HW4-apm382-Problem1-DG.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <p style=\"text-align: center;\">MIS 382N: Advanced Predictive Modeling</p>\n",
    "# <p style=\"text-align: center;\">Assignment 4</p>\n",
    "## <p style=\"text-align: center;\">Total points: 50 </p>\n",
    "## <p style=\"text-align: center;\">Due: Mon, November 14</p>\n",
    "\n",
    "\n",
    "\n",
    "Your homework should be written in a **Jupyter notebook**. Please submit **only one** ipynb file from each group, and include the names of all the group members. Also, please make sure your code runs and the graphics (and anything else) are displayed in your notebook before submitting."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Problem 1 - MNIST (15 pts)\n",
    "In this question you classify hand-written digits. We want to use MNIST data set and try Multi-layer Perceptron (MLP) classifier using sklearn package in Python. In order to simplify the problem, we classify digits into 8 classes (digits 0,1,2,...7) and ignore records for digits 8 and 9.  Use the code below to access the data set and extract data with labels 0 to 7, and split the data set into train set and test set.\n",
    "\n",
    "1. Fit a Multilayer Perceptron Classifier using the standard options on sklearn's MLP on train data. Report the root MSE for both train and test data. (5 pts)\n",
    "\n",
    "    Use these parameters for your model: \n",
    "                    {hidden_layer_sizes=(50,), max_iter=10, alpha=1e-4,\n",
    "                    solver='sgd', verbose=10, tol=1e-4, random_state=42,\n",
    "                    learning_rate_init=.1}\n",
    "                    \n",
    "2. To find better parameters for the MLP Classifier model, try an exhaustive search over all parameters of the data. Use sklearn's GridSearchCV to find the best subset of parameters from the set:\n",
    "                    { alpha = [0.1,0.01,0.001], activation : ['logistic', 'relu'] }\n",
    "    which parameters resulted in a more accurate model? Can you explain why? (5 pts)\n",
    "\n",
    "3. Select 5 misclassified images and display them. (5 pts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING: pylab import has clobbered these variables: ['mat']\n",
      "`%matplotlib` prevents importing * from pylab and numpy\n"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from sklearn.datasets import fetch_mldata\n",
    "from sklearn.model_selection import (train_test_split,KFold)\n",
    "from sklearn.neural_network import MLPClassifier\n",
    "from sklearn import metrics\n",
    "from sklearn.grid_search import GridSearchCV\n",
    "\n",
    "%pylab inline\n",
    "\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "\n",
    "mnist = fetch_mldata(\"MNIST original\")\n",
