predict(X_scaled[1000:1100])\n",
    "print zero_one_loss(y_pred, y[1000:1100])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "KNNClassifier(algorithm='kd_tree', k=5, kd_tree_=None, kernel=None,\n",
       "       kernel_params={}, leaf_size=10, metric=None, p=2.0,\n",
       "       weights='uniform')"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "knn2 = KNNClassifier(algorithm='kd_tree', leaf_size=10)\n",
    "knn2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Elapsed time: 0.438 sec\n"
     ]
    }
   ],
   "source": [
    "with Stopwatch(True) as s:\n",
    "    knn2.fit(X_scaled[:1000], y[:1000])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Elapsed time: 0.455 sec\n",
      "0.21\n"
     ]
    }
   ],
   "source": [
    "with Stopwatch(True) as s:\n",
    "    y_pred = knn2.predict(X_scaled[1000:1100])\n",
    "print zero_one_loss(y_pred, y[1000:1100])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### GridSearchCV (uses stratified K-Fold CV)\n",
    "This class will be used for convenient hyper-parameters grid search for simple models. This class desing as many others is inspired by one of `sklearn`, yet have some extensions (such as model saving, that is supported for all models here, and possibility to specify order for parameters exploration). \n",
    "\n",
    "One more feature is the following -- parameter `refit`, which controls order of exploring parameters. \n",
    "\n",
    "If set to `True`, then for each combination of parameters we refit our model for each new train/test split to get mean accuracy score for given set of parameters as soon as possible. This makes sense for each ML algorithm (typically parametric), with explicit training procedure.\n",
    "\n",
    "If set to `False`, then for each possible split we fit our model **once**, and after that we evaluate this model on all possible combination of parameters. This makes sense and yields results **significantly** faster for such models (typically non-parametric), as k-NN, in particular.\n",
    "\n",
    "Below small demo of output for `refit`=True:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "param_grid = ({'weights': ['uniform', 'distance'], 'k': [2, 3]}, {'p': [1., np.inf], 'k': [2]})\n",
    "grid_cv1 = GridSearchCV(model=KNNClassifier(algorithm='kd_tree', leaf_size=1), param_grid=param_grid, \n",
    "                        train_test_splitter_params=dict(shuffle=True, random_seed=1337), n_splits=4, \n",
    "                        refit=True, save_models=False, verbose=True)\n",
    "grid_cv1.fit(X_scaled[:1000], y[:1000]); # rebuilding tree on each iteration\n",
    "\n",
    "# Training KNNClassifier on 1000 samples x 444 features.\n",
    "# 4-fold CV for each of 6 params combinations == 24 fits ...\n",
    "\n",
    "# iter:  1/24 +--- elapsed:   1.026 sec   ...\n",
    "# iter:  2/24 ++-- elapsed:   2.022 sec   ...\n",
    "# iter:  3/24 +++- elapsed:   3.010 sec   ...\n",
    "# iter:  4/24 ++++ elapsed:   4.012 sec - mean acc.: 0.7940 +/- 2 * 0.038\n",
    "# iter:  5/24 +--- elapsed:   5.017 sec - best acc.: 0.7940 at {'k': 2, 'weights': 'uniform'}\n",
    "# iter:  6/24 ++-- elapsed:   6.017 sec - best acc.: 0.7940 at {'k': 2, 'weights': 'uniform'}\n",
    "# iter:  7/24 +++- elapsed:   7.042 sec - best acc.: 0.7940 at {'k': 2, 'weights': 'uniform'}\n",
    "# iter:  8/24 ++++ elapsed:   8.054 sec - mean acc.: 0.8070 +/- 2 * 0.029\n",
    "# iter:  9/24 +--- elapsed:   9.093 sec - best acc.: 0.8070 at {'k': 2, 'weights': 'distance'}\n",
    "# iter: 10/24 ++-- elapsed:  10.105 sec - best acc.: 0.8070 at {'k': 2, 'weights': 'distance'}\n",
    "# iter: 11/24 +++- elapsed:  11.138 sec - best acc.: 0.8070 at {'k': 2, 'weights': 'distance'}\n",
    "# iter: 12/24 ++++ elapsed:  12.157 sec - mean acc.: 0.8209 +/- 2 * 0.024\n",
    "# iter: 13/24 +--- elapsed:  13.198 sec - best acc.: 0.8209 at {'k': 3, 'weights': 'uniform'}\n",
    "# iter: 14/24 ++-- elapsed:  14.308 sec - best acc.: 0.8209 at {'k': 3, 'weights': 'uniform'}\n",
    "# iter: 15/24 +++- elapsed:  15.596 sec - best acc.: 0.8209 at {'k': 3, 'weights': 'uniform'}\n",
    "# iter: 16/24 ++++ elapsed:  16.607 sec - mean acc.: 0.7811 +/- 2 * 0.029\n",
    "# iter: 17/24 +--- elapsed:  17.706 sec - best acc.: 0.8209 at {'k': 3, 'weights': 'uniform'}\n",
    "# iter: 18/24 ++-- elapsed:  18.770 sec - best acc.: 0.8209 at {'k': 3, 'weights': 'uniform'}\n",
    "# iter: 19/24 +++- elapsed:  19.840 sec - best acc.: 0.8209 at {'k': 3, 'weights': 'uniform'}\n",
    "# iter: 20/24 ++++ elapsed:  20.889 sec - mean acc.: 0.8140 +/- 2 * 0.031\n",
    "# iter: 21/24 +--- elapsed:  21.866 sec - best acc.: 0.8209 at {'k': 3, 'weights': 'uniform'}\n",
    "# iter: 22/24 ++-- elapsed:  22.843 sec - best acc.: 0.8209 at {'k': 3, 'weights': 'uniform'}\n",
    "# iter: 23/24 +++- elapsed:  23.811 sec - best acc.: 0.8209 at {'k': 3, 'weights': 'uniform'}\n",
    "# iter: 24/24 ++++ elapsed:  24.766 sec - mean acc.: 0.4880 +/- 2 * 0.018"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "and for `refit`=True: (difference is not big because too many features and too few parameter combinations are used)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "grid_cv2 = GridSearchCV(model=KNNClassifier(algorithm='kd_tree', leaf_size=1), param_grid=param_grid, \n",
    "                        train_test_splitter_params=dict(shuffle=True, random_seed=1337), n_splits=4, \n",
    "                        refit=False, save_models=False, verbose=True)\n",
    "grid_cv2.fit(X_scaled[:1000], y[:1000]); # building tree only on each 6-th iteration\n",
    "\n",
    "# Training KNNClassifier on 1000 samples x 444 features.\n",
    "# 4-fold CV for each of 6 params combinations == 24 fits ...\n",
    "\n",
    "# iter:  1/24 +--- elapsed:   1.019 sec - best acc.: 0.8110  [1/4 splits] at {'k': 2, 'weights': 'uniform'}\n",
    "# iter:  2/24 +--- elapsed:   1.834 sec - best acc.: 0.8228  [1/4 splits] at {'k': 2, 'weights': 'distance'}\n",
    "# iter:  3/24 +--- elapsed:   2.645 sec - best acc.: 0.8386  [1/4 splits] at {'k': 3, 'weights': 'uniform'}\n",
    "# iter:  4/24 +--- elapsed:   3.448 sec - best acc.: 0.8386  [1/4 splits] at {'k': 3, 'weights': 'uniform'}\n",
    "# iter:  5/24 +--- elapsed:   4.277 sec - best acc.: 0.8386  [1/4 splits] at {'k': 3, 'weights': 'uniform'}\n",
    "# iter:  6/24 +--- elapsed:   5.058 sec - best acc.: 0.8386  [1/4 splits] at {'k': 3, 'weights': 'uniform'}\n",
    "# iter:  7/24 ++-- elapsed:   6.073 sec - best acc.: 0.8055  [2/4 splits] at {'k': 2, 'weights': 'uniform'}\n",
    "# iter:  8/24 ++-- elapsed:   6.878 sec - best acc.: 0.8174  [2/4 splits] at {'k': 2, 'weights': 'distance'}\n",
    "# iter:  9/24 ++-- elapsed:   7.672 sec - best acc.: 0.8353  [2/4 splits] at {'k': 3, 'weights': 'uniform'}\n",
    "# iter: 10/24 ++-- elapsed:   8.475 sec - best acc.: 0.8353  [2/4 splits] at {'k': 3, 'weights': 'uniform'}\n",
    "# iter: 11/24 ++-- elapsed:   9.336 sec - best acc.: 0.8353  [2/4 splits] at {'k': 3, 'weights': 'uniform'}\n",
    "# iter: 12/24 ++-- elapsed:  10.125 sec - best acc.: 0.8353  [2/4 splits] at {'k': 3, 'weights': 'uniform'}\n",
    "# iter: 13/24 +++- elapsed:  11.311 sec - best acc.: 0.7806  [3/4 splits] at {'k': 2, 'weights': 'uniform'}\n",
    "# iter: 14/24 +++- elapsed:  12.127 sec - best acc.: 0.7980  [3/4 splits] at {'k': 2, 'weights': 'distance'}\n",
    "# iter: 15/24 +++- elapsed:  12.918 sec - best acc.: 0.8166  [3/4 splits] at {'k': 3, 'weights': 'uniform'}\n",
    "# iter: 16/24 +++- elapsed:  13.722 sec - best acc.: 0.8166  [3/4 splits] at {'k': 3, 'weights': 'uniform'}\n",
    "# iter: 17/24 +++- elapsed:  14.576 sec - best acc.: 0.8166  [3/4 splits] at {'k': 3, 'weights': 'uniform'}\n",
    "# iter: 18/24 +++- elapsed:  15.538 sec - best acc.: 0.8166  [3/4 splits] at {'k': 3, 'weights': 'uniform'}\n",
    "# iter: 19/24 ++++ elapsed:  16.519 sec - best acc.: 0.7940 +/- 2 * 0.038 at {'k': 2, 'weights': 'uniform'}\n",
    "# iter: 20/24 ++++ elapsed:  17.322 sec - best acc.: 0.8070 +/- 2 * 0.029 at {'k': 2, 'weights': 'distance'}\n",
    "# iter: 21/24 ++++ elapsed:  18.106 sec - best acc.: 0.8209 +/- 2 * 0.024 at {'k': 3, 'weights': 'uniform'}\n",
    "# iter: 22/24 ++++ elapsed:  19.095 sec - best acc.: 0.8209 +/- 2 * 0.024 at {'k': 3, 'weights': 'uniform'}\n",
    "# iter: 23/24 ++++ elapsed:  19.933 sec - best acc.: 0.8209 +/- 2 * 0.024 at {'k': 3, 'weights': 'uniform'}\n",
    "# iter: 24/24 ++++ elapsed:  20.688 sec - best acc.: 0.8209 +/- 2 * 0.024 at {'k': 3, 'weights': 'uniform'}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "best model as well as other \"best\" stuff are available:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "grid_cv2.best_model_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "finally all results can be converted to `pandas.DataFrame` and stored to excel or whatever. For more see docstrings in code."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df = grid_cv2.to_df()\n",
    "df.to_excel('test.xlsx')\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5-Fold CV on 5k images"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### load data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "param_grid = {'weights': ['uniform', 'distance'], \n",
    "              'k': range(2, 31),\n",
    "              'p': [1., 2., 3., np.inf]}\n",
    "param_order = ['k', 'weights', 'p']\n",
    "grid_cv_knn_1 = GridSearchCV(model=KNNClassifier(algorithm='kd_tree', leaf_size=10), \n",
    "                             param_grid=param_grid,\n",
    "                             param_order=param_order,\n",
    "                             train_test_splitter_params=dict(shuffle=True, random_seed=1337), \n",
    "                             n_splits=5, \n",
    "                             refit=False, \n",
    "                             save_models=True,\n",
    "                             dirpath='tmp/',\n",
    "                             save_params=dict(\n",
    "                                 params_mask=dict(kd_tree_=False), # do not save tree\n",
    "                                 json_params=dict(indent=4)),\n",
    "                             verbose=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "[params for params in grid_cv_knn_1.gen_params()][:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "grid_cv_knn_1.number_of_combinations()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "grid_cv_knn_1.fit(X_knn_1, y_knn_1);\n",
    "\n",
    "# Training KNNClassifier on 4994 samples x 444 features.\n",
    "# 5-fold CV for each of 232 params combinations == 1160 fits ...\n",
    "\n",
    "# iter:    1/1160 +---- elapsed:  34.320 sec - best acc.: 0.9084  [1/5 splits] at {'p': 1.0, 'k': 2, 'weights': 'uniform'}\n",
    "# iter:    2/1160 +---- elapsed:  49.252 sec - best acc.: 0.9203  [1/5 splits] at {'p': 1.0, 'k': 2, 'weights': 'distance'}\n",
    "# iter:    3/1160 +---- elapsed:  63.681 sec - best acc.: 0.9203  [1/5 splits] at {'p': 1.0, 'k': 2, 'weights': 'distance'}\n",
    "# ...\n",
    "# iter:  925/1160 ++++- elapsed: 20728.7 sec - best acc.: 0.9217  [4/5 splits] at {'p': 1.0, 'k': 3, 'weights': 'uniform'}\n",
    "# iter:  926/1160 ++++- elapsed: 20780.0 sec - best acc.: 0.9217  [4/5 splits] at {'p': 1.0, 'k': 3, 'weights': 'uniform'}\n",
    "# iter:  927/1160 ++++- elapsed: 20794.5 sec - best acc.: 0.9217  [4/5 splits] at {'p': 1.0, 'k': 3, 'weights': 'uniform'}\n",
    "# iter:  928/1160 ++++- elapsed: 20809.0 sec - best acc.: 0.9217  [4/5 splits] at {'p': 1.0, 'k': 3, 'weights': 'uniform'}\n",
    "# iter:  929/1160 +++++ elapsed: 20843.3 sec - best acc.: 0.9091 +/- 2 * 0.007 at {'p': 1.0, 'k': 2, 'weights': 'uniform'}\n",
    "# iter:  930/1160 +++++ elapsed: 20858.1 sec - best acc.: 0.9195 +/- 2 * 0.003 at {'p': 1.0, 'k': 2, 'weights': 'distance'}\n",
    "# iter:  931/1160 +++++ elapsed: 20872.5 sec - best acc.: 0.9195 +/- 2 * 0.003 at {'p': 1.0, 'k': 2, 'weights': 'distance'}\n",
    "# ...\n",
    "# iter: 1158/1160 +++++ elapsed: 25924.2 sec - best acc.: 0.9209 +/- 2 * 0.004 at {'p': 1.0, 'k': 3, 'weights': 'uniform'}\n",
    "# iter: 1159/1160 +++++ elapsed: 25939.9 sec - best acc.: 0.9209 +/- 2 * 0.004 at {'p': 1.0, 'k': 3, 'weights': 'uniform'}\n",
    "# iter: 1160/1160 +++++ elapsed: 25955.6 sec - best acc.: 0.9209 +/- 2 * 0.004 at {'p': 1.0, 'k': 3, 'weights': 'uniform'}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df = grid_cv_knn_1.to_df()\n",
    "df.to_excel('knn_1_full.xlsx')\n",
    "df.sort_values(by='mean_score', ascending=False).head(10).to_excel('knn_1_best.xlsx')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Approach #2: remove (almost) constant features + standartize + **kernelized** k-NN"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3-Fold CV on 2.5k images"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Unfortunately, kd-trees in `scipy` only supported for l_p metric, and not for custom function, so k-NN must be predicted in brute-force mode"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "param_grid_0 = [{'weights': ['uniform'], 'k': range(2, 12 + 1)},\n",
    "                {'weights': ['distance'], 'k': (2, 3, 4)}]\n",
    "param_grid = []\n",
    "for d in param_grid_0:\n",
    "    d1 = d.copy()\n",
    "    d1.update({'kernel': ['rbf'],\n",
    "               'kernel_params': [dict(gamma=gamma) for gamma in np.logspace(-7, 2, 10)]})\n",
    "    param_grid.append(d1)\n",
    "    d2 = d.copy()\n",
    "    d2.update({'kernel': ['sigmoid'],\n",
    "               'kernel_params': [dict(gamma=gamma) for gamma in (1e-4, 1e-2, 1.)]})\n",
    "    param_grid.append(d2)\n",
    "    d3 = d.copy()\n",
    "    d3.update({'kernel': ['poly'],\n",
    "               'kernel_params': [dict(degree=degree) for degree in (2, 3, 4)]})\n",
    "    param_grid.append(d3)\n",
    "param_order = [['kernel_params', 'k']] * len(param_grid)\n",
    "\n",
    "grid_cv_knn_2 = GridSearchCV(model=KNNClassifier(algorithm='brute'), \n",
    "                             param_grid=param_grid,\n",
    "                             param_order=param_order,\n",
    "                             train_test_splitter_params=dict(shuffle=True, random_seed=1337), \n",
    "                             n_splits=3, \n",
    "                             refit=True, \n",
    "                             save_models=True,\n",
    "                             dirpath='tmp/',\n",
    "                             save_params=dict(json_params=dict(indent=4)),\n",