    "# rescale the data, use the traditional train/test split\n",
    "X = (mnist.data / 255.)[:48200]\n",
    "y = mnist.target[:48200]\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(X,y,test_size = 0.1, random_state=42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(43380L, 784L)"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 1 - Fit a MLP"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 1, loss = 0.24522635\n",
      "Iteration 2, loss = 0.10589741\n",
      "Iteration 3, loss = 0.07488529\n",
      "Iteration 4, loss = 0.05895084\n",
      "Iteration 5, loss = 0.04782934\n",
      "Iteration 6, loss = 0.03945315\n",
      "Iteration 7, loss = 0.03320940\n",
      "Iteration 8, loss = 0.02872414\n",
      "Iteration 9, loss = 0.02451143\n",
      "Iteration 10, loss = 0.02132893\n",
      "Precision:0.99563632295\n",
      "Recall: 0.995620101429\n",
      "Accuracy: 0.995620101429\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x15927c88>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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DdtZh2jzciq2bf6Z9m14seucTuvR6tFTrtuijj6lSpTJzpk1h8oSxjBgztlTLK0ogt6U/\nyvv6Acya9zJJyaPIycmxPdaXy5bjcDiYOyOFHl06M2Fyiu0x8zvRwPcFvcqacpMUv/9hLddefRUA\nF13QgI2bt5R4Wdc2uZIft/7C+GnDmZg6giX/W8l5F9Tn+9XWkNXLv/yaqxpfDkDtujV4dtRTzH7r\nRVrdewsAl15xISuWrPJ+dhVXNb6sNKvGTTe0oEfXzgB43B7Cw+2t4AdyW/qjvK8fQO2aNZkwZqTt\ncQCaxzfh2UFPA7ArLY1KcXFBievrRAPfF/RfWVNuTp+zsrKIqxh7/H14WBhutxtnCYZarFK1Mqef\ncQo9OgykZu3TmThjBA7nXzsvK+swcXGxREdH8crsd5g74w3CwsKY8eoLbFonxFaMJfNQlvXZzGxi\nfcpVEtFRUcfX8cmBCfTq1qVUyytKILelP8r7+gG0aBbPrrQ025afn9PpJCFpOF8sWcrYUclBi3s8\nfhmsAfqr3NQUY2NjycrOPv7e7faU+CA/8OdBVixdTW5uLtt/+Z2jR3OIi/vrSxQbG01GRiaHDx/h\n5Vlvk3M0h8PZh1m9cg31zz+LzEOZxMTGWJ+tGMOhjMzSrRywe/ceOnbryR23tuTmG68v9fIKE8ht\n6a/yvn7/huSkZ1j49mskJY/kyJGj/3ZxQoZtR4Ix5gtjzFf5XiuNMV/ZEe+ShhexbMVKANau38A5\nZ9cr8bLWfLuea+OvBODkU6oRHRPNqhXfc1mjhgA0bnoV33+zjrpn1Wbu29ZF8/DwMC654kI2rd/K\nmm830KS5dXp2XbOrjp92l9S+9P106dWHvr260+q2lqValj8CuS39Ud7Xz5cHj+0xFn64mBmz5wIQ\nGRGJ0+nE6Qxuzc3hcPj9KmvsPH0eAEwHWgMuG+MA1unJym9W80hH69RrWGJCiZe17POvufSKi3j5\nvRQcDgfDE8ax6/fdJI3uR3iFcH75cTuffvglAAvf+ZiX30vh2LFjvP/Wx/zy43Z2/ZbG8HGDmP3m\ni+Tk5DCg17BSrVvq7LkcOpTJ1NRZpMyYhcMBUyaMIyIiolTLPZFAbkt/lPf18xWMa2jXN2/K4CHJ\ntOv8OLm5uQx4so9t2/JEQvn02eHx2PfLZYzpB/woIu8Wd96cjHT7f1J9aCezSlkiKlUrdUZ7vElv\nv7+/k5eOL1MZ1NYbLSIyxs7lK6VUoJWbu89KqbIjyJcwA0qTolIq4MriDRR/aVJUSgVcKN9o0aSo\nlAq4UK4plr8nVpVSqhS0pqiUCjgduEoppXwE+pqiMeYU4FvgeiAGWARs9f7zFBF50xjTCegMHAOS\nReQDY0wUMB84BcgA2opIemGxNCkqpQIukDnRGBMOpAB5DdYvA8aKyAs+nzkV6AlcipU0lxtjPgG6\nAetEZKgx5j5gMNC7sHiaFJVSZd3zwBRgoPf9ZUB9Y8ydWLXFPsCVwHIRcQEZxphtQEOgMTDaO99H\nWEmxUJoUvYLd7O6eJk8ELdZbSycELZZSELjTZ2NMO2CviHxqjBkEOIBVwHQRWWOMGQg8C/wAHPSZ\nNROoDMT5TD8EVCqy7AEpuVJK+QhgJ7PtgRuMMV8AFwNzgI9EZI333xd4px/k7wkvDvgT6zpinM+0\nA0UF1JqiUirgAvWcoojE5/1tjPkc6Aq8b4zpKSKrgRbAd8BqINkYEwFEA+cCG4CvgJZYN2laAsuK\niqlJUSkVcGH2Nn7uCkwyxuQAu4HOIpJpjJkILMc6xR4kIjnGmCnAHGPMMuAo8GBRC9ekqJQKCSLS\n3OftP4Z7FJFUIDXftMNAm+LE0aSolAo4bfuslFI+yuIoff7SpKiUCjitKSqllI8QzonlJym6XC4S\nkoazKy2NsLAwkhIGULdObVtirduwkfGTpjAzZRJbZCsjx75AeFgYFSpEMGLIYKqedFKxlznulWFk\nZ1qtmPbs/IN3535I98EdAUjbsZsXh8zA4/HwWL+HOe/i+hzOOgxAcu8XOJx9BIAadU9nzLwkHm32\nOC5XbqnXLc8Hiz/h1TfeYv7MaSVaZlFcLheJw0awMy0N1zEXndq3pWmTf1xH13h++Df2X0FCueuw\ncpMUl61Yidudy7zUqaxctZqJk1MYN3pEwOPMmvcyCz9cTEx0NACjx00gof9T1D/7LN58ZwGps+fR\nr0+vYi0zvIK1G57pPPL4tIHjejN34mts/mEbvYZ05sr4S1j15fecdd6ZPNttNJkZWX9bRnRMFB36\nPsixo8cCtm4Am0V49/1FJV6mPxZ99DFVqlRmxJBEDmZkcO9D9iap8hrv39p/BQnl0+ciW7QYYy4K\nRkFKq06dWuTm5uLxeMjMyiS8QgVb4tSuWZMJY/5KXmNGDKP+2WcBkJubS2RUZLGXeaapTVR0JEmT\n+zM0ZQD1LziLkX3Hs/mHbYSHh3FStcpkZVo1wzNqn0r3wR0ZNWswLVo1Ob6M7oM7Mnfi6xw9khOw\ndTtw4CAvTpnGgCcLbT9fajfd0IIeXTsD4HF7CA+397e6vMb7t/ZfQRwO/19ljT9753XgvEAEM8ZE\nisjRQCwrv5joGH7flcYd9zzAgYMHmfSCPQMJtmgWz660tOPvq1erCsAPa9fz2pvvMHva5GIv8+jh\nHN6d8wGfLljC6bVPJWlSf7q2eopqp1Zl2NQBZB3K5hfZTlR0JIte/YQF8z4iLMzJ8OmD+HHjz1zd\n4gpWL1vD9h9/L9VB5rtubrebZ5NH0q93LyIiImwdxD06KgqArKwsnhyYQK9uXWyLVZ7j/Vv7ryCh\nXFP0JyluMsYkYjXCPpw3UUSWnmgGY8ztwCSsfs0SROR17z99BDQ/0XylMe+V12h8dSN6Pd6VPXv/\noGO3Hrz72nwq2FRj9LX4k8+YMXsekyc8T5UqlYs9/67taaT9tgeAtB17yDh4iJNOrsK+3el0a9WP\nG+6M57F+DzMhcRoLX/mYYznHOAasX72JM+vXIb7lNaTv2c8NrZtSpVoVhqQMIOGx5FKt0+Ytwo7f\nfmf46DEcOXqUX37ZznMvTKB/H3s6sti9ew+9+w/kgTb3cPON19sS478UL9j7rzzxJylWBZp5X3k8\nFJ7cErAaaTuBN40xUSIyB+x7eKly5UrHT0vi4iricuWSm+vG7py48MPFvLXgPWZOnUSluLiiZyjA\n9XfGU+ecWkwdOYeqJ1chJjaa7s90YMaY+aT9tofs7CO4c93UqHs6/Uf34In7EggLD+P8Swz/e38Z\n3Vr1O76s6R+MI7HrqFKtkwcPDc4/j3dfmw/ArrQ0+ic8a9sXal/6frr06kNC/ye58vLLbInxX4oX\n7P1XkHL9nKKINCvqMwXIEZE/AYwxrYDPjTE7wL46/MMP3Efi0BG07dwNl8tF7+5diSrB9b3icLvd\njB43njNOO43e/QbicMDll15Ct04di7WcTxcs4YkhnRk5czAet5uJz1p3CZ8Y2pljOS6OHjnKpCEz\nOLA/gy8WLef5+UNwHXPx+cJl/P7Lrr8ty+Mp/S9PsA/o1NlzOXQok6mps0iZMQuHA6ZMGEdERITG\nK4GykJBC+e6zw+MpPE8ZY+oAM4C6wHXAK0AHEfm1kHnmAvuAwSKSZYypBXwMVBGRM/wpWE5GenAv\nggSZ9qeoyqqIStVKndHG3T3M7+9v37cHl6kM6k9/ilOBMVidNu4BXgXmFjFPB2Ad3pqhiPyGdfr9\nRolLqpRSQeDPNcXqIvKJMWa0iHiA6caY7oXN4O0SfHa+aXsoYmwEpVT5EMqnz/4kxcPGmJp4a33G\nmMZY/ZIppVSB7O1O0V7+JMU+WMMJnmWM+QHrbvS9tpZKKRXSynVNUUS+NcZcAdTHugYpIlLyZhNK\nqXIvhHOiX838KgOjsG6uTAcGG2Ni7C6YUkr9G/y5+5wKuIB2QGesEbGC192GUirkhDmcfr/KGn+u\nKZ4tIvf4vO9tjFlnV4GUUqGvXJ8+A2KMuTrvjTGmIbDNviIppUKd0+Hw+1XWnLCmaIz5BesxnGjg\nHmPMFiAXq8ccTYpKqXKpsNPnpsEqhFKqfCmXj+SIyHYAY0wEcBOQv4/9opr6qUIEsz3y7dd0C1os\ngIVfTQlqPIpovx9wIfyFD5ZQ3kT+3Gj5CKvjle0+0zxoUlRKnUC5rCn6qC4iDW0viVKq3AjlZn7+\n3H3+3BhzvTGm7D1QpJQqkxwOh9+vssafmuIO4BPAY4wB61TaIyJhdhZMKRW6ymCu85s/SfEJoK6I\n7LC7MEqp8qEsPn/oL3+S4k4g3e6CKKXKj7J4Wuwvf5