    "                             verbose=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "[params for params in grid_cv_knn_2.gen_params()][:3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "grid_cv_knn_2.number_of_combinations()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X_knn_2, y_knn_2 = load_small(2500)\n",
    "grid_cv_knn_2.fit(X_knn_2, y_knn_2)\n",
    "\n",
    "# Training KNNClassifier on 2494 samples x 444 features.\n",
    "# 3-fold CV for each of 224 params combinations == 672 fits ...\n",
    "\n",
    "# iter:   1/672 +-- elapsed:  99.099 sec   ...\n",
    "# iter:   2/672 ++- elapsed: 197.839 sec   ...\n",
    "# iter:   3/672 +++ elapsed: 294.787 sec - mean acc.: 0.8693 +/- 2 * 0.009\n",
    "# iter:   4/672 +-- elapsed: 390.949 sec - best acc.: 0.8693 at {'kernel_params': {'gamma': 9.9999999999999995e-08}, 'k': 2, 'weights': 'uniform', 'kernel': 'rbf'}\n",
    "# iter:   5/672 ++- elapsed: 487.090 sec - best acc.: 0.8693 at {'kernel_params': {'gamma': 9.9999999999999995e-08}, 'k': 2, 'weights': 'uniform', 'kernel': 'rbf'}\n",
    "# ...\n",
    "# iter: 668/672 ++- elapsed: 56102.7 sec - best acc.: 0.8889 at {'kernel_params': {'gamma': 9.9999999999999995e-08}, 'k': 2, 'weights': 'distance', 'kernel': 'rbf'}\n",
    "# iter: 669/672 +++ elapsed: 56140.9 sec - mean acc.: 0.3946 +/- 2 * 0.015\n",
    "# iter: 670/672 +-- elapsed: 56179.3 sec - best acc.: 0.8889 at {'kernel_params': {'gamma': 9.9999999999999995e-08}, 'k': 2, 'weights': 'distance', 'kernel': 'rbf'}\n",
    "# iter: 671/672 ++- elapsed: 56217.2 sec - best acc.: 0.8889 at {'kernel_params': {'gamma': 9.9999999999999995e-08}, 'k': 2, 'weights': 'distance', 'kernel': 'rbf'}\n",
    "# iter: 672/672 +++ elapsed: 56253.5 sec - mean acc.: 0.3797 +/- 2 * 0.020"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df = grid_cv_knn_2.to_df()\n",
    "df.to_excel('knn_2_full.xlsx')\n",
    "df.sort_values(by='mean_score', ascending=False).head(25).to_excel('knn_2_best.xlsx')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Approach #3, #4: Same as above but with PCA (unwhitened/whitened)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## interesting observation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\mathbf{x}_{PCA}=W^T(\\mathbf{x}-\\pmb{\\mu})=\\left(\\sqrt{n}W^TS^{-1}\\right)\\frac{1}{\\sqrt{n}}S(\\mathbf{x}-\\pmb{\\mu})=\n",
    "\\left[\\frac{1}{\\sqrt{n}}S\\mathbf{x}\\right]_{PCA\\;whitened},\n",
    "$$\n",
    "where $S$ is matrix with singular values of $X$, and even more interesting:\n",
    "$$\n",
    "\\mathbf{x}_{PCA}=W^T(\\mathbf{x}-\\pmb{\\mu})=\n",
    "\\frac{1}{\\sqrt{n}}S \\left(\\sqrt{n}S^{-1}W^T\\right)(\\mathbf{x}-\\pmb{\\mu})=\n",
    "\\frac{1}{\\sqrt{n}}S\\cdot\\mathbf{x}_{PCA\\;whitened},\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**therefore computing distance between vectors after applying PCA w/o whitening is the same as to apply PCA whitening and then to compute distance between** *weighted* **vectors according to the respective singular values!**\n",
    "(I wanted to try it as a separate approach, but it is == approach #3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### compute & apply PCA for all training set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X, y = load_mnist(mode='train', path='data/')\n",
    "X /= 255.\n",
    "with Stopwatch(verbose=True) as s:\n",
    "    pca = PCA().fit(X)\n",
    "pca.save('models/pca_full.json') # ~13 Mb"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### load PCA model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "pca_full = load_model('models/pca_full.json'); pca_full"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sum(pca_full.explained_variance_ratio_[:154]) # <- to explain 95% of the variance we need 154 components"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### load small stratified subset of data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def load_small2(n_samples):\n",
    "    X, y = load_mnist(mode='train', path='data/')\n",
    "    X_scaled = X / 255. # only divide by 255\n",
    "    tts = TrainTestSplitter(shuffle=True, random_seed=1337)\n",
    "    indices, _ = tts.split(y, train_ratio=n_samples/60000., stratify=True)\n",
    "    return X_scaled[indices], y[indices]\n",
    "X_sm, y_sm = load_small2(1000) # approx"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5k images 3-Fold CV for non-kernelized k-NN + number of PCA components"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "param_grid = ({'weights': ['distance'],\n",
    "               'k': [2, 3, 4],\n",
    "               'p': [1, 2]\n",
    "              },\n",
    "              {'weights': ['uniform'],\n",
    "               'k': [2, 3, 4, 6, 9, 12, 15],\n",
    "               'p': [1, 2]\n",
    "              })\n",
    "grid_search_params = dict(model=KNNClassifier(algorithm='kd_tree'), \n",
    "                          param_grid=param_grid,\n",
    "                          # param_order=param_order,\n",
    "                          train_test_splitter_params=dict(shuffle=True, random_seed=1337), \n",
    "                          n_splits=3, \n",
    "                          refit=False, \n",
    "                          # save_models=True,\n",
    "                          # dirpath='tmp/',\n",
    "                          # save_params=dict(json_params=dict(indent=4)),\n",
    "                          verbose=True)\n",
    "\n",
    "for n_components in xrange(5, 151, 5):\n",
    "    print \"[PCA n_components = {0}]\\n\\n\".format(n_components)\n",
    "    X_current = pca_full.set_params(n_components=n_components, whiten=False).transform(X_sm)\n",
    "    grid_cv_knn_pca_1 = GridSearchCV(**grid_search_params).fit(X_current, y_sm)\n",
    "    df = grid_cv_knn_pca_1\\\n",
    "         .to_df()\\\n",
    "         .sort_values(by='mean_score', ascending=False)\\\n",
    "         .to_excel('cv_results/knn_3_pca_{0}_{1:.4f}.xlsx'.format(n_components, grid_cv_knn_pca_1.best_score_))\n",
    "    print \"\\n\\n\"\n",
    "    \n",
    "# [PCA n_components = 5]\n",
    "\n",
    "\n",
    "# Training KNNClassifier on 4994 samples x 5 features.\n",
    "# 3-fold CV for each of 20 params combinations == 60 fits ...\n",
    "\n",
    "# iter:  1/60 +-- elapsed:   0.673 sec - best acc.: 0.6936  [1/3 splits] at {'p': 1, 'k': 2, 'weights': 'distance'}\n",
    "# iter:  2/60 +-- elapsed:   1.340 sec - best acc.: 0.6990  [1/3 splits] at {'p': 2, 'k': 2, 'weights': 'distance'}\n",
    "# iter:  3/60 +-- elapsed:   1.998 sec - best acc.: 0.6990  [1/3 splits] at {'p': 2, 'k': 2, 'weights': 'distance'}\n",
    "# ...\n",
    "# iter: 58/60 +++ elapsed:  41.769 sec - best acc.: 0.7369 +/- 2 * 0.003 at {'p': 2, 'k': 12, 'weights': 'uniform'}\n",
    "# iter: 59/60 +++ elapsed:  42.429 sec - best acc.: 0.7369 +/- 2 * 0.003 at {'p': 1, 'k': 15, 'weights': 'uniform'}\n",
    "# iter: 60/60 +++ elapsed:  43.073 sec - best acc.: 0.7369 +/- 2 * 0.003 at {'p': 1, 'k': 15, 'weights': 'uniform'}\n",
    "# ...\n",
    "# ...\n",
    "# ...\n",
    "# iter: 58/60 +++ elapsed: 133.416 sec - best acc.: 0.9381 +/- 2 * 0.004 at {'p': 2, 'k': 2, 'weights': 'distance'}\n",
    "# iter: 59/60 +++ elapsed: 136.472 sec - best acc.: 0.9381 +/- 2 * 0.004 at {'p': 2, 'k': 2, 'weights': 'distance'}\n",
    "# iter: 60/60 +++ elapsed: 138.300 sec - best acc.: 0.9381 +/- 2 * 0.004 at {'p': 2, 'k': 2, 'weights': 'distance'}\n",
    "\n",
    "\n",
    "\n",
    "# [PCA n_components = 115]\n",
    "\n",
    "\n",
    "# Training KNNClassifier on 4994 samples x 115 features.\n",
    "# 3-fold CV for each of 20 params combinations == 60 fits ...\n",
    "\n",
    "# iter:  1/60 +-- elapsed:   3.008 sec - best acc.: 0.9263  [1/3 splits] at {'p': 1, 'k': 2, 'weights': 'distance'}\n",
    "# iter:  2/60 +-- elapsed:   4.943 sec - best acc.: 0.9394  [1/3 splits] at {'p': 2, 'k': 2, 'weights': 'distance'}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ... same with whitening"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "param_grid = ({'weights': ['distance'],\n",
    "               'k': [2, 3, 4],\n",
    "               'p': [1, 2]\n",
    "              },\n",
    "              {'weights': ['uniform'],\n",
    "               'k': [2, 3, 4, 6, 9, 12, 15],\n",
    "               'p': [1, 2]\n",
    "              })\n",
    "grid_search_params = dict(model=KNNClassifier(algorithm='kd_tree'), \n",
    "                          param_grid=param_grid,\n",
    "                          # param_order=param_order,\n",
    "                          train_test_splitter_params=dict(shuffle=True, random_seed=1337), \n",
    "                          n_splits=3, \n",
    "                          refit=False, \n",
    "                          # save_models=True,\n",
    "                          # dirpath='tmp/',\n",
    "                          # save_params=dict(json_params=dict(indent=4)),\n",
    "                          verbose=False)\n",
    "\n",
    "for n_components in xrange(10, 151, 5):\n",
    "    print \"[PCA n_components = {0}]\".format(n_components)\n",
    "    X_current = pca_full.set_params(n_components=n_components, whiten=True).transform(X_sm)\n",
    "    grid_cv_knn_pca_1 = GridSearchCV(**grid_search_params).fit(X_current, y_sm)\n",
    "    df = grid_cv_knn_pca_1\\\n",
    "         .to_df()\\\n",
    "         .sort_values(by='mean_score', ascending=False)\\\n",
    "         .to_excel('cv_results/knn_3_pca_whiten_{0}_{1:.4f}.xlsx'.format(n_components, grid_cv_knn_pca_1.best_score_))\n",
    "# [PCA n_components = 10]\n",
    "# [PCA n_components = 15]\n",
    "# [PCA n_components = 20]\n",
    "# [PCA n_components = 25]\n",
    "# [PCA n_components = 30]\n",
    "# [PCA n_components = 35]\n",
    "# [PCA n_components = 40]\n",
    "# [PCA n_components = 45]\n",
    "# [PCA n_components = 50]\n",
    "# [PCA n_components = 55]\n",
    "# [PCA n_components = 60]\n",
    "# [PCA n_components = 65]\n",
    "# [PCA n_components = 70]\n",
    "# [PCA n_components = 75]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1k images 3-Fold CV for kernelized k-NN + number of PCA components"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "param_grid = ({'weights': ['distance'],\n",
    "               'k': [2, 3, 4],\n",
    "               'kernel': ['rbf'],\n",
    "               'kernel_params': [dict(gamma=x) for x in [1e-1, 1e-2, 1e-4, 1e-6]]\n",
    "              },\n",
    "              {'weights': ['uniform'],\n",
    "               'k': [2, 3, 4, 6, 9, 12],\n",
    "               'kernel': ['rbf'],\n",
    "               'kernel_params': [dict(gamma=x) for x in [1e-1, 1e-2, 1e-4, 1e-6]]\n",
    "              },\n",
    "              {'weights': ['distance'],\n",
    "               'k': [2, 3, 4],\n",
    "               'kernel': ['poly'],\n",
    "               'kernel_params': [dict(degree=x) for x in [2, 3, 4]]\n",
    "              },\n",
    "              {'weights': ['uniform'],\n",
    "               'k': [2, 3, 4, 6],\n",
    "               'kernel': ['poly'],\n",
    "               'kernel_params': [dict(degree=x) for x in [2, 3, 4]]\n",
    "              })\n",
    "grid_search_params = dict(model=KNNClassifier(algorithm='brute'), \n",
    "                          param_grid=param_grid,\n",
    "                          # param_order=param_order,\n",
    "                          train_test_splitter_params=dict(shuffle=True, random_seed=1337), \n",
    "                          n_splits=3, \n",
    "                          refit=True, \n",
    "                          # save_models=True,\n",
    "                          # dirpath='tmp/',\n",
    "                          # save_params=dict(json_params=dict(indent=4)),\n",
    "                          verbose=True)\n",
    "\n",
    "for n_components in xrange(5, 151, 5):\n",
    "    print \"[PCA n_components = {0}]\\n\\n\".format(n_components)\n",
    "    X_current = pca_full.set_params(n_components=n_components, whiten=False).transform(X_sm)\n",
    "    grid_cv_knn_pca_2 = GridSearchCV(**grid_search_params).fit(X_current, y_sm)\n",
    "    df = grid_cv_knn_pca_2\\\n",
    "         .to_df()\\\n",
    "         .sort_values(by='mean_score', ascending=False)\\\n",
    "         .to_excel('cv_results/knn_4_pca_krnl_{0}_{1:.4f}.xlsx'.format(n_components, grid_cv_knn_pca_2.best_score_))\n",
    "    print \"\\n\"\n",
    "# [PCA n_components = 5]\n",
    "\n",
    "\n",
    "# Training KNNClassifier on 996 samples x 5 features.\n",
    "# 3-fold CV for each of 57 params combinations == 171 fits ...\n",
    "\n",
    "# iter:   1/171 +-- elapsed:  18.874 sec   ...\n",
    "# iter:   2/171 ++- elapsed:  39.243 sec   ...\n",
    "# iter:   3/171 +++ elapsed:  58.217 sec - mean acc.: 0.6879 +/- 2 * 0.029\n",
    "# ...\n",
    "# iter: 169/171 +-- elapsed: 2299.67 sec - best acc.: 0.7149 at {'kernel': 'rbf', 'k': 6, 'weights': 'uniform', 'kernel_params': {'gamma': 0.1}}\n",
    "# iter: 170/171 ++- elapsed: 2306.23 sec - best acc.: 0.7149 at {'kernel': 'rbf', 'k': 6, 'weights': 'uniform', 'kernel_params': {'gamma': 0.1}}\n",
    "# iter: 171/171 +++ elapsed: 2313.28 sec - mean acc.: 0.5814 +/- 2 * 0.011\n",
    "# ...\n",
    "# ...\n",
    "# ...\n",
    "# iter: 169/171 +-- elapsed: 1869.40 sec - best acc.: 0.8704 at {'kernel': 'rbf', 'k': 2, 'weights': 'distance', 'kernel_params': {'gamma': 0.1}}\n",
    "# iter: 170/171 ++- elapsed: 1876.34 sec - best acc.: 0.8704 at {'kernel': 'rbf', 'k': 2, 'weights': 'distance', 'kernel_params': {'gamma': 0.1}}\n",
    "# iter: 171/171 +++ elapsed: 1882.34 sec - mean acc.: 0.3715 +/- 2 * 0.043\n",
    "\n",
    "\n",
    "# [PCA n_components = 95]\n",
    "\n",
    "\n",
    "# Training KNNClassifier on 996 samples x 95 features.\n",
    "# 3-fold CV for each of 57 params combinations == 171 fits ...\n",
    "\n",
    "# iter:   1/171 +-- elapsed:  15.785 sec   ...\n",
    "# iter:   2/171 ++- elapsed:  31.366 sec   ...\n",
    "# iter:   3/171 +++ elapsed:  46.182 sec - mean acc.: 0.8674 +/- 2 * 0.024\n",
    "# iter:   4/171 +-- elapsed:  60.642 sec - best acc.: 0.8674 at {'kernel': 'rbf', 'k': 2, 'weights': 'distance', 'kernel_params': {'gamma': 0.1}}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ... same with whitening"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "param_grid = ({'weights': ['distance'],\n",
    "               'k': [2, 3, 4],\n",
    "               'kernel': ['rbf'],\n",
    "               'kernel_params': [dict(gamma=x) for x in [1e-1, 1e-2, 1e-4, 1e-6]]\n",
    "              },\n",
    "              {'weights': ['uniform'],\n",
    "               'k': [2, 3, 4, 6, 9, 12],\n",
    "               'kernel': ['rbf'],\n",
    "               'kernel_params': [dict(gamma=x) for x in [1e-1, 1e-2, 1e-4, 1e-6]]\n",