PiBmPMCuB47zgi0sG2Uiml1L/En6T4gfel\nlFJ+CeGKol9J8QvbSxEALpeLxGEj2JmWhuuYi07t29K0SWNbYq3bsJHxk6YwM2US/RMSSd+/H4/H\nGkryogsv4LnhQ2yJm75/P/c/2pHpL02gbp3apVrWpNdHkZWZDcDunXt5ITEFgGYtr+WOB2+mz8OD\nAWjToRXxt1xDVmY2b816n2+WrgFg/mdT2LndGnh989qtzJ74WonLEox9Z8UYacVwHaNT+7Z8+PGn\npKfvx4OHXbt2e/ddUkDj+vI9buzkcrlISBrOrrQ0wsLCSEoYUOrjpbicIfxMjj9JcQnWw9oOoAJw\nGrAGuMLGchXboo8+pkqVyowYksjBjAzufciepDhr3sss/HAxMdHRADyXPBSAjEOHeKxbT57ua88o\nfS6Xi2EjxwRk2NYKFazd/nTHoX+bfta5dbmp9V8j2tY5uxbxt1xDrwcG4XQ4eGH+cNZ8vYHqp1bl\nx00/k9RrTKnLAsHZd4sW58UYbMV4uB2fvP8O4N13j/eybd/BP48bOy1bsRK3O5d5qVNZuWo1Eyen\nMG70CNvj+grlGy1FPnsoImeKSD3v/2sC1wCb7C9a8dx0Qwt6dO0MgMftITzcn3xffLVr1mTCmJH/\nmD556gweaHMP1apWtSXu2AmTaHNPa045uXqpl1XP1CEqOpLkqYMYNf0ZzIVnE1cplra97mfKqNnH\nP1e7Xg3Wrd5EriuXY8dc7NyRRr36tTnn/HpUP7Uao1MTGfrS09Soc3qpyhOMfXfT9S3o0bVTgTEm\nT0v17rv8LVkD50THjR3q1KlFbm4uHo+HzKxMwitUCErc8qLYD2SLyDfAZcWdzxgTbYyxbXT66Kgo\nYqKjycrK4smBCfTq1sWWOC2axRMW9vdHNPf/+Servv2OO2+/1ZaYCxZ+QNWqJ3FNoysD0sz3yJEc\n3pz9PgldRjBx2AwGPvcET43owbTn5nDk8FHwDqb+67YdXHjZeURGRxJXuSLnX2yIio4ife9+Xpv+\nLk93HMprMxbw9KiepSpPMPbd32M8Q69uVhI+vu9uaxnwmL4KOm7sEhMdw++70rjjngcYOuI5Hrov\n+EMqORz+v8qaIn+SjTGJPm8dwPlY4z8XNd/5wAjgT+BlYAaQa4x5QkQWlay4hdu9ew+9+w/kgTb3\ncPON19sRokCf/u8Lbr3pRtseQ1iw8AOcTicrV61my9ZtJCQNY+LY0SWule78dRe7duwGYNeO3Zxy\nxsm43W56Du5ERGQEtevVoHO/R5k2Zi7vv/YxI1IGsTdtH1vWbuPggQx27dhNbq4bgE1rhKonVyn1\nOgZj3+3es4fe/QfxwL13c/MNVoxP//clt950Q0g/QpLfvFdeo/HVjej1eFf27P2Djt168O5r86kQ\nxBpjKG9Pf85TfNfOg3WN0Z+r6inAYKAu8BbWwFdHsDqYCHhS3Je+ny69+pDQ/0muvLzYFdli8/BX\nle3rb76lS8d2tsWaPW3y8b87dO1B4sD+pTpNv+mu5tQ9pzYvJadS9eST+P3XXXRu1ReAU06vzsAx\nTzBtzFwqVYkjJjaKJ9s+S0xsNMlTE/h122906P0gGQcP8dashdQzdfhjd+keYw3GvrNi9CWhX9+/\nxfh69Wpb911+vseNXSpXrnT88kBcXEVcrlxyc90E8yw6hHOiX6P5lfRWqlNElgBLjDHNRGQvgDHG\nVcLlFSp19lwOHcpkauosUmbMwuGAKRPGERERYUc4HD6/Fb/u2EHNGjVsifOPuAE42Ba/8zlPDn+c\nsXOG4HZ7GDe44K6+Mg4cona9mkx8dQTHco4xY+w8AF5PtU6Zr2xyKbmuXJ5PmFzg/P4Kxr5LnTOX\nQ4cOMTUBiDhEAAAgAElEQVR1Nimps3DgYPL45/l1x2/UPCM4+w7+ftzY5eEH7iNx6Ajadu6Gy+Wi\nd/euAblBVxyhXFN0eE5wkcqn5+0CiUi9whZsjEn1zt9ZRNzeaQOAS0TkvqIKlpORHuRO8sov7U8x\nwEL4C++PiErVSr2Cb3ef4PdOufulJ8rUBi1uz9sPAgnAeD+W3Qm4PS8hev0OTPS7dEqpkBTKj+QU\n2fM2gDHmZGAqcDYQLyLfFbVgbzJ8L9+0+SUvqlIqVIRwTiz6kRxjzAPAemAjcJk/CVEp9d9WLvtT\n9NYOU4BzgJYi8n3QSqWUUv+Swq4pbgZigXeAHt4OZo/TXnKUUidSBiuAfissKT4ZtFIopcqVctkh\nhIjMCWZBlFLlR1m8Vugve3pNUEqpAPEOmjcdMIAb6AocBWZ7328Qke7ez3YCOgPHgGQR+cAYEwXM\nB04BMoC2InLCZlg6Qp9SKuAC3CHE7ViD5TXGajo8AhgHDBKReMBpjGlljDkV6AlcDdwMjDTGVAC6\nAetEpAkwz7uME9KkqJQKuEA+kiMi72HV/gDqYHUyc6mILPNO+wi4AbgSWC4iLhHJALYBDYHGwGKf\nzxba40hhj+S4+Xszv2NYVdVIIENE7Ot8TikV0gJ9SVFE3MaY2cCdwL1YSTDPIaASEAcc9JmeCVTO\nNz3vsydU2I0WJ4AxZgqwAnhZRDzGmLuxqqYqRAS7LfLDzfsFNd78zwPTA7gKHDua+YlIO2PMKcBq\nwLcL8zjgANb1wkr5pv/pnR6X77Mn5M/pcyMRmS8iHm/B3qaMDUWglCpbAnlN0RjzsLczGbC