    "              },\n",
    "              {'weights': ['distance'],\n",
    "               'k': [2, 3, 4],\n",
    "               'kernel': ['poly'],\n",
    "               'kernel_params': [dict(degree=x) for x in [2, 3, 4]]\n",
    "              },\n",
    "              {'weights': ['uniform'],\n",
    "               'k': [2, 3, 4, 6],\n",
    "               'kernel': ['poly'],\n",
    "               'kernel_params': [dict(degree=x) for x in [2, 3, 4]]\n",
    "              })\n",
    "grid_search_params = dict(model=KNNClassifier(algorithm='brute'), \n",
    "                          param_grid=param_grid,\n",
    "                          # param_order=param_order,\n",
    "                          train_test_splitter_params=dict(shuffle=True, random_seed=1337), \n",
    "                          n_splits=3, \n",
    "                          refit=True, \n",
    "                          # save_models=True,\n",
    "                          # dirpath='tmp/',\n",
    "                          # save_params=dict(json_params=dict(indent=4)),\n",
    "                          verbose=True)\n",
    "\n",
    "for n_components in xrange(5, 151, 5):\n",
    "    print \"[PCA n_components = {0}]\\n\\n\".format(n_components)\n",
    "    X_current = pca_full.set_params(n_components=n_components, whiten=True).transform(X_sm)\n",
    "    grid_cv_knn_pca_2 = GridSearchCV(**grid_search_params).fit(X_current, y_sm)\n",
    "    df = grid_cv_knn_pca_2\\\n",
    "         .to_df()\\\n",
    "         .sort_values(by='mean_score', ascending=False)\\\n",
    "         .to_excel('cv_results/knn_4_pca_krnl_whiten_{0}_{1:.4f}.xlsx'.format(n_components, grid_cv_knn_pca_2.best_score_))\n",
    "    print \"\\n\"\n",
    "# [PCA n_components = 5]\n",
    "\n",
    "\n",
    "# Training KNNClassifier on 996 samples x 5 features.\n",
    "# 3-fold CV for each of 57 params combinations == 171 fits ...\n",
    "\n",
    "# iter:   1/171 +-- elapsed:  16.284 sec   ...\n",
    "# iter:   2/171 ++- elapsed:  32.904 sec   ...\n",
    "# iter:   3/171 +++ elapsed:  54.273 sec - mean acc.: 0.6939 +/- 2 * 0.018\n",
    "# ...\n",
    "# iter: 169/171 +-- elapsed: 2319.17 sec - best acc.: 0.7199 at {'kernel': 'rbf', 'k': 9, 'weights': 'uniform', 'kernel_params': {'gamma': 0.1}}\n",
    "# iter: 170/171 ++- elapsed: 2325.68 sec - best acc.: 0.7199 at {'kernel': 'rbf', 'k': 9, 'weights': 'uniform', 'kernel_params': {'gamma': 0.1}}\n",
    "# iter: 171/171 +++ elapsed: 2331.78 sec - mean acc.: 0.5984 +/- 2 * 0.013\n",
    "# ...\n",
    "# ...\n",
    "# ...\n",
    "# iter: 169/171 +-- elapsed: 2504.95 sec - best acc.: 0.7972 at {'kernel': 'rbf', 'k': 2, 'weights': 'distance', 'kernel_params': {'gamma': 0.1}}\n",
    "# iter: 170/171 ++- elapsed: 2511.18 sec - best acc.: 0.7972 at {'kernel': 'rbf', 'k': 2, 'weights': 'distance', 'kernel_params': {'gamma': 0.1}}\n",
    "# iter: 171/171 +++ elapsed: 2517.55 sec - mean acc.: 0.1124 +/- 2 * 0.001\n",
    "\n",
    "\n",
    "# [PCA n_components = 85]\n",
    "\n",
    "\n",
    "# Training KNNClassifier on 996 samples x 85 features.\n",
    "# 3-fold CV for each of 57 params combinations == 171 fits ...\n",
    "\n",
    "# iter:   1/171 +-- elapsed:  15.737 sec   ...\n",
    "# iter:   2/171 ++- elapsed:  32.295 sec   ...\n",
    "# iter:   3/171 +++ elapsed:  48.847 sec - mean acc.: 0.7892 +/- 2 * 0.035"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Approach #5 Artificially augment dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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s1vPq6+stPrYo7rlGRG2GNeLozo7ordXQ0GDxsUVxrQYisitqmGpg8BKRXWHw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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1f77100a10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ISUlBXV0dQkND8c4775i6C8+ZMwcbNmxQZZBERKK0sMbb6p5rN1saa+HFEdG9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\n8BIRqez/ALXfzfBsx0+XAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1f770e9b50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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u3Ihz585h1qxZuHz5Mk8+EFGbpvmpBgDo0KED3nzzTRQWFiIuLs6092lxcTG6\ndOli9Q4SEdka2cR76NAhLFu2DLW1tQgODsbKlStN1YXnzZuHzZs3q9JJIiJRWpjjbXHNtdsljbXw\n4Iio/dH8VINczTXO9RJRW6SFQaHVa66JHAS9Xi8US2S11vjx44VizZs3T6idyMq7mzdvCsWqqalR\nbJObmysU69q1a4ptdu/eLRTr0KFDim1EX8yiz6UlzzxbchAg8jjb8qBD7RqHbZEWrmpgzTUisima\nH/ECrLlGRNpiE4mXiEhLmHiJiFTGxEtEpDImXiIilWn+qgYiIq3Rwoi3xfvxEhFR63DES0Q2RQsj\nXp1k5V6KrJIRXQlUX1+v2KZ79+5CsXr37m2x+7y9cZAl2pWVlQnFEunXb7/9JhRLZE5MtH4bUWuU\nlJS0OobBYHhg9y2KI14isilaGPHKJt7r16/j1KlTGDZsGCorK5GamooLFy6gZ8+emD59Ojw9PdXq\nJxGREC0kXtnvj7NmzYLRaAQALFmyBK6urpg5cyZ69OiB+fPnq9JBIqKWaGxsNOufmmRHvFVVVQgN\nDQVwa/7j3XffBQD0798f+/bts37viIhaSPMjXh8fHyxbtgz5+fkYNGgQDh48CKPRiD179tj81nJE\npE2a3wg9MTERGRkZeO+991BUVITGxkZ4eXlhyJAhWLBggVp9JCISpoURr2ziPXr0KD744APU1NRg\n6NChiImJgYuLCwAgIiKCNdeIqM3RQuKVnWpYv349MjMzkZOTgyeffBKRkZGmKhBaeHBE1P5ofqrh\nzpprEyZMgKenJ2uuEVGbpvlNcixRc00kQYt+2jg4OCi2uXTpklCs8+fPC7UT6b/oh5BIPTJ7e7E1\nLRUVFYptvLy8hGJxVVr7IlKXDdBubTYtfBtnzTUiIpWx5hoR2RTNj3iJiLSGiZeISGVMvEREKrNW\n4k1ISMCZM2eg0+kQHR2N/v37m27Lzs7G6tWrodfrMWTIEMyYMUM2Fk9nE5FNscYmOXl5eSgsLER6\nejqWLl2K+Pj4JrfHx8dj7dq12LFjB44fP44LFy7IxmPiJSKbYo0FFDk5OQgJCQEA9OrVC5WVlabC\nBpcuXYK7uzu8vb2h0+kQHByM3Nxc2XhMvERkU6yReI1GY5P9xz08PExb5t59m6enp2I1C87xEpFN\nUePkmtx9iNy/1ROvmnWMiIiskXgNBoNphAvcymu3V/YZDIYmqwGvXLmiWPeNUw1ERAoCAwORlZUF\nADh79iwUGFjmAAAHZUlEQVS8vb3h5OQEAOjWrRuqq6tx+fJlNDQ04OjRoxg8eLBsPKtXGSYisgWr\nVq3CyZMnodfrERsbix9++AGurq4ICQnBqVOnsHLlSgDAqFGjMHXqVNlYTLxERCrjVAMRkcqYeImI\nVMbES0SkMtUTb0JCAsLCwvDyyy8jPz+/VbFWrFiBsLAwhIaG4tChQ63uW11dHZ577jns3bu3VXH2\n7duHP/7xjxg/fjyOHTtmdpyamhq8+eabiIiIwMsvv4yvvvrKrDjnzp3Dc889h23btgEAiouLER4e\njilTpuCtt95CfX292bF+/fVXvPLKKwgPD8e0adNQVlZmdqzbvvzyS/j6+grHaS5WQ0MD5syZg9DQ\nULzyyiumklXmxMrLy8OkSZMQERGB119/vUWx7n6NtubYNxfL3GN/v/eOOcf+7niff/55q45/uyCp\n6OTJk9Jrr70mSZIknT9/Xpo4caLZsXJzc6VXX31VkiRJqqiokIYOHdrq/q1atUr685//LGVmZpod\no6KiQhoxYoRUU1MjlZaWSjExMWbH2rp1q7Rq1SpJkiTpypUr0qhRo1oco6amRpo6daq0aNEiaevW\nrZIkSVJUVJSUlZUlSdKtx7xjxw6zY82fP186cOCAqb8rVqwwO5YkSVJdXZ00ZcoUKSgoqFWPcdu2\nbVJ8fLwkSZKUkZEhHTlyxOxYf/rTn6T//ve/kiRJUmpqqpSWliYUq7nXaFRUlPTpp59KktSyY3+/\nWJ988okkSS079vd775hz7O8Xz9zj316oOuKVW+/cUv7+/khOTgYA/O53v0NtbW2rLpwuKCjAxYsX\nERwcbHYM4NYuRYGBgejYsSO8vLwQFxdndixPT09TiZ9r1641WZYoytHREevXr29SBujkyZMYNmwY\nAGDYsGHIzs42O9aiRYswcuRIU3+vXbtmdiwASE1NRXh4uFCZJ7lY//73vzFmzBgAQGhoqOnxmhPL\ny8sL5eXlAG49Dx4eHkKx7n6N1tTUIC8vD8OHDwfQsmPf3Ot94cKFGDVqFICWHfv7vXfMOfb3e5xH\njx416/i3F6omXrn1zi1lZ2eHjh07AgB27dqF4ODgVhXgXLFiBaKiosz++9uKiopQW1uLN954A1Om\nTEFOTo7ZsUaPHo3i4mKMGDECERERZvXPzs4OHTp0aPK72tpa05urU6dOwjW4movVsWNH2NnZobGx\nEdu3b8eLL75odqyLFy/i/PnzGDFiRIs+RJuLVVRUhGPHjiE8PBxz5sxBZWWl2bHmz5+PmTNnYvTo\n0fj2228xfvx44Vi3X6P//Oc/MXTo0FYd+7tf787OzmYf+7tjFRYWmnXs7/c4zT3+7cUDPbnWmhHq\nbZ9//jn27NmDmJgYs2Ps3bsX/v7+6Nq1a6v7JUkSrl69ipSUFCQkJCA6OtrsWPv27UOXLl3w2Wef\n4cMPP2zV6Pl+LPEcNDY2Yu7cuXjmmWfwzDPPmB0nMTHRIh9+wK3H1atXL2zZsgW9e/dGamqq2bHe\neecdrFu3DgcPHoSfnx+2b9/eor///PPPsXv3bsTExDQ53uYc+7tf76059nfGWr58eauP/Z2Ps7Gx\n0WLH3xapmnjl1jub48svv0RaWho2bNgAFxcXs+McO3YMn376KSZOnIhdu3bh/fffN3uk6uXlBT8/\nP+h0OjzyyCNwdnY2fU1tqW+++QZBQUEAAF9fXxQXF1skUTo7O+PGjRsAxNaVK1mwYAF69uyJv/71\nr2bHuHLlCi5evIjZs2dj4sSJKC0tRXh4uNnxvLy84O/vDwAYPHiw4v6ocn766Sc88cQTAID/+7//\na9FJ4btfo6059s293s099nfGqq6ubvWxv7tvljz+tkjVxCu33rmlqqqqkJSUhNTUVLi6uraqX6tX\nr8auXbuwc+dOhIaGYsaMGQgICDArVmBgIE6cOAFJklBRUYGamhqz5mYB4NFHH8Xp06cB3Prq7OTk\n1KrplNsCAgJMz0NWVpYpuZtj37596NChA2bOnNmqPnl7eyMrKwvp6enYuXMnOnfujC1btpgdb8iQ\nIfjiiy8A3Hqt9ezZ0+xYnTt3NiWO/Px8+Pj4CP1dc69Rc499c7HMPfZ3x2rtsW+ub5Y8/rZI9SXD\nd6937tOnj1lxMjIysHbtWvTo0QOSJEGn02HFihXo0qVLq/q3du1adO/eHePGjTM7RkZGBnbt2gWd\nTocZM2Zg6NChZsWpqalBdHQ0ysrKcPPmTfz973/H008/3aIYZ86cwcKFC1FeXg69Xg83Nzds3LgR\nUVFRuHHjBrp27YqEhATo9XqzYjU2NsLR0RHOzs7Q6XTo3bs3YmNjzYq1detWuLm5AQCeffZZHD58\nuFWPMT4+HqWlpXB2dkZiYqLQB2BzseLi4rBixQo4ODjA3d0dy5YtE/qG1dxrNDExEW+//XaLj/2d\nsYBb0xTFxcVwdXVt8bFXeu+05NjLxUtISGjx8W8vuFcDEZHKuHKNiEhlTLxERCpj4iUiUhkTLxGR\nyph4iYhUxsRLRKQyJl4iIpUx8RIRqez/AVdwDDv3y+GIAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1f7730c810>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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79+8XynXx4kXFmLq6OqFclrx+LPlXYUsUE5Fjtsa/fDVfeLnnGhFpjU2sTsY9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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1f77295ed0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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KysoQFRUFAPD390djYyNaWloAAJcuXYK7uzt8fHyg0WgQHh6O8vJy0XoMXiKy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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1f7722a950>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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KeKqhFbTGqiLR37D79u1TjJk5c6ZQrr59+yrGjBs3TiiXSEuiQ4cOCeXau3ev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\n4SUiUtn/A4GRWSw/p2lzAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1f77479350>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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BgA4dOpgaVlFRgeHDh0On02H//v2qNJKISJTmhxrWrVuHtWvXIjIyEiNGjABw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\nFl4iIpWx8BIRqez/Ac8qGt4NqJI9AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1f761a90d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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6zBdeeEEoVmZmpmIbLbyZ1SI6hmjPc/bQQw8JtWvdurViG73/LLUwxit7H+/58+eRkpKC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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1f75fc1b10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X, y = load_mnist(mode='train', path='data/')\n",
    "aug = RandomAugmentator(transform_shape=(28, 28), random_seed=1337)\\\n",
    "      .add('RandomRotate', angle=(-10., 15.))\\\n",
    "      .add('Dropout', p=(0., 0.1))\\\n",
    "      .add('RandomGaussian', sigma=(0., 0.5))\\\n",
    "      .add('RandomShift', x_shift=(-2, 2), y_shift=(-2, 2))\n",
    "for z in aug.transform(X[:2]/255., 3):\n",
    "    plot_greyscale_image(z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "pca_full = load_model('models/pca_full.json')\n",
    "\n",
    "def load_big2():\n",
    "    X, y = load_mnist(mode='train', path='data/')\n",
    "    X_scaled = X / 255. # only divide by 255\n",
    "    tts = TrainTestSplitter(shuffle=True, random_seed=1337)\n",
    "    train, test = tts.split(y, train_ratio=50005./60000., stratify=True)\n",
    "    return X_scaled[train], y[train], X_scaled[test], y[test] # 49999 train, 10001 val\n",
    "X_train, y_train, X_test, y_test = load_big2()\n",
    "\n",
    "X_train = X_train[:5000]\n",
    "y_train = y_train[:5000]\n",
    "X_test = X_test[:1000]\n",
    "y_test = y_test[:1000]\n",
    "\n",
    "N = 3\n",
    "aug = RandomAugmentator(transform_shape=(28, 28), random_seed=1337)\n",
    "aug.add('RandomRotate', angle=(-7., 10.))\n",
    "aug.add('RandomGaussian', sigma=(0., 0.5))\n",
    "aug.add('RandomShift', x_shift=(-1, 1), y_shift=(-1, 1))\n",
    "aug.add('Dropout', p=(0.8, 1.0))\n",
    "X_train_aug = aug.transform(X_train, N)\n",
    "y_train_aug = np.repeat(y_train, N + 1)\n",
    "print X_train_aug.shape\n",
    "\n",
    "pca_full.set_params(n_components=35, whiten=False)\n",
    "X_train_aug = pca_full.transform(X_train_aug)\n",
    "X_test = pca_full.transform(X_test)\n",
    "knn = KNNClassifier(algorithm='kd_tree', k=2, p=2, weights='distance')\n",
    "with Stopwatch(verbose=True) as s: knn.fit(X_train_aug, y_train_aug)\n",
    "with Stopwatch(verbose=True) as t: y_pred = knn.predict(X_test)\n",
    "print accuracy_score(y_test, y_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# k-NN best models from all approaches"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### X_train (60000) = 50k train : 10k validation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Approaches 1, 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def load_big():\n",
    "    X, y = load_mnist(mode='train', path='data/')\n",
    "    X_scaled = X / 255.\n",
    "    X_scaled = VarianceThreshold(0.1).fit_transform(X_scaled)\n",
    "    X_scaled = StandardScaler(copy=False).fit_transform(X_scaled)\n",
    "    tts = TrainTestSplitter(shuffle=True, random_seed=1337)\n",
    "    train, test = tts.split(y, train_ratio=50005./60000., stratify=True)\n",
    "    return X_scaled[train], y[train], X_scaled[test], y[test] # 49999 train, 10001 val"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X_train, y_train, X_test, y_test = load_big()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "knns_best = []\n",
    "# from approach 1\n",
    "knns_best.append(KNNClassifier(algorithm='brute', k=3, p=1., weights='uniform'))\n",
    "knns_best.append(KNNClassifier(algorithm='brute', k=2, p=1., weights='distance'))\n",
    "# from approach 2\n",
    "knns_best.append(KNNClassifier(algorithm='brute', k=2, weights='distance', kernel='rbf', kernel_params=dict(gamma=1e-5)))\n",
    "knns_best.append(KNNClassifier(algorithm='brute', k=3, weights='uniform', kernel='rbf', kernel_params=dict(gamma=1e-5)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# -------------------------------------------\n",
    "# def f(x):\n",
    "#     return knn._predict_x(x)\n",
    "# from joblib import Parallel, delayed\n",
    "# p = Parallel(n_jobs=1, max_nbytes=None)\n",
    "# print p(delayed(f)(x) for x in X_test[:2]) # <-- NOT WORKING, CANNOT PICKLE INSTANCE METHODS\n",
    "# ----------------------------------------------\n",
    "import pathos.multiprocessing as mp\n",
    "pool = mp.ProcessingPool(4)\n",
    "for knn in knns_best:\n",
    "    knn.fit(X_train, y_train)\n",
    "    y_pred = pool.map(knn._predict_x, X_test) # knn.predict(X_test) in parallel\n",
    "    print accuracy_score(y_test, y_pred)\n",
    "# 0.96650...\n",
    "# 0.96400...\n",
    "# 0.96110...\n",
    "# 0.96150..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Approach 3 (w/o whitening)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "pca_full = load_model('models/pca_full.json')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def load_big2():\n",
    "    X, y = load_mnist(mode='train', path='data/')\n",
    "    X_scaled = X / 255. # only divide by 255\n",
    "    tts = TrainTestSplitter(shuffle=True, random_seed=1337)\n",
    "    train, test = tts.split(y, train_ratio=50005./60000., stratify=True)\n",
    "    return X_scaled[train], y[train], X_scaled[test], y[test] # 49999 train, 10001 val\n",
    "X_train, y_train, X_test, y_test = load_big2()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Elapsed time: 0.077 sec\n",