6H8wF\nvjXGxHun3QIsw0qWjY0xEcaYysC5wAbgKyCvF+GW3s+ekD93n7OMMe2BN7CS6CPoONBKqUIE+JGc\nd4BZxpglWDmrF7AFmOG9kbIZeMt7JjsRWI7VD+wgEcnxnu3OMcYsw7pr/WBhwfxJig8Dk7B6t3ED\nn2ElRqWUKlAgc6KIZAMFdTfYtIDPpgKp+aYdBtr4G8+fTma3A7cbY6qKyH5/F6yU+u9ylMcWLXmM\nMRdjDT8QY4y5ClgKtNEOIpRSJxLCDVr8utEyEWgNpIvILqwHIVNsLZVSSv1L/EmKMSKyOe+NiHyK\n9ayiUkoVqFz2p+hjvzGmId4HuY0xDwF6bVEpdULlspccH92AOUADY8wBrKYzD9laqhLweDwMH/08\nsnUbkZERJCUMpFZNe0dpS9+/n/sf7cj0lyZQt05tW2MBrNuwkfGTpjAzZZKtcezYlqPmJZKdeRiA\nvbv28dFrn9G+34O4c90cy3Ex6dkZHDpwiBZ3NqFF63hyXbm8M3Mha1asp1XbW2h49QXggdhKMVSu\nWpmut/QtU+vnj1Def8VVBiuAfvMnKUaJSGNjTCwQJiIZ3hsuZcrnXy4lJyeH+TOnsW7DRsaMn8jE\n50fbFs/lcjFs5JigDR05a97LLPxwMTHR0UV/uJQCvS3DK1iH2dBuf7U8eXZqf1JHz+e3n3bSonU8\nd7a9hffnLebm+1rw9MNDiIyKYOiMgaz7ehPvzfmI9+Z8BMDT43oxb/wbZWr9/BHK+++/5oTXFI0x\n1xpjmgDvGmOuAy4DLjbGNAfmBquA/vr+h7Vce7WVqy+6oAEbN2+xNd7YCZNoc09rTjm5uq1x8tSu\nWZMJY0YGJVagt2Wd+rWIjI5k0It9eealpzi7QT3GD0zht592AhAW5iQn5xhnNziTLT9sw53r5nDW\nEXb/tofa59Q8vpwrm11KZkYWG1ZvPlEovwT7WIHQ3n8lEuBucoKpsBstNwBDgNOBod6/hwADsUb2\n85u3vaKtsrKyiKsYe/x9eFgYbre7kDlKbsHCD6ha9SSuaXRl0IYcbtEsnrCwsKDECvS2zDmSw/vz\nFjOi5zhmjJpLr+GdyPjzEAD1LzqLm+5tzgevfEJ0bPTxU2yAI9lHian4V83qznYteXP6+yUuR55g\nHit5Qnn/lUS5vNEiIkkAxphHgFdFxOVtUhMhIlmFLdQYUz/fpLnGmEe9y91auiIXLDY2lqzs7OPv\n3W4PTqc9PaMtWPgBTqeTlatWs2XrNhKShjFx7GiqVa1qS7xgC/S23LV9N7t/2wPA7t/2cuhgFlWq\nV+bci8+hdbtbGfnEeDIPZnE46zAxsX8lwaiYKLIPWeWoUfd0MjOy2bvzjxKXI08wj5V/Q1lYvzKY\n6/zmz5Y6Cqzx/l0b2GKMaVXEPJ8B72M9zzgVq8fcqdj4fOMlDS9i2YqVAKxdv4Fzzq5nVyhmT5vM\nzJRJzEyZxLn1zyE5aXDQEqIH+6umgd6WzVtdx6O97wfgpOpViI6JosFl53LTvc1J6jKafbutpvQ/\nbvwFc/E5hIWHER0bTY26p7PDe4p9YaPz+eGr9aUqR55gHiv5heL+KwmH0+H3q6zx50bLM3g7ZRSR\nn4wxlwGfkG+g+3wux0qAU0TkU2PMFyLSrNSlLUSLZvGs/GY1j3TsAsCwxAQ7wx0X7F9EB/YHDPS2\n/HzBMh5/tgNDpg/A4/YwZdgsBrzwBH/sTuep53uABzZ9L7w1/X0+ev0zhqUOBBy8+tLb5LpyATi9\n9qmsW7WptKsG/HvHCoTm/iuJUK4pOjxFXBQzxmwRkXPzTVsrIg2LmC8ceB7YC9xQ3KSYk5EepKt1\nKtC0P8XQFlGpWqlT2tcjZ/n9/b1qYPsylUL9qSkuN8a8Crzsfd8GWFnUTCLiAnobY9qhwx4o9Z8S\nyjVFf5Jid6zBYLpgDUmwFJjsbwARmY016pZS6j+iLN5V9ldhY7ScJiK7gVOxOpj1fWL2NGCHzWVT\nSqmgK6ymOAO4DViC1e7Zke//wb+lpZQKCSFcUSz0OcXbvP8/M3jFUUqVB46w0M2KhZ0+zyxsRhHp\nEPjiKKXKg1C+pljYXeEl3lcccAbwOdbziScVMZ9SSoWswk6f5wAYYx4HrhYRt/f9G8DXwSmeUioU\nhXBF0a9HcioDVYF93venAhVtK5FSKuSF8umzP0kxGVhnjFkBhAGNsJ5bVEqpAoVwTvRriNN5xpjP\ngGuwHsXpKiJ7bS+ZUip0hXBW9GeI0wigPXAuVg3xCWPMKBHJsbtwKjQFuy3yE7cNDWq8CYsSgxov\nFJXF3m/85c9d5JewriFeitXM72wg1c5CKaVCWwh3vO1XUrxMRAYBx0QkG2gLXGJvsZRSoaxc9rzt\nw+M9hc7rCqi6z99KKfUPZTDX+c2fmuJ4rJ60TzPGjAe+BV6wtVRKKfUv8aem+BHwHdAM65Gc20Vk\nna2lUkqFthCuKvqTFJeJyHlAYPqCV0qVe6F899mfpLjWO6LfN8Dx8SdFRPtTVEoVqLwnxUbely/t\nT1EpVS7506IlJPpT9Hg8DB/9PLJ1G5GRESQlDKRWzRoarwRcLheJw0awMy0N1zEXndq3pWmTxrbE\nAvvWLa5KRQZMf4oJfV6iQmQFHnyyDbm5uez97Q/mP/caAPGtG3PVzVficXv47PUv+P7LH4iKiaRj\nUjsioyM4luNi9rB5HDqQWaIyrNuwkfGTpjAzZRJbZCvd+/ajbu1aALS5+y5uur55qdczv2AfmwUJ\n4UuKhfaneAYwCTgHWA4MFJEDwSpYcX3+5VJycnKYP3Ma6zZsZMz4iUx8frTGK4FFH31MlSqVGTEk\nkYMZGdz7kL1J0Y51c4Y5eeCpNuQcsRpe3dr+ZhbNWszm1Vto98wjXHDV+fyy6Vca33EtIzo8R0RU\nBRLnDuL7L3/g6lsasfOnXSyYupBrb72KGx5swTuTCxvRt2Cz5r3Mwg8XExMdDcCmLULbhx7g0Qfv\nL9W6FSXYx2ZBQvn0ubBHcmYBW4B+QBSleAzHGOM0xtQwxtjWD+P3P6zl2quvAuCiCxqwcfMWu0KV\n+3g33dCCHl07A+BxewgP9+cqS8nZsW53P96KpQtWcDD9IAC/bf2dilViAYiKiSQ3N5esjGxGdHgO\nj8dDpWqVOXbUSqA7f95FVEyU9dnYKHKP5ZaoDLVr1mTCmJHH32/avIWly7+iXefHeXb4SLIPHy5k\n7pIL9rFZkFB+eLuwJFVDRAaJyGKgM3BlcRZsjEn1/r8RsBV4B9hgjLmqpIUtTFZWFnEVY4+/Dw8L\nw+122xGq3MeLjooiJjqarKwsnhyYQK9uXWyJkyfQ63bVzVdy6M9MtnwrgPXF++P3P2jT624S5w4k\nrkpFtq75EbBONeNbN6bf5N6s+uRbqzwHsznvCsPgOQO4/v7mrPigyBF9C9SiWTxhYWHH3194QQOe\nfKI7s6dNpmaNM5gyzZ7WssE+NgvkKMarjCmsCnC8wwcROWaMKW4HEHnXIpOBW0Rkm/eU/FUgvpjL\nKlJsbCxZ2dnH37vdHpxO+zoIL+/xdu/eQ+/+A3mgzT3cfOP1tsWBwK/b1S0b4XF7OPdyQ82zz6Bt\nwkPUPLsmyR1Gs2fHXprc2Zh7etzJ6+PfBmDJu8tZ9v5X9BzTlR/X/Uyzu5vwySv/Y8WilZxR73S6\nDO9IcofnSr2ezZs2Ia6i1RVpi6bxjHzenjYQwT5WypvibKmSNu3LFZFtACKyq5gx/XZJw4tYtsL6\nRV+7fgPnnG3vzfHyHG9f+n669OpD317daXVbS9vi5An0ur3Q60XG957E+N6T+P3HncwePp99u/Zx\nJPsoAAf3HSS6Ygyn1DyZzsOsoYbcuW6O5bjwuN1kZWRxOMs6tc08kElUTGSpypOna88+bNy0GYCv\nV3/L+eeagCw3v2AfmwVxOp1+v8qawmqKDYwxP/u8r+F97wA8IlLUlq5sjPkOiDXGdAReBsYC20tV\n4hNo0Syeld+s5pGO1qnesMQEO8L8J+Klzp7LoUOZTE2dRcqMWTgcMGXCOCIiImyJF4x1m//cqzyW\n1I5cVy65Lhfzn3udP/f+yW/bfqff5N54PB42rtrMj+t+Zu/OfTzc/37iW19HWJjz+J3q0npmwFOM\nHPMCFSqEU61aNZIGPR2Q5eYX7GOzQGUv1/nN4fEUXAE0xtQpbEYRKTK5GWMigYZANtZ1xQ5Aqogc\nK2renIx07XRC+UX7UwysiErVSn2l78dX3vH7+3v2g3eVqSuLhQ1cVeoanYgcxWoJkyeltMtUSik7\n2fushVLqP6ksPmrjL02KSqnAC92cqElRKRV4odyiRZOiUirw9PRZKaX+EsI5UZOiUirw9EaLUkr5\nCvA1RW8fCqNEpJkx5mJgEdazzwBTRORNY0wnrH4ajgHJIvKBMSYKmA+cAmQAbUUkvbBYmhSVUgEX\nyJqiMaYf8AiQ16nlZcBYEXnB5zOnAj2xxqePAZYbYz4BugHrRGSoMeY+YDDQu7B4mhSVUmXdj0Br\nYJ73/WVAfWPMnVi1xT5YvXgtFxEXkGGM2YbVmq4xkNeZ5EdYSbFQmhRVyAt2s7sHmj4Z1Hivfjk2\nqPECIZCP5IjIu/maHa8CpovIGmPMQOBZ4AfgoM9nMoHKQJzP9ENApaLihXCzbaVUWeVwOvx+lcAC\nEVmT9zdwMVbi8014ccCfWNcR43ymFTl6gCZFpVTgORz+v4rvY2PM5d6/W2CNS78aaGyMiTDGVAbO\nBTYAXwF5/d+1BJYVtXA9fVZKBZzNj+R0A170dny9G+gsIpnGmIlY40k5gEEikmOMmQLMMcYsA44C\nDxa1cE2KSqkyz9tr1zXev9dg3UDJ/5lUIDXftMNAm+LE0qSolAq80H12W5OiUirwtEMIpZTy4SiD\nY6/4K3RLrpRSNtCaolIq8PT0uWxo80j744OA1zjjDIYOHmRrvHUbNjJ+0hRmpkyyNQ5Yg7YPH/08\nsnUbkZERJCUMpFbNGiEfC8DlcpE4bAQ709JwHXPRqX1bmjb5x83FgHG73SQlj+LX7TtwOB0kDujP\nWfXOLHrGQjz3chLZmdZYy3t37uODVz/lsacfJjc3l2M5Ll4cPJ2MA4e4/eGbaXxzI9y5bt6ZuYjV\nS9ZwZ9uWXHLNhXjwEBsXS5Vqleh0U58SlyXY+68g2ktOGZCTkwNA6hT7ExTArHkvs/DDxcRERwcl\n3udfLiUnJ4f5M6exbsNGxoyfyMTnRxc9YxmPBbDoo4+pUqUyI4YkcjAjg3sfsjcpfrlsOQ6Hg7kz\nUlj93RomTE4p1fqFV7C+Rkldnjs+bci0AUwfNY8dP/7ODXfFc2e7lrw1431ufeB6Hr+9H1Ex0Yx9\nbSirl6xhwZwPWTDnQwAGju/N3PGlG1I12PuvQKGbE4OXFI0x1YF0