      "Elapsed time: 19.782 sec\n",
      "0.975402459754\n"
     ]
    }
   ],
   "source": [
    "pca_full.set_params(n_components=35)\n",
    "X_train = pca_full.transform(X_train)\n",
    "X_test = pca_full.transform(X_test)\n",
    "knn = KNNClassifier(algorithm='kd_tree', k=3, p=2, weights='uniform')\n",
    "with Stopwatch(verbose=True) as s: knn.fit(X_train, y_train) # Elapsed time: 0.064 sec\n",
    "with Stopwatch(verbose=True) as t: y_pred = knn.predict(X_test) # Elapsed time: 18.823 sec <- FAST!\n",
    "print accuracy_score(y_test, y_pred)\n",
    "# 0.9754..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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DlD47ppRF5E7WVeEY41afxmDSBdrf34C7e4rg/Vr+N34OKQ9S8T+6ie92L+P073+QmZlp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\nIYyQFGghhBDCCP0/iqOm6NoleXcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1f75df35d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "C = confusion_matrix(y_test, y_pred)\n",
    "plot_confusion_matrix(C);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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nL6qUFDzc3Bg/ZhRVKlcyW58bN+OZPnsOZ8MjNC5NfHNx+ZXAVU+59Ouj67Js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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1f7604a850>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "C = confusion_matrix(y_test, y_pred, normalize='cols')\n",
    "plot_confusion_matrix(C, fmt=\".2f\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "pca_full.set_params(n_components=35)\n",
    "X_train = pca_full.transform(X_train)\n",
    "X_test = pca_full.transform(X_test)\n",
    "knn = KNNClassifier(algorithm='kd_tree', k=2, p=2, weights='distance')\n",
    "with Stopwatch(verbose=True) as s: knn.fit(X_train, y_train) # Elapsed time: 0.067 sec\n",
    "with Stopwatch(verbose=True) as t: y_pred = knn.predict(X_test) # Elapsed time: 17.848 sec\n",
    "print accuracy_score(y_test, y_pred)\n",
    "# 0.9751..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "pca_full.set_params(n_components=35)\n",
    "X_train = pca_full.transform(X_train)\n",
    "X_test = pca_full.transform(X_test)\n",
    "knn = KNNClassifier(algorithm='kd_tree', k=2, p=1, weights='distance')\n",
    "with Stopwatch(verbose=True) as s: knn.fit(X_train, y_train) \n",
    "with Stopwatch(verbose=True) as t: y_pred = knn.predict(X_test)\n",
    "print accuracy_score(y_test, y_pred)\n",
    "# 0.9747..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "pca_full.set_params(n_components=30)\n",
    "X_train = pca_full.transform(X_train)\n",
    "X_test = pca_full.transform(X_test)\n",
    "knn = KNNClassifier(algorithm='kd_tree', k=3, p=2, weights='uniform')\n",
    "with Stopwatch(verbose=True) as s: knn.fit(X_train, y_train)\n",
    "with Stopwatch(verbose=True) as t: y_pred = knn.predict(X_test)\n",
    "print accuracy_score(y_test, y_pred)\n",
    "# 0.9746..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### ... with whitening"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "pca_full.set_params(n_components=35, whiten=True)\n",
    "X_train = pca_full.transform(X_train)\n",
    "X_test = pca_full.transform(X_test)\n",
    "knn = KNNClassifier(algorithm='kd_tree', k=3, p=2, weights='uniform')\n",
    "with Stopwatch(verbose=True) as s: knn.fit(X_train, y_train)\n",
    "with Stopwatch(verbose=True) as t: y_pred = knn.predict(X_test)\n",
    "print accuracy_score(y_test, y_pred)\n",
    "# 0.9723..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Approach 4 (w/ and w/o whitening)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "pca_full.set_params(n_components=35, whiten=False)\n",
    "X_train = pca_full.transform(X_train)\n",
    "X_test = pca_full.transform(X_test)\n",
    "knn = KNNClassifier(algorithm='brute', k=3, weights='uniform', kernel='rbf', kernel_params=dict(gamma=1e-4))\n",
    "knn.fit(X_train, y_train)\n",
    "y_pred = []\n",
    "for (i, x) in enumerate(X_test):\n",
    "    y_pred.append(knn._predict_x(x))\n",
    "    if (i + 1) % 10 == 0:\n",
    "        print \"computed {0}/{1} ... accuracy {2:.4f}\".format(i + 1, len(X_test), accuracy_score(y_test[:len(y_pred)], y_pred))\n",
    "print accuracy_score(y_test, y_pred)\n",
    "# ...\n",
    "# computed 2960/10001 ... accuracy 0.9743\n",
    "# computed 2970/10001 ... accuracy 0.9744\n",
    "# ...\n",
    "# computed 3030/10001 ... accuracy 0.9743\n",
    "# computed 3040/10001 ... accuracy 0.9743"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "pca_full.set_params(n_components=20, whiten=True)\n",
    "X_train = pca_full.transform(X_train)\n",
    "X_test = pca_full.transform(X_test)\n",
    "knn = KNNClassifier(algorithm='brute', k=3, weights='uniform', kernel='rbf', kernel_params=dict(gamma=1e-4))\n",
    "knn.fit(X_train, y_train)\n",
    "y_pred = []\n",
    "for (i, x) in enumerate(X_test):\n",
    "    y_pred.append(knn._predict_x(x))\n",
    "    if (i + 1) % 10 == 0:\n",
    "        print \"computed {0}/{1} ... accuracy {2:.4f}\".format(i + 1, len(X_test), accuracy_score(y_test[:len(y_pred)], y_pred))\n",
    "print accuracy_score(y_test, y_pred)\n",
    "# 0.9655..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Approach 6: exponential decay on normalized explained variance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "pca_full = load_model('models/pca_full.json')\n",
    "def load_big2(train_ratio=50005./60000.):\n",
    "    X, y = load_mnist(mode='train', path='data/')\n",
    "    X_scaled = X / 255. # only divide by 255\n",
    "    tts = TrainTestSplitter(shuffle=True, random_seed=1337)\n",
    "    train, test = tts.split(y, train_ratio=train_ratio, stratify=True)\n",
    "    return X_scaled[train], y[train], X_scaled[test], y[test]\n",
    "X_train_orig, y_train_orig, X_test_orig, y_test_orig = load_big2(57000./60000.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# train_ratio=50005./60000.\n",
    "pca_full.set_params(n_components=35, whiten=True)\n",
    "z = pca_full.explained_variance_ratio_[:35]\n",
    "z /= sum(z)\n",
    "# for alpha in (1e-6, 1e-4, 1e-2, 0.1, 1., 10.):\n",
    "# for alpha in np.logspace(0.0, 5.0, num=11):\n",
    "# for alpha in (5., 7., 8., 9., 11., 12., 14., 16.):\n",
    "for alpha in np.arange(11.0, 13.0, 0.2):\n",
    "    print \"alpha =\", alpha\n",
    "    X_train = pca_full.transform(X_train_orig)\n",
    "    X_test = pca_full.transform(X_test_orig)\n",
    "    X_train *= np.exp(alpha * z)\n",
    "    X_test  *= np.exp(alpha * z)\n",
    "#     knn = KNNClassifier(algorithm='kd_tree', k=2, p=2, weights='distance')\n",
    "#     knn.fit(X_train, y_train)\n",
    "#     print knn.evaluate(X_test, y_test)\n",
    "    knn = KNNClassifier(algorithm='kd_tree', k=3, p=2, weights='uniform')\n",
    "    knn.fit(X_train, y_train)\n",
    "    print knn.evaluate(X_test, y_test)# train_ratio=50005./60000.\n",
    "pca_full.set_params(n_components=35, whiten=True)\n",
    "z = pca_full.explained_variance_ratio_[:35]\n",
    "z /= sum(z)\n",
    "# for alpha in (1e-6, 1e-4, 1e-2, 0.1, 1., 10.):\n",
    "# for alpha in np.logspace(0.0, 5.0, num=11):\n",
    "# for alpha in (5., 7., 8., 9., 11., 12., 14., 16.):\n",
    "for alpha in np.arange(11.0, 13.0, 0.2):\n",
    "    print \"alpha =\", alpha\n",
    "    X_train = pca_full.transform(X_train_orig)\n",
    "    X_test = pca_full.transform(X_test_orig)\n",
    "    X_train *= np.exp(alpha * z)\n",
    "    X_test  *= np.exp(alpha * z)\n",
    "#     knn = KNNClassifier(algorithm='kd_tree', k=2, p=2, weights='distance')\n",
    "#     knn.fit(X_train, y_train)\n",
    "#     print knn.evaluate(X_test, y_test)\n",
    "    knn = KNNClassifier(algorithm='kd_tree', k=3, p=2, weights='uniform')\n",
    "    knn.fit(X_train, y_train)\n",
    "    print knn.evaluate(X_test, y_test)\n",
    "# alpha = 1e-06\n",
    "# 0.971102889711\n",
    "# 0.972302769723\n",
    "# 0.971102889711\n",
    "# alpha = 0.0001\n",
    "# 0.971102889711\n",
    "# 0.972302769723\n",
    "# alpha = 0.01\n",
    "# 0.971102889711\n",
    "# 0.972302769723\n",
    "# alpha = 0.1\n",
    "# 0.971202879712\n",
    "# 0.972302769723\n",
    "# alpha = 1.0\n",
    "# 0.97200279972\n",
    "# 0.972802719728\n",
    "# alpha = 10.0\n",
    "# 0.973802619738\n",
    "# 0.97700229977\n",
    "# ...\n",
    "# alpha = 5.0\n",
    "# 0.973402659734\n",
    "# 0.974802519748\n",
    "# alpha = 7.0\n",
    "# 0.97400259974\n",
    "# 0.975602439756\n",
    "# alpha = 8.0\n",
    "# 0.974102589741\n",
    "# 0.976202379762\n",
    "# alpha = 9.0\n",
    "# 0.973802619738\n",
    "# 0.976302369763\n",
    "# alpha = 11.0\n",
    "# 0.97400259974\n",
    "# 0.977302269773\n",
    "# alpha = 12.0\n",
    "# 0.974202579742\n",
    "# 0.977502249775\n",
    "# alpha = 14.0\n",
    "# 0.973402659734\n",
    "# 0.976602339766\n",
    "# alpha = 16.0\n",
    "# 0.972902709729\n",
    "# 0.976202379762\n",
    "# alpha = 11.2\n",
    "# 0.977402259774\n",
    "# alpha = 11.4\n",
    "# 0.977602239776\n",
    "# alpha = 11.6\n",
    "# [*] 0.977802219778\n",
    "# alpha = 11.8\n",
    "# [*] 0.977802219778\n",
    "# alpha = 12.0\n",
    "# 0.977502249775\n",
    "# alpha = 12.2\n",
    "# 0.977402259774\n",
    "# alpha = 12.4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# train_ratio=57000./60000.\n",
    "pca_full.set_params(n_components=35, whiten=True)\n",
    "z = pca_full.explained_variance_ratio_[:35]\n",
    "z /= sum(z)\n",
    "alpha = 11.6\n",
    "\n",
    "aug = RandomAugmentator(transform_shape=(28, 28), random_seed=1337)\n",
    "aug.add('RandomRotate', angle=(-7., 10.))\n",
    "aug.add('RandomGaussian', sigma=(0., 0.5))\n",
    "aug.add('RandomShift', x_shift=(-1, 1), y_shift=(-1, 1))\n",
    "aug.add('Dropout', p=(0., 0.2))\n",
    "\n",
    "for N in xrange(10): # augment by a factor of (1 + N)\n",
    "    X_train = aug.transform(X_train_orig, N)\n",
    "    y_train = np.repeat(y_train_orig, N + 1)\n",
    "    \n",
    "    X_train = pca_full.transform(X_train)\n",
    "    X_test = pca_full.transform(X_test_orig)\n",
    "    X_train *= np.exp(alpha * z)\n",
    "    X_test  *= np.exp(alpha * z)\n",
    "    \n",
    "    knn = KNNClassifier(algorithm='kd_tree', k=3, p=2, weights='uniform')\n",
    "    knn.fit(X_train, y_train)\n",
    "    print \"N = {0}, acc. = {1:.5f}\".format(N, knn.evaluate(X_test, y_test_orig))\n",
    "# N = 0, acc. = 0.97904\n",
    "# N = 1, acc. = 0.98137\n",
    "# N = 2, acc. = 0.98137\n",
    "# N = 3, acc. = 0.98303\n",
    "# N = 4, acc. = 0.98337\n",
    "# N = 5, acc. = 0.98370\n",
    "# N = 6, acc. = 0.98370\n",
    "# N = 7, acc. = 0.98237\n",
    "# [*] N = 8, acc. = 0.98536\n",
    "# N = 9, acc. = 0.98436"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Approach #NN"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "nn = load_model('tmp/16nn.json')\n",
    "X_train, _ = load_mnist('train', 'data/')\n",
    "X_train /= 255.\n",
    "nn.forward_pass(X_train)\n",
    "np.save('data/train_feats.npy', leaky_relu(nn.layers[13]._last_input))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X = np.load('data/train_feats.npy')\n",
    "_, y = load_mnist('train', 'data/')\n",
    "tts = TrainTestSplitter(shuffle=True, random_seed=1337)\n",
    "train, test = tts.split(y, train_ratio=50005./60000., stratify=True) # 49999 : 10001\n",
    "param_grid = dict(\n",
    "    k=[2, 3, 4, 5],\n",
    "    p=[1., 2., 3.],\n",
    "    weights=['uniform', 'distance']\n",
    ")\n",
    "grid_cv = GridSearchCV(None, param_grid=param_grid)\n",
    "knn = KNNClassifier(algorithm='kd_tree')\n",
    "knn.fit(X[train], y[train])\n",
    "for params in grid_cv.gen_params():\n",
    "    knn.reset_params().set_params(**params)\n",
    "    acc = knn.evaluate(X[test], y[test])\n",
    "    print \"{0:.4f} at {1}\".format(acc, params)\n",
    "# (Sorted)\n",
    "# 0.9906 at {'p': 1.0, 'k': 5, 'weights': 'distance'}\n",
    "# 0.9912 at {'p': 2.0, 'k': 5, 'weights': 'distance'}\n",
    "# 0.9919 at {'p': 3.0, 'k': 5, 'weights': 'distance'}\n",
    "# 0.9926 at {'p': 1.0, 'k': 4, 'weights': 'distance'}\n",
    "# 0.9929 at {'p': 2.0, 'k': 4, 'weights': 'distance'}\n",
    "# 0.9934 at {'p': 3.0, 'k': 4, 'weights': 'distance'}\n",
    "# 0.9943 at {'p': 2.0, 'k': 3, 'weights': 'distance'}\n",
    "# 0.9945 at {'p': 1.0, 'k': 3, 'weights': 'distance'}\n",
    "# 0.9950 at {'p': 3.0, 'k': 3, 'weights': 'distance'}\n",
    "# 0.9957 at {'p': 2.0, 'k': 2, 'weights': 'uniform'}\n",
    "# 0.9958 at {'p': 3.0, 'k': 2, 'weights': 'uniform'}\n",
    "# 0.9959 at {'p': 1.0, 'k': 2, 'weights': 'uniform'}\n",
    "# 0.9960 at {'p': 2.0, 'k': 2, 'weights': 'distance'}\n",
    "# 0.9962 at {'p': 3.0, 'k': 2, 'weights': 'distance'}\n",
    "# 0.9963 at {'p': 1.0, 'k': 2, 'weights': 'distance'}\n",
    "# 0.9964 at {'p': 2.0, 'k': 4, 'weights': 'uniform'}\n",
    "# 0.9965 at {'p': 3.0, 'k': 4, 'weights': 'uniform'}\n",
    "# 0.9967 at {'p': 1.0, 'k': 4, 'weights': 'uniform'}\n",
    "# 0.9968 at {'p': 3.0, 'k': 3, 'weights': 'uniform'}\n",
    "# 0.9969 at {'p': 1.0, 'k': 3, 'weights': 'uniform'}\n",
    "# 0.9969 at {'p': 1.0, 'k': 5, 'weights': 'uniform'}\n",
    "# 0.9970 at {'p': 2.0, 'k': 5, 'weights': 'uniform'}\n",
    "# 0.9970 at {'p': 3.0, 'k': 5, 'weights': 'uniform'}\n",
    "# [*] 0.9971 at {'p': 2.0, 'k': 3, 'weights': 'uniform'}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Logistic Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Approach #1: no preprocessing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X, y = load_mnist(mode='train', path='data/')\n",
    "X /= 255.\n",
    "train, test = TrainTestSplitter(shuffle=True, random_seed=1337).split(y, train_ratio=0.85)\n",
    "y = one_hot(y)\n",
    "logreg = LogisticRegression(n_batches=10, \n",
    "                            random_seed=1337, \n",
    "                            optimizer_params=dict(\n",
    "                                max_epochs=100, \n",
    "                                learning_rate=1e-3)\n",
    "                            )\n",
    "logreg.fit(X[train], y[train], X_val=X[test], y_val=y[test])\n",
    "y_pred = logreg.predict(X[test])\n",
    "print accuracy_score(y_pred, y[test])\n",
    "# 0.92755..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X, y = load_mnist(mode='train', path='data/')\n",
    "X /= 255.\n",
    "train, test = TrainTestSplitter(shuffle=True, random_seed=1337).split(y, train_ratio=0.85)\n",
    "y = one_hot(y)\n",
    "logreg = LogisticRegression(n_batches=10, \n",
    "                            random_seed=1337, \n",
    "                            optimizer_params=dict(\n",
    "                                max_epochs=100, \n",
    "                                learning_rate=1e-3)\n",
    "                            )\n",
    "logreg.fit(X[train], y[train], X_val=X[test], y_val=y[test])\n",
    "y_pred = logreg.predict(X[test])\n",
    "print accuracy_score(y_pred, y[test])\n",
    "# 0.92766..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Validation for L2, learning rate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X, y = load_mnist(mode='train', path='data/')\n",
    "X /= 255.\n",
    "train, test = TrainTestSplitter(shuffle=True, random_seed=1337).split(y, train_ratio=0.85)\n",
    "y = one_hot(y)\n",
    "\n",
    "for lr in (5 * 1e-5, 1e-4, 2 * 1e-4, 5 * 1e-4, 1e-3, 2 * 1e-3, 5 * 1e-3, 1e-2):\n",
    "    for L2 in (0., 1e-6, 1e-5, 1e-4, 1e-3, 1e-2, 0.1, 1.):\n",
    "        logreg = LogisticRegression(L2=L2,\n",
    "                                    n_batches=10, \n",
    "                                    random_seed=1337, \n",
    "                            optimizer_params=dict(\n",
    "                                max_epochs=600,\n",
    "                                early_stopping=50,\n",
    "#                                 verbose=True,\n",
    "                                learning_rate=lr,\n",
    "                                plot=False)\n",
    "                            )\n",
    "        logreg.fit(X[train], y[train], X_val=X[test], y_val=y[test])\n",
    "        acc = logreg.evaluate(X[test], y[test])\n",
    "        print \"{0:.4f}, lr = {1}, L2 = {2}\".format(acc, lr, L2)\n",
    "# 0.9051, lr = 1e-05, L2 = 1e-06\n",
    "# 0.9051, lr = 1e-05, L2 = 1e-05\n",
    "# 0.9051, lr = 1e-05, L2 = 0.0001\n",
    "# 0.9051, lr = 1e-05, L2 = 0.001\n",
    "# 0.9049, lr = 1e-05, L2 = 0.01\n",
    "# 0.9046, lr = 1e-05, L2 = 0.1\n",
    "# 0.9009, lr = 1e-05, L2 = 1.0\n",
    "# 0.9250, lr = 2e-05, L2 = 1e-06\n",
    "# 0.9250, lr = 2e-05, L2 = 1e-05\n",
    "# 0.9250, lr = 2e-05, L2 = 0.0001\n",
    "# 0.9251, lr = 2e-05, L2 = 0.001\n",
    "# 0.9248, lr = 2e-05, L2 = 0.01\n",
    "# 0.9248, lr = 2e-05, L2 = 0.1\n",
    "# 0.9268, lr = 5e-05, L2 = 0.0\n",
    "# 0.9268, lr = 5e-05, L2 = 1e-06\n",
    "# 0.9268, lr = 5e-05, L2 = 1e-05\n",
    "# 0.9267, lr = 5e-05, L2 = 0.0001\n",
    "# 0.9268, lr = 5e-05, L2 = 0.001\n",
    "# 0.9270, lr = 5e-05, L2 = 0.01\n",
    "# 0.9262, lr = 5e-05, L2 = 0.1\n",
    "# 0.9216, lr = 5e-05, L2 = 1.0\n",
    "# 0.9264, lr = 0.0001, L2 = 0.0\n",
    "# 0.9264, lr = 0.0001, L2 = 1e-06\n",
    "# 0.9266, lr = 0.0001, L2 = 1e-05\n",
    "# 0.9266, lr = 0.0001, L2 = 0.0001\n",
    "# 0.9266, lr = 0.0001, L2 = 0.001\n",
    "# 0.9268, lr = 0.0001, L2 = 0.01\n",
    "# 0.9262, lr = 0.0001, L2 = 0.1\n",
    "# 0.9220, lr = 0.0001, L2 = 1.0\n",
    "# 0.9267, lr = 0.0002, L2 = 0.0\n",
    "# 0.9267, lr = 0.0002, L2 = 1e-06\n",
    "# 0.9266, lr = 0.0002, L2 = 1e-05\n",
    "# 0.9266, lr = 0.0002, L2 = 0.0001\n",
    "# 0.9276, lr = 0.0002, L2 = 0.001\n",
    "# 0.9264, lr = 0.0002, L2 = 0.01\n",
    "# 0.9262, lr = 0.0002, L2 = 0.1\n",
    "# 0.9218, lr = 0.0002, L2 = 1.0\n",
    "# 0.9281, lr = 0.0005, L2 = 0.0\n",
    "# 0.9281, lr = 0.0005, L2 = 1e-06\n",
    "# 0.9282, lr = 0.0005, L2 = 1e-05\n",
    "# 0.9280, lr = 0.0005, L2 = 0.0001\n",
    "# 0.9278, lr = 0.0005, L2 = 0.001\n",
    "# 0.9274, lr = 0.0005, L2 = 0.01\n",
    "# 0.9264, lr = 0.0005, L2 = 0.1\n",
    "# 0.9212, lr = 0.0005, L2 = 1.0\n",
    "# 0.9276, lr = 0.001, L2 = 0.0\n",
    "# 0.9277, lr = 0.001, L2 = 1e-06\n",
    "# 0.9277, lr = 0.001, L2 = 1e-05\n",
    "# 0.9277, lr = 0.001, L2 = 0.0001\n",
    "# 0.9281, lr = 0.001, L2 = 0.001\n",
    "# 0.9271, lr = 0.001, L2 = 0.01\n",
    "# 0.9260, lr = 0.001, L2 = 0.1\n",
    "# 0.9224, lr = 0.001, L2 = 1.0\n",
    "# 0.9299, lr = 0.002, L2 = 0.0\n",
    "# 0.9293, lr = 0.002, L2 = 1e-06\n",
    "# 0.9292, lr = 0.002, L2 = 1e-05\n",
    "# 0.9297, lr = 0.002, L2 = 0.0001\n",
    "# 0.9292, lr = 0.002, L2 = 0.001\n",
    "# 0.9291, lr = 0.002, L2 = 0.01\n",
    "# 0.9281, lr = 0.002, L2 = 0.1\n",
    "# 0.9232, lr = 0.002, L2 = 1.0\n",
    "# 0.9294, lr = 0.005, L2 = 0.0\n",
    "# [*] 0.9301, lr = 0.005, L2 = 1e-06\n",
    "# 0.9294, lr = 0.005, L2 = 1e-05\n",
    "# 0.9293, lr = 0.005, L2 = 0.0001\n",
    "# 0.9294, lr = 0.005, L2 = 0.001\n",
    "# 0.9299, lr = 0.005, L2 = 0.01\n",
    "# 0.9277, lr = 0.005, L2 = 0.1\n",
    "# 0.9227, lr = 0.005, L2 = 1.0\n",
    "# 0.9274, lr = 0.01, L2 = 0.0\n",
    "# 0.9266, lr = 0.01, L2 = 1e-06\n",
    "# 0.9276, lr = 0.01, L2 = 1e-05\n",
    "# 0.9286, lr = 0.01, L2 = 0.0001\n",
    "# 0.9274, lr = 0.01, L2 = 0.001\n",
    "# 0.9291, lr = 0.01, L2 = 0.01\n",
    "# 0.9261, lr = 0.01, L2 = 0.1\n",
    "# 0.9201, lr = 0.01, L2 = 1.0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Approach #2: PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "logregs = []\n",
    "for i, n_components in enumerate(xrange(301, 401, 20)):\n",
    "    pca_full = load_model('models/pca_full.json')\n",
    "    pca_full.set_params(n_components=n_components, whiten=False)\n",
    "\n",
    "    X, y = load_mnist(mode='train', path='data/')\n",
    "    X /= 255.\n",
    "    X = pca_full.transform(X)\n",
    "\n",
    "    train, test = TrainTestSplitter(shuffle=True, random_seed=1337).split(y, train_ratio=0.85)\n",
    "    y = one_hot(y)\n",
    "\n",
    "    logreg = LogisticRegression(n_batches=10, \n",
    "                                random_seed=1337, \n",
    "                                optimizer_params=dict(\n",
    "                                    max_epochs=500, \n",
    "                                    learning_rate=1e-3, \n",
    "                                    plot=False)\n",
    "                                )\n",
    "    logregs.append(logreg)\n",
    "#     logregs[i].set_params(optimizer_params=dict(max_epochs=100, learning_rate=1e-3, plot=False))\n",
    "    logreg.fit(X[train], y[train], X_val=X[test], y_val=y[test])\n",
    "    y_pred = logreg.predict(X[test])\n",
    "    print \"PCA {0} --- {1:.4f}\".format(n_components, accuracy_score(y_pred, y[test]))\n",
    "\n",
    "#   W/O whitening    | with\n",
    "# ---------------------------\n",
    "# PCA 15  --- 0.8441 | \n",
    "# PCA 20  --- 0.8783 |\n",
    "# PCA 25  --- 0.8874 |\n",
    "# PCA 30  --- 0.8936 | 0.8931\n",
    "# PCA 35  --- 0.9027 | 0.9029\n",
    "# PCA 40  --- 0.9056 | 0.9051\n",
    "# PCA 45  --- 0.9076 | 0.9077\n",
    "# PCA 50  --- 0.9087 | 0.9083\n",
    "# PCA 55  --- 0.9132 | 0.9134\n",
    "# PCA 60  --- 0.9129 | 0.9129\n",
    "# PCA 65  --- 0.9133 | 0.9129\n",
    "# PCA 70  --- 0.9176 | 0.9173\n",
    "# PCA 75  --- 0.9189 | 0.9186\n",
    "# PCA 80  --- 0.9206 | 0.9200\n",
    "# PCA 85  --- 0.9207 | 0.9207\n",
    "# PCA 90  --- 0.9213 | 0.9212\n",
    "# PCA 95  --- 0.9203 | 0.9198\n",
    "# PCA 100 --- 0.9184 | 0.9188\n",
    "# PCA 105 --- 0.9203 | 0.9198\n",
    "# PCA 110 --- 0.9209 | 0.9202\n",
    "# PCA 115 --- 0.9210 | 0.9209\n",
    "# PCA 120 --- 0.9217 | 0.9212\n",
    "# PCA 125            | 0.9228 [*]\n",
    "# PCA 130            | 0.9210\n",
    "# PCA 135            | 0.9220\n",
    "# PCA 140            | 0.9211\n",
    "# PCA 145            | 0.9202\n",
    "# PCA 150            | 0.9208\n",
    "# PCA 155            | 0.9223\n",
    "# PCA 165          --- 0.9210\n",
    "# PCA 170          --- 0.9207\n",
    "# PCA 175          --- 0.9214\n",
    "# PCA 180          --- 0.9211\n",
    "# PCA 185          --- 0.9208\n",
    "# PCA 190 -         -- 0.9208\n",
    "# PCA 195          --- 0.9204\n",
    "# PCA 200          --- 0.9208\n",
    "# ...\n",
    "# PCA 220          --- 0.9209\n",
    "# PCA 230          --- 0.9214\n",
    "# PCA 240          --- 0.9207\n",
    "# ...\n",
    "# PCA 301          --- 0.9207\n",
    "# PCA 321          --- 0.9204\n",
    "# ..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Approach #3: augment data (x5) for logreg and save to file"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### save data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X, y = load_mnist(mode='train', path='data/')\n",
    "X /= 255.  \n",
    "X = X.astype(np.float32)\n",
    "aug = RandomAugmentator(transform_shape=(28, 28), random_seed=1337)\n",
    "aug.add('RandomRotate', angle=(-5., 7.))\n",
    "aug.add('RandomGaussian', sigma=(0., 0.5))\n",
    "aug.add('RandomShift', x_shift=(-1, 1), y_shift=(-1, 1))\n",
    "aug.add('Dropout', p=(0., 0.2))\n",
    "X_aug = aug.transform(X, 4)\n",
    "y_aug = np.repeat(y, 5)\n",
    "y_aug = one_hot(y_aug)\n",
    "np.save('data/X_aug_logreg.npy', X_aug)\n",
    "np.save('data/y_aug_logreg.npy', y_aug)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### load data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X = np.load('data/X_aug_logreg.npy')\n",
    "y = np.load('data/y_aug_logreg.npy')\n",
    "train, test = TrainTestSplitter(shuffle=True, random_seed=1337).split(y, train_ratio=29./30.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### grid searchs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X = np.load('data/X_aug_logreg.npy')#[:25000]\n",
    "y = np.load('data/y_aug_logreg.npy')#[:25000]\n",
    "train, test = TrainTestSplitter(shuffle=True, random_seed=1337).split(y, train_ratio=29./30.)\n",
    "\n",
    "for lr in reversed([1e-2, 1e-3, 1e-4, 1e-5, 1e-6]):\n",
    "    for L2 in (1e-8, 1e-6, 1e-4, 1e-2, 1.):\n",
    "        plot = (L2 == 1e-8)\n",
    "        logreg = LogisticRegression(L2=L2,\n",
    "                                    n_batches=64,\n",
    "                                    # n_batches=10,\n",
    "                                    random_seed=1337, \n",
    "                                    optimizer_params=dict(\n",
    "                                        max_epochs=800,\n",
    "                                        # max_epochs=20,\n",
    "                                        early_stopping=50, \n",
    "                                        learning_rate=lr, \n",
    "                                        plot=plot,\n",
    "                                        plot_dirpath='learning_curves_logreg_{0}/'.format(lr)\n",
    "                                    ))\n",
    "        logreg.fit(X[train], y[train], X_val=X[test], y_val=y[test])\n",
    "        acc = logreg.evaluate(X[test], y[test])\n",
    "        print \"{0:.4f}, lr = {1}, L2 = {2}\".format(acc, lr, L2)\n",
    "\n",
    "        s = '{0:.4f}'.format(acc).replace('.', '_')\n",
    "        t = 'models/logreg/logreg_{0}_{1}_{2}.json'.format(s, lr, L2)\n",
    "        logreg.save(t)\n",
    "        logreg_loaded = load_model(t)#.fit([[0.]], [[1]])\n",
    "\n",
    "        print \"{0:.4f}\".format(logreg.evaluate(X[test], y[test]))\n",
    "        \n",
    "# 0.7843, lr = 1e-06, L2 = 1e-08\n",
    "# 0.7843, lr = 1e-06, L2 = 1e-06\n",
    "# 0.7843, lr = 1e-06, L2 = 0.0001\n",
    "# 0.7843, lr = 1e-06, L2 = 0.01\n",
    "# 0.7855, lr = 1e-06, L2 = 1.0\n",
    "# 0.8754, lr = 1e-05, L2 = 1e-08\n",
    "# 0.8754, lr = 1e-05, L2 = 1e-06\n",
    "# ...\n",
    "# 0.8805, lr = 1e-4, L2 whaterer\n",
    "# ...\n",
    "# 0.86.., lr = 1e-3, L2 whaterer"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Approach #4: Exponential decay on singular values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "pca_full = load_model('models/pca_full.json')\n",
    "def load_big2():\n",
    "    X, y = load_mnist(mode='train', path='data/')\n",
    "    X_scaled = X / 255. # only divide by 255\n",
    "    tts = TrainTestSplitter(shuffle=True, random_seed=1337)\n",
    "    train, test = tts.split(y, train_ratio=50005./60000., stratify=True)\n",
    "    return X_scaled[train], y[train], X_scaled[test], y[test] # 49999 train, 10001 val\n",
    "X_train_orig, y_train, X_test_orig, y_test = load_big2()\n",
    "y_train = one_hot(y_train)\n",
    "y_test = one_hot(y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "pca_full.set_params(n_components=35, whiten=True)\n",
    "z = pca_full.explained_variance_ratio_[:35]\n",
    "z /= sum(z)\n",
    "for alpha in (1e-6, 1e-4, 1e-2, 0.1, 1., 2., 5., 10., 16., 25., 100.):\n",
    "    print \"alpha =\", alpha\n",
    "    X_train = pca_full.transform(X_train_orig)\n",
    "    X_test = pca_full.transform(X_test_orig)\n",
    "    X_train *= np.exp(alpha * z)\n",
    "    X_test *= np.exp(alpha * z)\n",
    "    logreg = LogisticRegression(L2=1e-6,\n",
    "                                n_batches=10, \n",
    "                                random_seed=1337, \n",
    "                                optimizer_params=dict(\n",
    "                                    max_epochs=600,\n",
    "                                    early_stopping=50,\n",
    "#                                 verbose=True,\n",
    "                                    learning_rate=0.005,\n",
    "                                    plot=False)\n",
    "                                )\n",
    "    logreg.fit(X_train, y_train, X_val=X_test, y_val=y_test)\n",
    "    print logreg.evaluate(X_test, y_test)\n",
    "# alpha = 1e-06\n",
    "# 0.90800919908\n",
    "# alpha = 0.0001\n",
    "# 0.90800919908\n",
    "# alpha = 0.01\n",
    "# 0.90800919908\n",
    "# alpha = 0.1\n",
    "# 0.90800919908\n",
    "# alpha = 1.0\n",
    "# 0.90800919908\n",
    "# alpha = 2.0\n",
    "# 0.908109189081\n",
    "# alpha = 5.0\n",
    "# 0.907709229077\n",
    "# alpha = 10.0\n",
    "# 0.907809219078\n",
    "# alpha = 16.0\n",
    "# 0.907209279072\n",
    "# alpha = 25.0\n",
    "# 0.906409359064\n",
    "# alpha = 100.0\n",
    "# 0.505749425057"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Approach #NN"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X_train = np.load('data/train_feats.npy')    \n",
    "_, y_train = load_mnist('train', 'data/')\n",
    "\n",
    "tts = TrainTestSplitter(shuffle=True, random_seed=1337)\n",
    "train, val = tts.split(y_train, train_ratio=50005./60000., stratify=True) # 49999 : 10001\n",
    "\n",
    "param_grid = dict(\n",
    "    L2=[0] + np.logspace(-4., 1., 11).tolist(),\n",
    ")\n",
    "logreg_params = dict(n_batches=32,\n",
    "                     random_seed=1337,\n",
    "                     optimizer_params=dict(\n",
    "                         max_epochs=750,\n",
    "                         learning_rate=0.001,\n",
    "                         early_stopping=50,\n",
    "                         plot=False,\n",
    "                         verbose=False\n",
    "                     ))\n",
    "for params in GridSearchCV(param_grid=param_grid).gen_params():\n",