EbFl6FLZ9iOHDx+mS8/e5Oa6\n6fV4Fy66oIEdoQCoXbMmE8aMZGBicIbX/P6HtVx79VUAXHRBAzZu3lIuYgHcdEMLbry+OQAet4fw\ncHsPy+bxTWh6nZV0d6WlUSkurog5Cle3fi2ioiIZ/NKTOJ1OXnnpbcYNmMzB/RkAOMPCOJZzjCOH\nj7J31z6iYqKJionEnev+23IaNb+MQwczWf/N5lKVJ9j7ryBaUyyAMaY9UAur37NXgCNAjDHmcRH5\nLNDxoiIjaf/IQ9zV6na27/iNbk/0ZdHbr+O06S5Yi2bx7EpLs2XZBcnKyjp+aQAgPCwMt9tty/oF\nMxZAdFTU8bhPDkygV7cutsTx5XQ6SUgazhdLljJ2VHKplnX0SA7vzf2I/723lNNrnUrCpL70vHMA\nAOais7mlTQueeWwEAOl7/mTC28k4HE7enbXob8tp3e5WXhg4pVRlgeDvv/LGzp/kx4GmwPvAHSKy\n1RhzBvAeEPCkWLdObWrXqglAndq1qFK5Mn/sS+fUU04OdKh/RWxsLFnZ2cffu90e2w7yYMbKs3v3\nHnr3H8gDbe7h5huvtzVWnuSkZ0jfv58H2z3Ge2+8SlRUZImWk7Z9N7t/22v9/dseDh3I5KTqlTn3\nkvrc1f42knuNI/NgFpc3uZgq1SvT9dancACDJ/djyw/b+Gnzr9Q483SyDmWxZ+cfpV6vf2P/5ecI\nC90EbGfJj4lIFlZ3PT8DiMguwJbT53ffX8SY8S8CsPePP8jKzubk6tXsCPU3HntW5x8uaXgRy1as\nBGDt+g2cc3a9chELYF/6frr06kPfXt1pdVvLomcopYUfLmbG7LkAREZE4nQ6cZbibmnzVk1o2/d+\nAE6qXoXo2CgaXH4et7RpQWKnUfyRZnX0nJmRRc7RHHJdubhcuWQfyiY2LgaAi65swPcr1pdyzSzB\n3n8FsrdDCFvZWVN83xjzHlZPFYuMMR8DNwOf2xGsdavbGTxkOG07dcPhcDB08KCg/Do6gnRFuUWz\neFZ+s5pHOlqnlsMSE8pFLIDU2XM5dCiTqamzSJkxC4cDpkwYR0REhC3xrm/elMFDkmnX+XFyc3MZ\n8GSfUsX633tL6Z7UkWGpA/G4PUweOpNB4/vwR9o+nh7bEw8eNn4nvDntPX7a9Csj5wzGnetm8w9b\nWffNJgDOqHMaa7/eEJD1C/b+K0goX1N0eDz21XSMMfHATUB1IB2rZ9wP/Jk3JyM9OFUwpYqpvHcy\nG1GpWqkz2t4VS/3+/p5ybZMylUFtvc0nIkuAJXbGUEqVQfrwtlJK/SWUT581KSqlAk+TolJK/UW7\nDlNKKV9aU1RKqb/oNUWllPKlSVEppf4SytcUQ7eBolJK2UBrikqpwAvh02dbm/mVhjbzU8pyU6PH\nghrvi83vljqj/bn+O7+/vyddeFmZyqBaU1RKBZ5eU1RKqfJBa4pKqYBzOEK3vqVJUSkVeCF8o0WT\nolIq4LRFi1JK+QrhGy2aFJVSAac1RaWU8qVJUSmlfOjd53+fx+Nh+Ojnka3biIyMIClhILVq1rAt\nnsvlIiFpOLvS0ggLCyMpYQB169S2LZ7b7SYpeRS/bt+Bw+kgcUB/zqp3pi2xXC4XicNGsDMtDdcx\nF53at6Vpk8a2xPKVvn8/9z/akekvTbB1Wwb7WLEj3tS3nifzkDW28+6de5g2dh5PDX2cipVicTqd\njBwwgd0793Lng7dwY6tmeDxu3pj1Pks+/gqAN76Yzm+/pgGw6QchdcLLpVvJfEK5Q4hykxQ//3Ip\nOTk5zJ85jXUbNjJm/EQmPj/atnjLVqzE7c5lXupUVq5azcTJKYwbPcK2eF8uW47D4WDujBRWf7eG\nCZNTbFu/RR99TJUqlRkxJJGDGRnc+5D9SdHlcjFs5JgSD0hfHME+VgIdr0IF62v7ZPvE49P6J/fg\n04VLWPrJShpe0YDa9WqSnXWY29rcSKfWfYmMjmT2woks+fgrzqh1Gls3/swzPUaWet3KI9uSojGm\nkohk2LX8/L7/YS3XXn0VABdd0ICNm7fYGq9OnVrk5ubi8XjIzMokvEIFW+M1j29C0+usxLQrLY1K\ncXG2xbrphhbceH1zADxuD+Hh9v92jp0wiTb3tCbVO0i9nYJ9rAQ63lnnnklUdCTPTU/EGeYkdfzL\nXHDpefwkvzIm9Vl2/76XF0ekknM0h06t++LxeKh28kkcPZoDQP0G9Tj5tGqMnTWUo0eOMnn0LH7/\ndVep1/NvQviaop0n/ruNMR1tXP7fZGVlEVcx9vj78LAw3G63bfFiomP4fVcad9zzAENHPMdD991r\nW6w8TqeThKThjB47nltvvsm2ONFRUcRER5OVlcWTAxPo1a2LbbEAFiz8gKpVT+KaRlcSjP5Jgn2s\nBDrekSNHeX3mAvp3GsoLQ6aS8Fwfzqh1KocOZtKv4xD27t7Hg53uAqxT9zsfvIVJr4zks4XWaMPp\nf/zJy1Pf4sn2ibwy7W0Gje5duhUsgMMZ5verrLEzKa4FLjHGfG6MibcxDgCxsbFkZWcff+92e3A6\n7Vu9ea+8RuOrG7Hw7dd465W5JCQN49ixY7bFy5Oc9AwL336NpOSRHDly1LY4u3fvoWO3ntxxa0tu\nvvF62+KAlRRXrlpNh6492LJ1GwlJw0jfv9+2eME+VgId7/dfd/HpwqUA7NyeRsaBQ3jcHr76YjUA\nX32