    "    logreg = LogisticRegression(**logreg_params).set_params(**params)\n",
    "    logreg.fit(X_train[train], one_hot(y_train[train]), X_val=X_train[val], y_val=one_hot(y_train[val]))\n",
    "    acc = logreg.evaluate(X_train[val], one_hot(y_train[val]))\n",
    "    print \"{0:.5f} at {1}\".format(acc, val_acc, params)\n",
    "    \n",
    "# (Sorted)\n",
    "#     0.99590 val at {'learning_rate': 0.005, 'L2': 3.1622776601683795}\n",
    "#     0.99610 val at {'learning_rate': 0.005, 'L2': 0.31622776601683794}\n",
    "#     0.99710 val at {'learning_rate': 0.005, 'L2': 0.0031622776601683794}\n",
    "#     0.99710 val at {'learning_rate': 0.005, 'L2': 10.0}\n",
    "#     0.99730 val at {'learning_rate': 0.005, 'L2': 0.031622776601683791}\n",
    "#     0.99760 val at {'learning_rate': 0.005, 'L2': 0.0}\n",
    "#     0.99770 val at {'learning_rate': 0.005, 'L2': 0.0001}\n",
    "#     0.99780 val at {'learning_rate': 0.005, 'L2': 0.001}\n",
    "#     0.99780 val at {'learning_rate': 0.005, 'L2': 0.01}\n",
    "#     0.99790 val at {'learning_rate': 0.005, 'L2': 0.1}\n",
    "#     0.99790 val at {'learning_rate': 0.005, 'L2': 1.0}\n",
    "# [*] 0.99810 val at {'learning_rate': 0.005, 'L2': 0.00031622776601683794}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## RBM"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X, y = load_mnist('train', 'data/')\n",
    "indices, _ = TTS(shuffle=True, random_seed=1337).split(y, train_ratio=4.005/60., stratify=True)\n",
    "X = X[indices]\n",
    "X = X[:4000]\n",
    "X /= 255.\n",
    "param_grid = dict(\n",
    "    n_hidden=[128, 256, 384],\n",
    "    learning_rate=[0.05, 0.01, 0.005, '0.05->0.005', '0.01->0.001'],\n",
    "    k=[1, 4],\n",
    "    random_seed=[1337, 42],\n",
    ")\n",
    "rbm = RBM(persistent=True,\n",
    "          n_epochs=40,\n",
    "          early_stopping=12,\n",
    "          momentum='0.5->0.99',\n",
    "          batch_size=10,\n",
    "          verbose=False)\n",
    "done = 0\n",
    "for thr in (False, True):\n",
    "    if thr:\n",
    "        X = (X > 0.5).astype(np.float32)\n",
    "    for params in GS(param_grid=param_grid).gen_params(): # 60\n",
    "        done += 1\n",
    "        rbm.reset_params().set_params(**params)\n",
    "        rbm.fit(X)\n",
    "        mse = rbm.best_recon\n",
    "        dirpath = 'tmp/rbm_ge0.5/' if thr else 'tmp/rbm/'\n",
    "        rbm.save(dirpath + '{0:.5f}.json'.format(mse))\n",
    "        print \"mse {0:.5f} [{1}/120] at {2}!\".format(mse, done, params)\n",
    "# (Sorted)\n",
    "# [*] mse 0.06684 [25/120] at {'k': 1, 'random_seed': 1337, 'learning_rate': '0.01->0.001', 'n_hidden': 256}!\n",
    "# ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "rbm = load_model('models/rbm.json')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ceeaZOP/884sctLVv3x533nknHn/8cVxxxRXIzMxEjRo1kJOTg6+++grHH388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hHsFaA9eQdTGad1sAHerTPnnlPWp+9Fm71vvg564t9gD0gq8W+sY55ndvspYcnAS5JsV9WY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\nhMHHzWLCAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8aa84ce4d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_rbm_filters(rbm.best_W)\n",
    "plt.savefig('rbm_filters.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### nudge and try again"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# non-random nudging in all directions\n",
    "\n",
    "X, y = load_mnist('train', 'data/')\n",
    "X /= 255.\n",
    "indices, _ = TrainTestSplitter(shuffle=True, random_seed=1337).split(y, train_ratio=4.005/60., stratify=True)\n",
    "X = X[indices]\n",
    "X = X[:4000]\n",
    "\n",
    "X_aug = []\n",
    "for x in X:\n",
    "    X_aug.append(x)\n",
    "    for t in RandomAugmentator(transform_shape=(28, 28), out_shape=(784,))\\\n",
    "             .add('RandomShift', x_shift=(-1, -1), y_shift=( 0,  0))\\\n",
    "             .transform_x(x, 1):\n",
    "        X_aug.append(t)\n",
    "    for t in RandomAugmentator(transform_shape=(28, 28), out_shape=(784,))\\\n",
    "             .add('RandomShift', x_shift=( 1,  1), y_shift=( 0,  0))\\\n",
    "             .transform_x(x, 1):\n",
    "        X_aug.append(t)\n",
    "    for t in RandomAugmentator(transform_shape=(28, 28), out_shape=(784,))\\\n",
    "             .add('RandomShift', x_shift=( 0,  0), y_shift=( 1,  1))\\\n",
    "             .transform_x(x, 1):\n",
    "        X_aug.append(t)\n",
    "    for t in RandomAugmentator(transform_shape=(28, 28), out_shape=(784,))\\\n",
    "             .add('RandomShift', x_shift=( 0,  0), y_shift=(-1, -1))\\\n",
    "             .transform_x(x, 1):\n",
    "        X_aug.append(t)\n",
    "X_aug = np.asarray(X_aug)\n",
    "np.save('data/X_rbm_small.npy', X_aug)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X_aug = np.load('data/X_rbm_small.npy')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "param_grid = dict(\n",
    "    learning_rate=['0.01->0.005', '0.05->0.001', '0.05->0.005', '0.01->0.001'],\n",
    "    batch_size=[5, 10, 20, 40],\n",
    "    random_seed=[1337, 42],\n",
    ")\n",
    "rbm = RBM(n_hidden=256,\n",
    "          k=1,\n",
    "          persistent=True,\n",
    "          n_epochs=60,\n",
    "          early_stopping=12,\n",
    "          momentum='0.5->0.99',\n",
    "          verbose=True)\n",
    "done = 0\n",
    "GS = GridSearchCV\n",
    "for params in GS(param_grid=param_grid).gen_params():\n",
    "    done += 1\n",
    "    if done <= 16:\n",
    "        continue\n",
    "    rbm.reset_params().set_params(**params)\n",
    "    rbm.fit(X_aug)\n",
    "    mse = rbm.best_recon\n",
    "    rbm.save('tmp/rbm_{0:.5f}.json'.format(mse))\n",
    "    print \"mse {0:.5f} [{1}/40] at {2}!\".format(mse, done, params)\n",
    "# (Sorted:) \n",
    "# [*] mse 0.06809 [19/40] at {'learning_rate': '0.05->0.001', 'random_seed': 1337, 'batch_size': 20}!\n",
    "# ..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### extract features and save features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "rbm = load_model('models/rbm.json')\n",
    "X, _ = load_mnist('train', 'data/')\n",
    "X /= 255.\n",
    "F = np.dot(X, rbm.best_W) + rbm.hb # rbm.propup(X)\n",
    "# F.min(), F.max(), F.mean() --> -3773.89447221 2.30920675476 -140.968359014\n",
    "F = StandardScaler().fit_transform(F)\n",
    "np.save('data/rbm_train.npy', F)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Approach #RBM"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X_train = np.load('data/rbm_train.npy')    \n",
    "_, y_train = load_mnist('train', 'data/')\n",
    "\n",
    "tts = TrainTestSplitter(shuffle=True, random_seed=1337)\n",
    "train, val = tts.split(y_train, train_ratio=50005./60000., stratify=True) # 49999 : 10001\n",
    "\n",
    "param_grid = dict(\n",
    "    L2=np.logspace(-6., 1., 15),\n",
    ")\n",
    "logreg_params = dict(n_batches=32,\n",
    "                     random_seed=1337,\n",
    "                     optimizer_params=dict(\n",
    "                         max_epochs=750,\n",
    "                         learning_rate=0.001,\n",
    "                         early_stopping=50,\n",
    "                         plot=False,\n",
    "                         verbose=False\n",
    "                     ))\n",
    "for params in GridSearchCV(param_grid=param_grid).gen_params():\n",
    "    logreg = LogisticRegression(**logreg_params).set_params(**params)\n",
    "    logreg.fit(X_train[train], one_hot(y_train[train]), X_val=X_train[val], y_val=one_hot(y_train[val]))\n",
    "    acc = logreg.evaluate(X_train[val], one_hot(y_train[val]))\n",
    "    print \"{0:.5f} at {1}\".format(acc, val_acc, params)\n",
    "    \n",
    "# 0.91800 test 0.92251 val at {'L2': 9.9999999999999995e-07}\n",
    "# 0.91760 test 0.92241 val at {'L2': 3.1622776601683792e-06}\n",
    "# ... D:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Neural Network"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### #1 augment data (x5) for NN and save to file"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X, y = load_mnist(mode='train', path='data/')\n",
    "X /= 255.\n",
    "X = X.astype(np.float32)\n",
    "aug = RandomAugmentator(transform_shape=(28, 28), random_seed=1337)\n",
    "aug.add('RandomRotate', angle=(-5., 7.))\n",
    "aug.add('RandomGaussian', sigma=(0., 0.5))\n",
    "aug.add('RandomShift', x_shift=(-1, 1), y_shift=(-1, 1))\n",
    "X_aug = aug.transform(X, 4)\n",
    "y_aug = np.repeat(y, 5)\n",
    "y_aug = one_hot(y_aug)\n",
    "np.save('data/X_aug_nn.npy', X_aug)\n",
    "np.save('data/y_aug_nn.npy', y_aug)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### load data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X = np.load('data/X_aug_nn.npy')\n",
    "y = np.load('data/y_aug_nn.npy')\n",
    "train, test = TrainTestSplitter(shuffle=True, random_seed=1337).split(y, train_ratio=29./30.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### NN models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "print \"Loading data ...\"\n",
    "X = np.load('data/X_aug_nn.npy')#[:30000]\n",
    "y = np.load('data/y_aug_nn.npy')#[:30000]\n",
    "train, test = TrainTestSplitter(shuffle=True, random_seed=1337).split(y, train_ratio=29./30.)\n",
    "\n",
    "nn = NNClassifier(layers=[\n",
    "                  FullyConnected(512),\n",
    "                  Activation('leaky_relu'),\n",
    "                  FullyConnected(256),\n",
    "                  Activation('leaky_relu'),\n",
    "                  FullyConnected(128),\n",
    "                  Activation('leaky_relu'),\n",
    "                  FullyConnected(32),\n",
    "                  Activation('leaky_relu'),\n",
    "                  FullyConnected(10),\n",
    "                  Activation('softmax')\n",
    "              ],\n",
    "              n_batches=1024,\n",
    "              shuffle=True,\n",
    "              random_seed=1337,\n",
    "              optimizer_params=dict(\n",
    "                  max_epochs=100,\n",
    "                  early_stopping=20,\n",
    "                  verbose=True,\n",
    "                  plot=True,\n",
    "                  plot_dirpath='learning_curves_NN/',\n",
    "                  learning_rate=1e-4\n",
    "              ))\n",
    "print \"Initializing NN ...\"\n",
    "nn.fit(X[train], y[train], X_val=X[test], y_val=y[test])\n",
    "print nn.evaluate(X[train], y[train], 'accuracy_score')\n",
    "\n",
    "#  1) validation accuracy --> 0.9929\n",
    "#  2) 512-256-128-32-10   Dropout(0.1)   --> 0.9906\n",
    "#  3) 512-256-128-32-10   Dropout(0.2)   --> 0.9897\n",
    "#  4) 600-300-128-32-10                  --> 0.9879\n",
    "#  5) 600-300-128-32-10   Dropout(0.1)   --> 0.9914\n",
    "#  6) 600-300-128-32-10   Dropout(0.12)  --> 0.9895\n",
    "#  7) 800-400-200-100-10  Dropout(0.12)  --> 0.9929\n",
    "#  8) 1024-512-256-128-10 Dropout(0.12)  --> 0.9944\n",
    "#  9) 1024-D.05-768-D.1-256-128-10       --> 0.9905\n",
    "# 10.a) 1024-768-256-128-10 Dropout(0.1) --> 0.9923\n",
    "# 10.b) 1024-768-256-128-10 Dropout(0.2) --> 0.9892\n",
    "# 10.c) 1024-768-256-128-10 Dropout(1/4) --> 0.9857\n",
    "# 10.d) 1024-768-256-128-10 Dropout(0.5) --> 0.9686\n",
    "# (...)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### #2 more thorough augmentation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X, y = load_mnist(mode='train', path='data/')\n",
    "X = X / 255.\n",
    "X = X.astype(np.float32)\n",
    "\n",
    "tts = TrainTestSplitter(shuffle=False, random_seed=1337)\n",
    "train, val = tts.split(y, train_ratio=55005.98/60000., stratify=True) # 55k : 5k\n",
    "X_train, y_train, X_val, y_val = X[train], y[train], X[val], y[val]\n",
    "\n",
    "y_val = one_hot(y_val)\n",
    "\n",
    "np.save('data/nn_X_val.npy', X_val)\n",
    "np.save('data/nn_y_val.npy', y_val)\n",
    "\n",
    "aug = RandomAugmentator(transform_shape=(28, 28), random_seed=1337)\n",
    "aug.add('RandomRotate', angle=(-5., 7.))\n",
    "aug.add('RandomGaussian', sigma=(0., 0.5))\n",
    "aug.add('RandomShift', x_shift=(-1, 1), y_shift=(-1, 1))\n",
    "\n",
    "X_train = aug.transform(X_train, 4)\n",
    "y_train = np.repeat(y_train, 5)\n",
    "y_train = one_hot(y_train)\n",
    "\n",
    "np.save('data/nn_X_train.npy', X_train)\n",
    "np.save('data/nn_y_train.npy', y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 1.a) 1024-D.05-768-D.1-256-128-10  --> 0.9880\n",
    "# 1.b) 1024-D.05-768-D.05-256-128-10 --> 0.9868\n",
    "# 1.c) 1024-768-256-128-10           --> 0.9896\n",
    "# 2)   1000-800-800-500-250-10       --> 0.9824\n",
    "# ... --> 0.9838\n",
    "# (...)\n",
    "# WORSE!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### back to #1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#     11) 800-1024-512-256-128              --> 0.9933\n",
    "#     12) 1337-911-666-128                  --> 0.9923\n",
    "#     13) 800-D.05-1024-D.1-512-256-128     --> 0.9936\n",
    "#     14) 800-D.05-1024-D.1-512-D.1-256-128 --> 0.9928\n",
    "#     15) 1337-D.05-911-D.1-666-128         --> 0.9939\n",
    "# [*] 16) 1337-D.05-911-D.1-666-333-128     --> 0.9948\n",
    "#     17) 1337-D.1-911-D.2-666-333-128      --> 0.9887\n",
    "#     18) ...                               --> 0.9930\n",
    "#     19) ...                               --> 0.9935\n",
    "#     20) 2048-D.1-1337-D.2-666-333         --> 0.9896\n",
    "#     21) 2048-D.15-1337-D.25-666-333       --> 0.9723\n",
    "#     22) 2048-D.05-1337-D.1-666-333        --> 0.9936\n",
    "#     23) 2048-D.1-1337-D.2-666-333-128     --> 0.9892"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Gaussian Processes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## some benchmarks"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### exact linear systems solving"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "GPClassifier(K_=None, algorithm='exact', cg_max_iter=None, cg_tol=1e-05,\n",
       "       f_=None, kernel='rbf', kernel_params={}, lml_=None, max_iter=100,\n",
       "       n_samples=1000, pi_=None, random_seed=None, sigma_n=0.0, tol=1e-05)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X, y = load_mnist('train', 'data/')\n",
    "X /= 255.\n",
    "y = one_hot(y)\n",
    "gp = GPClassifier(algorithm='exact')\n",
    "gp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "gp.reset_K()\n",
    "with Stopwatch(verbose=True):\n",
    "    gp.fit(X[:10], y[:10])\n",
    "gp.reset_K()\n",
    "with Stopwatch(verbose=True):\n",
    "    gp.fit(X[:100], y[:100])\n",
    "gp.reset_K()\n",
    "with Stopwatch(verbose=True):\n",
    "    gp.fit(X[:1000], y[:1000])\n",
    "gp.reset_K()\n",
    "with Stopwatch(verbose=True):\n",
    "    gp.fit(X[:2000], y[:2000])\n",
    "# Elapsed time: 0.046 sec\n",
    "# Elapsed time: 0.518 sec\n",
    "# Elapsed time: 59.686 sec\n",
    "# Elapsed time: 298.424 sec"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### via CG"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "gp = GPClassifier(algorithm='cg')\n",
    "gp.reset_K()\n",
    "with Stopwatch(verbose=True):\n",
    "    gp.fit(X[:100], y[:100])\n",
    "gp.reset_K()\n",
    "with Stopwatch(verbose=True):\n",
    "    gp.fit(X[:1000], y[:1000])\n",
    "gp.reset_K()\n",
    "with Stopwatch(verbose=True):\n",
    "    gp.fit(X[:2000], y[:2000])\n",
    "# Elapsed time: 0.044 sec\n",
    "# Elapsed time: 0.262 sec\n",
    "# Elapsed time: 50.412 sec\n",
    "# Elapsed time: 259.823 sec"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Approach #1. Raw data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "171\n"
     ]
    }
   ],
   "source": [
    "sigma_n = np.concatenate(([0], np.logspace(-8., -4., 2)))\n",
    "length_scale = np.logspace(-1., 2., 19)\n",
    "gamma = 0.5/length_scale**2\n",
    "# sigma_f = np.logspace(-2., 2., 7)\n",
    "param_grid = ({'sigma_n': sigma_n, \n",
    "              'kernel_params': [dict(sigma=1., gamma=gamma_) for gamma_ in gamma]},\n",
    "             {'sigma_n': sigma_n, \n",
    "              'kernel_params': [dict(sigma=0.1, gamma=gamma_) for gamma_ in gamma]},\n",
    "             {'sigma_n': sigma_n, \n",
    "              'kernel_params': [dict(sigma=10., gamma=gamma_) for gamma_ in gamma]})\n",
    "grid_cv = GridSearchCV(model=GPClassifier(algorithm='cg', random_seed=1337, tol=1e-8, cg_tol=1e-7, n_samples=1500), \n",
    "                       param_grid=param_grid,\n",
    "                       train_test_splitter_params=dict(shuffle=True, random_seed=1337), \n",
    "                       n_splits=2, \n",
    "                       refit=True,\n",
    "                       verbose=True)\n",
    "print grid_cv.number_of_combinations()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[{'kernel_params': {'gamma': 49.999999999999993, 'sigma': 1.0},\n",
       "  'sigma_n': 0.0},\n",
       " {'kernel_params': {'gamma': 49.999999999999993, 'sigma': 1.0},\n",
       "  'sigma_n': 1e-08},\n",
       " {'kernel_params': {'gamma': 49.999999999999993, 'sigma': 1.0},\n",
       "  'sigma_n': 0.0001}]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[params for params in grid_cv.gen_params()][:3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X, y = load_mnist(mode='train', path='data/')\n",
    "X /= 255.\n",
    "st = StandardScaler(copy=False, with_mean=True, with_std=False)\n",
    "X = st.fit_transform(X)\n",
    "tts = TrainTestSplitter(random_seed=1337, shuffle=True)\n",
    "indices, _ = tts.split(y, train_ratio=0.02, stratify=True) # 1195 samples\n",
    "X = X[indices]\n",
    "y = y[indices]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "grid_cv.fit(X, y);\n",
    "# Training GPClassifier on 1195 samples x 784 features.\n",
    "# 2-fold CV for each of 171 params combinations == 342 fits ...\n",
    "\n",
    "# iter:   1/342 +- elapsed:  21.159 sec   ...\n",
    "# iter:   2/342 ++ elapsed:  35.444 sec - mean acc.: 0.1113 +/- 2 * 0.014\n",
    "# iter:   3/342 +- elapsed:  49.669 sec - best acc.: 0.1113 at {'kernel_params': {'sigma': 1.0, 'gamma': 49.999999999999993}, 'sigma_n': 0.0}\n",
    "# ...\n",
    "# ...\n",
    "# ...\n",
    "# iter: 340/342 ++convergence is not reached\n",
    "#  elapsed: 16914.8 sec - mean acc.: 0.1046 +/- 2 * 0.001\n",
    "# iter: 341/342 +-convergence is not reached\n",
    "#  elapsed: 17005.8 sec - best acc.: 0.6686 at {'kernel_params': {'sigma': 0.1, 'gamma': 0.049999999999999989}, 'sigma_n': 0.0}\n",
    "# iter: 342/342 ++convergence is not reached\n",
    "#  elapsed: 17083.8 sec - mean acc.: 0.1046 +/- 2 * 0.001"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df = grid_cv.to_df()\n",
    "df.to_excel('cv_results/gp_raw_full.xlsx')\n",
    "df.sort_values(by='mean_score', ascending=False).head(25).to_excel('cv_results/gp_raw_best.xlsx')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Approach #2. PCA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### load data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "pca_full = load_model('models/pca_full.json')\n",
    "X, y = load_mnist(mode='train', path='data/')\n",
    "X /= 255.\n",
    "# st = StandardScaler(copy=False, with_mean=True, with_std=False)\n",
    "# X = st.fit_transform(X)\n",
    "tts = TrainTestSplitter(random_seed=1337, shuffle=True)\n",
    "indices, _ = tts.split(y, train_ratio=0.02, stratify=True) # 1195 samples\n",
    "X = X[indices]\n",
    "y = y[indices]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### PCA w/o whitening"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# for n_components in xrange(5, 151, 5):\n",
    "for n_components in xrange(12, 25):\n",
    "    gamma = np.array([0.3, 0.6, 1.5, 3.0, 5.1]) / n_components\n",
    "    param_grid = {'sigma_n': [1e-8],\n",
    "                  'kernel_params': [dict(sigma=0.1, gamma=gamma_) for gamma_ in gamma]}\n",
    "    grid_cv_params = dict(model=GPClassifier(algorithm='cg', random_seed=1337, tol=1e-8, cg_tol=1e-7, n_samples=1500), \n",
    "                           param_grid=param_grid,\n",
    "                           train_test_splitter_params=dict(shuffle=True, random_seed=1337), \n",
    "                           n_splits=2, \n",
    "                           refit=True,\n",
    "                           verbose=True)\n",
    "    print \"[PCA n_components = {0}]\\n\\n\".format(n_components)\n",
    "    X_current = pca_full.set_params(n_components=n_components, whiten=False).transform(X)\n",
    "    grid_cv = GridSearchCV(**grid_cv_params).fit(X_current, y)\n",
    "    df = grid_cv\\\n",
    "         .to_df()\\\n",
    "         .sort_values(by='mean_score', ascending=False)\\\n",
    "         .to_excel('cv_results/gp_pca_{0}_{1:.4f}.xlsx'.format(n_components, grid_cv.best_score_))\n",
    "    print \"\\n\\n\"\n",
    "# [PCA n_components = 5]\n",
    "\n",
    "\n",
    "# Training GPClassifier on 1195 samples x 5 features.\n",
    "# 2-fold CV for each of 5 params combinations == 10 fits ...\n",
    "\n",
    "# iter:  1/10 +- elapsed:  11.139 sec   ...\n",
    "# iter:  2/10 ++ elapsed:  22.108 sec - mean acc.: 0.5940 +/- 2 * 0.040\n",
    "# iter:  3/10 +- elapsed:  32.947 sec - best acc.: 0.5940 at {'kernel_params': {'sigma': 0.1, 'gamma': 0.059999999999999998}, 'sigma_n': 1e-08}\n",
    "# iter:  4/10 ++ elapsed:  41.796 sec - mean acc.: 0.6384 +/- 2 * 0.034\n",
    "# iter:  5/10 +- elapsed:  49.648 sec - best acc.: 0.6384 at {'kernel_params': {'sigma': 0.1, 'gamma': 0.12}, 'sigma_n': 1e-08}\n",
    "# iter:  6/10 ++ elapsed:  56.744 sec - mean acc.: 0.6728 +/- 2 * 0.018\n",
    "# iter:  7/10 +- elapsed:  63.334 sec - best acc.: 0.6728 at {'kernel_params': {'sigma': 0.1, 'gamma': 0.29999999999999999}, 'sigma_n': 1e-08}\n",
    "# iter:  8/10 ++ elapsed:  70.164 sec - mean acc.: 0.6410 +/- 2 * 0.012\n",
    "# iter:  9/10 +- elapsed:  75.789 sec - best acc.: 0.6728 at {'kernel_params': {'sigma': 0.1, 'gamma': 0.29999999999999999}, 'sigma_n': 1e-08}\n",
    "# iter: 10/10 ++ elapsed:  81.808 sec - mean acc.: 0.5172 +/- 2 * 0.003\n",
    "# ...\n",
    "# ...\n",
    "# ...\n",
    "# iter:  8/10 ++ elapsed:  80.497 sec - mean acc.: 0.7422 +/- 2 * 0.032\n",
    "# iter:  9/10 +- elapsed:  85.950 sec - best acc.: 0.7481 at {'kernel_params': {'sigma': 0.1, 'gamma': 0.042857142857142858}, 'sigma_n': 1e-08}\n",
    "# iter: 10/10 ++ elapsed:  91.393 sec - mean acc.: 0.5288 +/- 2 * 0.012\n",
    "\n",
    "\n",
    "\n",
    "# [PCA n_components = 40]\n",
    "\n",
    "\n",
    "# Training GPClassifier on 1195 samples x 40 features.\n",
    "# 2-fold CV for each of 5 params combinations == 10 fits ...\n",
    "\n",
    "# iter:  1/10 +- elapsed:  14.542 sec   ...\n",
    "# iter:  2/10 ++ elapsed:  28.153 sec - mean acc.: 0.5832 +/- 2 * 0.016\n",
    "# iter:  3/10 +- elapsed:  39.689 sec - best acc.: 0.5832 at {'kernel_params': {'sigma': 0.1, 'gamma': 0.0074999999999999997}, 'sigma_n': 1e-08}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### more thoroughly"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "n_components = 20\n",
    "whiten = False\n",
    "\n",
    "X = pca_full.set_params(n_components=n_components, whiten=whiten).transform(X)\n",
    "X = StandardScaler(copy=False, with_mean=True, with_std=False).fit_transform(X)\n",
    "\n",
    "sigma_n = [0., 1e-8, 1e-6, 1e-4, 1e-2]\n",
    "sigma_f = np.logspace(-2., 1., 6)\n",
    "gamma = np.linspace(0.04, 0.12, 16, True)\n",
    "param_grid = [{'sigma_n': sigma_n, 'kernel_params': [dict(sigma=sigma, gamma=gamma_) for gamma_ in gamma]} for sigma in sigma_f]\n",
    "grid_cv = GridSearchCV(model=GPClassifier(algorithm='cg', \n",
    "                                          random_seed=1337, \n",
    "                                          max_iter=200, \n",
    "                                          tol=1e-8, \n",
    "                                          cg_tol=1e-7, \n",
    "                                          n_samples=1500), \n",
    "                       param_grid=param_grid,\n",
    "                       train_test_splitter_params=dict(shuffle=True, random_seed=1337), \n",
    "                       n_splits=2, \n",
    "                       refit=True,\n",
    "                       verbose=True)\n",
    "grid_cv.number_of_combinations() # 480\n",
    "grid_cv.fit(X, y);\n",
    "# Training GPClassifier on 1195 samples x 20 features.\n",
    "# 2-fold CV for each of 480 params combinations == 960 fits ...\n",
    "\n",
    "# iter:   1/960 +- elapsed:   1.409 sec   ...\n",
    "# iter:   2/960 ++ elapsed:   2.614 sec - mean acc.: 0.6368 +/- 2 * 0.023\n",
    "# iter:   3/960 +- elapsed:   3.875 sec - best acc.: 0.6368 at {'kernel_params': {'sigma': 0.01, 'gamma': 0.040000000000000001}, 'sigma_n': 0.0}\n",
    "# ...\n",
    "# ...\n",
    "# ...\n",
    "# iter: 958/960 ++convergence is not reached\n",
    "#  elapsed: 9239.23 sec - mean acc.: 0.2006 +/- 2 * 0.075\n",
    "# iter: 959/960 +-convergence is not reached\n",
    "#  elapsed: 9253.45 sec - best acc.: 0.8677 at {'kernel_params': {'sigma': 0.63095734448019303, 'gamma': 0.082666666666666666}, 'sigma_n': 0.0}\n",
    "# iter: 960/960 ++convergence is not reached\n",
    "#  elapsed: 9267.46 sec - mean acc.: 0.7169 +/- 2 * 0.094"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# df = grid_cv.to_df()\n",
    "# df.to_excel('cv_results/gp_2_full.xlsx')\n",
    "df.sort_values(by='mean_score', ascending=False).head(64).to_excel('cv_results/gp_2_best.xlsx')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### PCA whitening"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "for n_components in xrange(5, 151, 5):\n",
    "    gamma = np.array([0.3, 0.6, 1.5, 3.0, 5.1]) / n_components\n",
    "    param_grid = {'sigma_n': [1e-8],\n",
    "                  'kernel_params': [dict(sigma=0.1, gamma=gamma_) for gamma_ in gamma]}\n",
    "    grid_cv_params = dict(model=GPClassifier(algorithm='cg', random_seed=1337, tol=1e-8, cg_tol=1e-7, n_samples=1500), \n",
    "                           param_grid=param_grid,\n",
    "                           train_test_splitter_params=dict(shuffle=True, random_seed=1337), \n",
    "                           n_splits=2, \n",
    "                           refit=True,\n",
    "                           verbose=True)\n",
    "    print \"[PCA n_components = {0}]\\n\\n\".format(n_components)\n",
    "    X_current = pca_full.set_params(n_components=n_components, whiten=True).transform(X)\n",
    "    grid_cv = GridSearchCV(**grid_cv_params).fit(X_current, y)\n",
    "    df = grid_cv\\\n",
    "         .to_df()\\\n",
    "         .sort_values(by='mean_score', ascending=False)\\\n",
    "         .to_excel('cv_results/gp_pca_whiten_{0}_{1:.4f}.xlsx'.format(n_components, grid_cv.best_score_))\n",
    "    print \"\\n\\n\"\n",
    "# the best is 0.79.. <-- worse"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Approach #3. Exponential decay on the normalized explained variance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "pca_full = load_model('models/pca_full.json')\n",
    "X, y = load_mnist(mode='train', path='data/')\n",
    "X /= 255.\n",
    "tts = TrainTestSplitter(random_seed=1337, shuffle=True)\n",
    "indices, _ = tts.split(y, train_ratio=0.03, stratify=True) # 1794 samples\n",
    "X = X[indices]\n",
    "y = y[indices]\n",
    "X = pca_full.set_params(n_components=20, whiten=True).transform(X)\n",
    "X = StandardScaler(copy=False, with_mean=True, with_std=False).fit_transform(X)\n",
    "z = pca_full.explained_variance_ratio_[:20]\n",
    "z /= sum(z)\n",
    "train, test = tts.split(y, train_ratio=0.5, stratify=True)\n",
    "# for alpha in np.logspace(-6., 2., 9):\n",
    "# for alpha in np.logspace(-3., 1.2, 9):\n",
    "# for alpha in np.arange(1.4, 9.8, 0.4):\n",
    "# for alpha in np.arange(5.4, 6.6, 0.1):\n",
    "for alpha in np.arange(6.05, 6.15, 0.01):\n",
    "    X_train = X[train] * np.exp(alpha * z)\n",
    "    X_test  = X[test]  * np.exp(alpha * z)\n",
    "    gp = GPClassifier(algorithm='cg',\n",
    "                      sigma_n=1e-8,\n",
    "                      kernel_params=dict(sigma=0.1, gamma=0.075),\n",
    "                      n_samples=1500,\n",
    "                      tol=1e-7,\n",
    "                      max_iter=200,\n",
    "                      random_seed=1337,\n",
    "                      cg_tol=1e-7)\n",
    "    gp.fit(X_train, y[train])\n",
    "    acc = gp.evaluate(X_test, y[test])\n",
    "    print \"{0:.4f}, alpha = {1}\".format(acc, alpha)\n",
    "# 0.8122, alpha = 0.01\n",
    "# 0.8111, alpha = 0.1\n",
    "# 0.8211, alpha = 1.0\n",
    "# -----\n",
    "# 0.8111, alpha = 0.125892541179\n",
    "# 0.8122, alpha = 0.421696503429\n",
    "# 0.8244, alpha = 1.41253754462\n",
    "# 0.8511, alpha = 4.73151258961\n",
    "# 0.4056, alpha = 15.8489319246\n",
    "# -----\n",
    "# 0.8478, alpha = 4.6\n",
    "# 0.8500, alpha = 5.0\n",
    "# 0.8433, alpha = 5.4\n",
    "# 0.8578, alpha = 5.8\n",
    "# 0.8544, alpha = 6.2\n",
    "# 0.8500, alpha = 6.6\n",
    "# ----\n",
    "# 0.8578, alpha = 5.9\n",
    "# 0.8578, alpha = 6.0\n",
    "# 0.8589, alpha = 6.1\n",
    "# 0.8544, alpha = 6.2\n",
    "# ----\n",
    "# 0.8556, alpha = 6.08\n",
    "# 0.8589, alpha = 6.09\n",
    "# 0.8589, alpha = 6.1\n",
    "# 0.8556, alpha = 6.11"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### more thoroughly"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "pca_full = load_model('models/pca_full.json')\n",
    "X, y = load_mnist(mode='train', path='data/')\n",
    "X /= 255.\n",
    "# st = StandardScaler(copy=False, with_mean=True, with_std=False)\n",
    "# X = st.fit_transform(X)\n",
    "tts = TrainTestSplitter(random_seed=1337, shuffle=True)\n",
    "indices, _ = tts.split(y, train_ratio=0.02, stratify=True) # 1195 samples\n",
    "X = X[indices]\n",
    "y = y[indices]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### first exp(alpha * z) and after that mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "n_components = 20\n",
    "whiten = True\n",
    "X = pca_full.set_params(n_components=n_components, whiten=whiten).transform(X)\n",
    "alpha = 6.1\n",
    "\n",
    "z = pca_full.explained_variance_ratio_[:20]\n",
    "z /= sum(z)\n",
    "X *= np.exp(alpha * z)\n",
    "X = StandardScaler(copy=False, with_mean=True, with_std=False).fit_transform(X)\n",
    "\n",
    "sigma_n = [0., 1e-4, 1e-2]\n",
    "sigma_f = [0.1, 0.3, 0.5, 0.7, 0.9]\n",
    "gamma = np.linspace(0.08, 0.11, 7, True)\n",
    "param_grid = [{'sigma_n': sigma_n, 'kernel_params': [dict(sigma=sigma, gamma=gamma_) for gamma_ in gamma]} for sigma in sigma_f]\n",
    "grid_cv = GridSearchCV(model=GPClassifier(algorithm='cg', \n",
    "                                          random_seed=1337, \n",
    "                                          max_iter=200, \n",
    "                                          tol=1e-8, \n",
    "                                          cg_tol=1e-7, \n",
    "                                          n_samples=1500), \n",
    "                       param_grid=param_grid,\n",
    "                       train_test_splitter_params=dict(shuffle=True, random_seed=1337), \n",
    "                       n_splits=2, \n",
    "                       refit=True,\n",
    "                       verbose=True)\n",
    "print grid_cv.number_of_combinations() # 105\n",
    "grid_cv.fit(X, y);\n",
    "# Training GPClassifier on 1195 samples x 20 features.\n",
    "# 2-fold CV for each of 105 params combinations == 210 fits ...\n",
    "\n",
    "# iter:   1/210 +-convergence is not reached\n",
    "#  elapsed:   9.902 sec   ...\n",
    "# iter:   2/210 ++convergence is not reached\n",
    "#  elapsed:  19.138 sec - mean acc.: 0.7798 +/- 2 * 0.030\n",
    "# iter:   3/210 +-convergence is not reached\n",
    "#  elapsed:  28.945 sec - best acc.: 0.7798 at {'kernel_params': {'sigma': 0.1, 'gamma': 0.080000000000000002}, 'sigma_n': 0.0}\n",
    "# ...\n",
    "# ...\n",
    "# ...\n",
    "# iter: 208/210 ++convergence is not reached\n",
    "#  elapsed: 2135.44 sec - mean acc.: 0.7606 +/- 2 * 0.022\n",
    "# iter: 209/210 +-convergence is not reached\n",
    "#  elapsed: 2145.34 sec - best acc.: 0.8702 at {'kernel_params': {'sigma': 0.7, 'gamma': 0.080000000000000002}, 'sigma_n': 0.01}\n",
    "# iter: 210/210 ++convergence is not reached\n",
    "#  elapsed: 2155.47 sec - mean acc.: 0.7615 +/- 2 * 0.022"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df = grid_cv.to_df()\n",
    "df.to_excel('cv_results/gp_3_full.xlsx')\n",
    "df.sort_values(by='mean_score', ascending=False).head(64).to_excel('cv_results/gp_3_best.xlsx')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Approach #4. RQ Kernel"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.1 find reasonable ranges for params for PCA-20"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "n_components = 20\n",
    "whiten = False\n",
    "\n",
    "X = pca_full.set_params(n_components=n_components, whiten=whiten).transform(X)\n",
    "X = StandardScaler(copy=False, with_mean=True, with_std=False).fit_transform(X)\n",
    "\n",
    "sigma_n = [0., 1e-8, 1e-6]\n",
    "l = np.logspace(-1., 2., 12)\n",
    "alpha = np.logspace(0., 2., 5)\n",
    "\n",
    "param_grid = [{'sigma_n': sigma_n, \n",
    "               'kernel_params': [dict(sigma=0.1, alpha=alpha_, l=l_) for alpha_ in alpha]} for l_ in l]\n",
    "grid_cv = GridSearchCV(model=GPClassifier(algorithm='cg', \n",
    "                                          kernel='RationalQuadratic',\n",
    "                                          random_seed=1337, \n",
    "                                          max_iter=200, \n",
    "                                          tol=1e-8, \n",
    "                                          cg_tol=1e-7, \n",
    "                                          n_samples=1500), \n",
    "                       param_grid=param_grid,\n",
    "                       train_test_splitter_params=dict(shuffle=True, random_seed=1337), \n",
    "                       n_splits=2, \n",
    "                       refit=True,\n",
    "                       verbose=True)\n",
    "grid_cv.number_of_combinations() # 180\n",
    "grid_cv.fit(X, y);\n",
    "# Training GPClassifier on 1195 samples x 20 features.\n",
    "# 2-fold CV for each of 180 params combinations == 360 fits ...\n",
    "\n",
    "# iter:   1/360 +-convergence is not reached\n",
    "#  elapsed:   8.978 sec   ...\n",
    "# iter:   2/360 ++convergence is not reached\n",
    "#  elapsed:  17.204 sec - mean acc.: 0.1138 +/- 2 * 0.002\n",
    "# iter:   3/360 +-convergence is not reached\n",
    "#  elapsed:  26.859 sec - best acc.: 0.1138 at {'kernel_params': {'alpha': 1.0, 'sigma': 0.1, 'l': 0.10000000000000001}, 'sigma_n': 0.0}\n",
    "# ...\n",
    "# ...\n",
    "# ...\n",
    "# iter: 358/360 ++convergence is not reached\n",
    "#  elapsed: 2948.18 sec - mean acc.: 0.1121 +/- 2 * 0.000\n",
    "# iter: 359/360 +-convergence is not reached\n",
    "#  elapsed: 2959.30 sec - best acc.: 0.8025 at {'kernel_params': {'alpha': 100.0, 'sigma': 0.1, 'l': 2.3101297000831593}, 'sigma_n': 0.0}\n",
    "# iter: 360/360 ++convergence is not reached\n",
    "#  elapsed: 2971.48 sec - mean acc.: 0.1121 +/- 2 * 0.000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df = grid_cv.to_df()\n",
    "df.to_excel('cv_results/gp_rq_full.xlsx')\n",
    "df.sort_values(by='mean_score', ascending=False).head(64).to_excel('cv_results/gp_rq_best.xlsx')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### [discarded] 4.2 PCA components (whiten|x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### [discarded] 4.3 Exponential decay ..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Approach #NN"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X = np.load('data/train_feats.npy')\n",
    "_, y = load_mnist('train', 'data/')\n",
    "tts = TrainTestSplitter(shuffle=True, random_seed=1337)\n",
    "indices, _ = tts.split(y, train_ratio=1300./60000., stratify=True)\n",
    "y = y[indices]\n",
    "y = one_hot(y)\n",
    "X = X[indices]\n",
    "\n",
    "# sigma_n = [0., 1e-4, 1e-2]\n",
    "sigma_n = [0, 1e-8, 1e-6]\n",
    "# sigma_f = [0.1, 1., 10.]\n",
    "# sigma_f = np.logspace(-1., 1., 5) \n",
    "sigma_f = np.logspace(-0.9, -0.2, 5)\n",
    "# length_scale = np.logspace(-1., 2., 19)\n",
    "# gamm = 0.5/length_scale**2\n",
    "# gamma = np.logspace(-4., -2.1, 19) \n",
    "gamma = np.logspace(-3.7, -3., 11)\n",
    "param_grid = [{'sigma_n': sigma_n, \n",
    "               'kernel_params': [dict(sigma=sigma, gamma=gamma_) for gamma_ in gamma]} for sigma in sigma_f]\n",
    "grid_cv = GridSearchCV(model=GPClassifier(algorithm='cg', \n",
    "                                          random_seed=1337, \n",
    "                                          max_iter=200, \n",
    "                                          tol=1e-8, \n",
    "                                          cg_tol=1e-7, \n",
    "                                          n_samples=1500), \n",
    "                       param_grid=param_grid,\n",
    "                       train_test_splitter_params=dict(shuffle=True, random_seed=1337), \n",
    "                       n_splits=2, \n",
    "                       refit=True,\n",
    "                       verbose=True)\n",
    "grid_cv.number_of_combinations() # 44\n",
    "grid_cv.fit(X, y);\n",
    "\n",
    "# Training GPClassifier on 1295 samples x 128 features.\n",
    "# 2-fold CV for each of 171 params combinations == 342 fits ...\n",
    "\n",
    "# iter:   1/342 +- elapsed:   3.584 sec   ...\n",
    "# ...\n",
    "# ...\n",
    "# ...\n",
    "# iter: 226/342 ++ elapsed: 4405.15 sec - mean acc.: 0.1042 +/- 2 * 0.001\n",
    "# iter: 227/342 +- elapsed: 4432.84 sec - best acc.: 0.9846 at {'kernel_params': {'sigma': 0.1, 'gamma': 0.00050000000000000001}, 'sigma_n': 0.0}\n",
    "# iter: 228/342 ++ elapsed: 4460.72 sec - mean acc.: 0.1042 +/- 2 * 0.001\n",
    "\n",
    "# --------------------------------------------------------------\n",
    "\n",
    "# Training GPClassifier on 1295 samples x 128 features.\n",
    "# 2-fold CV for each of 285 params combinations == 570 fits ...\n",
    "\n",
    "# iter:   1/570 +- elapsed:  28.242 sec   ...\n",
    "# iter:   2/570 ++ elapsed:  51.745 sec - mean acc.: 0.9799 +/- 2 * 0.005\n",
    "# ...\n",
    "# ...\n",
    "# ...\n",
    "# iter: 418/570 ++ elapsed: 9589.25 sec - mean acc.: 0.5370 +/- 2 * 0.119\n",
    "# iter: 419/570 +- elapsed: 9605.40 sec - best acc.: 0.9861 at {'kernel_params': {'sigma': 0.31622776601683794, 'gamma': 0.00033711476775509616}, 'sigma_n': 0.0}\n",
    "# iter: 420/570 ++ elapsed: 9620.88 sec - mean acc.: 0.6041 +/- 2 * 0.119\n",
    "\n",
    "# ---------------------------------------------------------------\n",
    "\n",
    "# Training GPClassifier on 1096 samples x 128 features.\n",
    "# 2-fold CV for each of 165 params combinations == 330 fits ...\n",
    "\n",
    "# iter:   1/330 +-convergence is not reached\n",
    "#  elapsed:  21.402 sec   ...\n",
    "# iter:   2/330 ++convergence is not reached\n",
    "#  elapsed:  41.644 sec - mean acc.: 0.9845 +/- 2 * 0.006\n",
    "# iter:   3/330 +-convergence is not reached\n",
    "#  elapsed:  59.386 sec - best acc.: 0.9845 at {'kernel_params': {'sigma': 0.12589254117941673, 'gamma': 0.00019952623149688788}, 'sigma_n': 0}\n",
    "# ...\n",
    "# ...\n",
    "# ...\n",
    "# iter: 328/330 ++convergence is not reached\n",
    "#  elapsed: 7163.06 sec - mean acc.: 0.8219 +/- 2 * 0.129\n",
    "# iter: 329/330 +-convergence is not reached\n",
    "#  elapsed: 7184.70 sec - best acc.: 0.9899 at {'kernel_params': {'sigma': 0.42169650342858211, 'gamma': 0.00085113803820237679}, 'sigma_n': 0}\n",
    "# iter: 330/330 ++convergence is not reached\n",
    "#  elapsed: 7208.78 sec - mean acc.: 0.8219 +/- 2 * 0.129"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df = grid_cv.to_df()\n",
    "df.to_excel('cv_results/gp_nn_full.xlsx')\n",
    "df.sort_values(by='mean_score', ascending=False).to_excel('cv_results/gp_nn_best.xlsx')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Approach #RBM"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X = np.load('data/rbm_train.npy')\n",
    "_, y = load_mnist('train', 'data/')\n",
    "tts = TrainTestSplitter(shuffle=True, random_seed=1337)\n",
    "indices, _ = tts.split(y, train_ratio=1100./60000., stratify=True) \n",
    "X = X[indices]\n",
    "y = y[indices]\n",
    "y = one_hot(y)\n",
    "\n",
    "sigma_n = [0.]\n",
    "sigma_f = [0.1]\n",
    "length_scale = np.logspace(-1., 2., 13)\n",
    "# gamma = np.logspace(-3.7, -3., 11)\n",
    "gamma = np.logspace(-5., -0., 19) \n",
    "param_grid = [{'sigma_n': sigma_n, \n",
    "               'kernel_params': [dict(sigma=sigma, gamma=gamma_) for gamma_ in gamma]} for sigma in sigma_f]\n",
    "grid_cv = GridSearchCV(model=GPClassifier(algorithm='cg', \n",
    "                                          random_seed=1337, \n",
    "                                          max_iter=200, \n",
    "                                          tol=1e-8, \n",
    "                                          cg_tol=1e-7, \n",
    "                                          n_samples=1500), \n",
    "                       param_grid=param_grid,\n",
    "                       train_test_splitter_params=dict(shuffle=True, random_seed=1337), \n",
    "                       n_splits=2, \n",
    "                       refit=True,\n",
    "                       verbose=True)\n",
    "print grid_cv.number_of_combinations()\n",
    "grid_cv.fit(X, y)\n",
    "#\n",
    "# [*] 0.683... D:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df = grid_cv.to_df()\n",
    "df.to_excel('cv_results/gp_rbm_full.xlsx')\n",
    "df.sort_values(by='mean_score', ascending=False).to_excel('cv_results/gp_rbm_best.xlsx')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Misc\n",
    "### Plot confusion matrices for final models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "_, y_test = load_mnist('test', 'data/')\n",
    "# knn_pred = np.load('data/knn_pred.npy')\n",
    "# nn_pred = unhot(np.load('data/nn_pred.npy'))\n",
    "# logreg_pred = unhot(np.load('data/logreg_pred.npy'))\n",
    "gp_pred = unhot(np.load('data/gp_pred.npy'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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gBn6/fpi9x9fRul3TbJffwKMulx+eosaXVVSWOVOVWl9TvW4DvqjXkJr13Pmi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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fbc1900bc90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# C = confusion_matrix(y_test, knn_pred)\n",
    "# ax = plot_confusion_matrix(C)\n",
    "# plt.title(\"Confusion matrix for k-NN model\", fontsize=18)\n",
    "# plt.savefig('confusion_matrix_knn.png', dpi=144)\n",
    "\n",
    "# C = confusion_matrix(y_test, knn_pred)\n",
    "# ax = plot_confusion_matrix(C)\n",
    "# plt.title(\"Confusion matrix for k-NN model\", fontsize=18)\n",
    "# plt.savefig('confusion_matrix_knn.png', dpi=144)\n",
    "\n",
    "# C = confusion_matrix(y_test, nn_pred)\n",
    "# ax = plot_confusion_matrix(C)\n",
    "# plt.title(\"Confusion matrix for NN model\", fontsize=18)\n",
    "# plt.savefig('confusion_matrix_nn.png', dpi=144)\n",
    "\n",
    "# C = confusion_matrix(y_test, logreg_pred)\n",
    "# ax = plot_confusion_matrix(C)\n",
    "# plt.title(\"Confusion matrix for LogReg model\", fontsize=18)\n",
    "# plt.savefig('confusion_matrix_logreg.png', dpi=144)\n",
    "\n",
    "C = confusion_matrix(y_test, gp_pred)\n",
    "ax = plot_confusion_matrix(C)\n",
    "plt.title(\"Confusion matrix for GP model\", fontsize=18)\n",
    "plt.savefig('confusion_matrix_gp.png', dpi=144)"
   ]
  }
 ],
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