xmvoNzjr++QWvfMTdTTrQ8IoGNLyiAbLhJ1Z4P7thzRaqnXxSictyIg6nw+9XWWNnUjwsIj2A\n/kAvY8x6Y8x4Y0wvO4Jd0vAilq1YCcDa9Rs45+x6doQ5rnLlSlSsWBGAuLiKuFy55ObaV9tY+OFi\nZnhPLSMjInE6nThtOqD2pe+nS68+9O3VnVa3tbQlhq/Z0yYzM2USM1MmcW79c0hOGky1qlVtixfs\nYyXQ8W65qwWPP90egGonn0RMxRiWf7aKq+IvB6Dh5Q349ccd1Kx7BkMm9AfAnesm5+gx3G43bbvf\nxz2P3g7AWaYue3fvK1V5yhvb+lM0xnwhIs183lcGmgBGRJ4vav7i9qeYd4dv67YfARiWmGDrHczs\nw4dJHDqCP9L34XK5eOT++2ytUR0+coTBQ5LZl55Obm4uj7V7lPjrrrUl1uix4/n4s885s25tPB7r\n8tCUCeOIiIiwJZ6vjt16MHhA/6DcfQ7WsVLaePn7UwwLD+Pp5J6cesbJeDwepj4/h/Q//uSpYd2J\niookKzOL4U+9QFZmNo90u5dGTS7D43azatn3zE95i9i4GBKe60N0TBQul4sJw6b/7ZpiIPpTzNr5\ns9/f39ga9cpUddHOpNhWROaUdH7tZFYpSyh2Mpu96xe/v78xZ5xZppKibbcVS5MQlVIhTh/eVkop\nH2XwBoq/NCkqpQJOO4RQSilfevqslFJ/0ZqiUkr50pqiUkrZwxjjACYDDYEjwGMi8rNd8UI3nSul\nyqwAN/O7E4gUkWuAgcA4O8uuSVEpFXgOh/+vojUGFgOIyCrgcjuLrklRKRVwAe4lpxJw0Oe9yxhj\nW+4qs9cUIypVC93bV0oF0Beb3/23i1BsAf7+ZgC+HYg6RcS23le0pqiUKutWAC0BjDFXAevtDFZm\na4pKKeX1LnCDMWaF9317O4PZ1kuOUkqFIj19VkopH5oUlVLKhyZFpZTyUW5utAS7KZA3ZiNglO+w\nCzbFCQdmAnWBCCBZRBbaGM8JTAcM4Aa6isgmu+L5xD0F+Ba4XkS22hzrO/569u0XEbF15EljzADg\nDqACMFlEZtkYqy3QDvAA0VjfidOCOeRwKCtPNcWgNgUyxvTDShz2j94ODwP7RKQJcAswyeZ4twMe\nEWkMDAZG2BwvL/GnANlFfTYAsSIBRKS592V3QowHrvYem02BWnbGE5E5ItJMRJoD3wE9NSH6rzwl\nxaA2BQJ+BFrbHCPPG1jJCax9ZutYqiLyHtDZ+7Yu8Ked8byeB6YAAR6VvUANgVhjzMfGmM+8NX47\n3QRsMMYsAN4HFtkcDwBjzOXA+SKSGox45UV5SopBbQokIu8CLruWny9WtohkGWPigDeBhCDEdBtj\nZgMTgJftjGWMaQfsFZFPgWC0ZMoGxojITUA34GU7jxWgOnAZcI833is2xvI1EBgSpFjlRnlKikFt\nChRsxphawOfAHBF5PRgxRaQdUB+YYYyJtjFUe6yHc78ALgbmeq8v2mUr3kQvItuAdOB0G+OlAx+L\niMt7rfSIMaa6jfHyhhSuLyJL7IxTHpWnpBjUpkA+bK/ZGGNOBT4G+gdjlERjzMPeGwNg3bTKxbrh\nYgsRifdeA2sG/AA8KiJ77YoHdADGAhhjzsD6MU2zMd5y4GafeDFYidJOTYD/2RyjXCo3d58JclMg\nH8FoEjQQqAIMNsYkemPeIiJHbYr3DjDLGLME6xh5wsZY+QVje6Zird8yrGTfwc6zChH5wBhznTHm\nG6wf0cdFxO71NICtT1+UV9rMTymlfJSn02ellCo1TYpKKeVDk6JSSvnQpKiUUj40KSqllA9Nikop\n5UOTYjljjLnAGOM2xhTaLtsYU9cYM6MUcf7xXJ8xpq0xZp8x5mSfaXWMMb+UNE6gl6NUUTQplj/t\nsNpHdy3ic3WBeqWIc6IHXGOxervx57OBiqlUwJSnFi3/ecaYMKxuxhoDK40xZ4rIL8aY67F6oXEA\n24GHsDp6ONMY8yLwFpCU1y+kMWYW8IWIzDXGJAPNgZOAfcBdRTTBewe40BjzgIi8mq98z2J1STbU\n+xfrf8cAAAK5SURBVP4XIB5oBtwK1PC+JgC1vXH3YXWXBhBtjHkdq7XGj0BHETno7Q3mBay+A/cB\nXURku7ct9X7gfOA+EVlX3G2q/nu0pli+3Ab8KiI/YjV77GKMiQDmA4+ISENgHfAo0BP4VkR6euf9\nRy3MGHMWVqcCV4vIucBPWAkVTtzm+yhWbfUF39PoE/CNeQVwI1ab3bHAB97yOrC63gI4BRgvIhd7\ny5JojKkAzAAeEJHLsfrR9L0ssFZEztOEqPylNcXypR2QVzt7EysZvg38LiLrgf+3d/euUQVhFId/\nUbQSP4LBVKKxOKYQJQGxMNjb2whBEMXCQgSxshJEm4CNiEmjaBFbCxtTCSIWfqKYF8l/kDYIkRCL\nd6KvgZvdymI5TzXcndmd6jD3XjhLRNyCP8WnW4qIJUk3JF0mT2enyBNar3UfJM0Bj4DrW0ytwfom\nIlaAFUnrZCMQ5Ml2XxsvRsTbNn4GPCZbfI4AL1r7OsCu8r3veu3XrHIoDoh2KjsLTEq6Rt4F7OXv\nrefGvN38W7EGeWKrAbWjzZ0gQ3aGDNk1+m8Fuk22Pp/v9TvNal3cUdCwVsZDZNnuNmApIibanoeA\nA2Xezz73awb49nmQTAMLEXEwIsYi4hBwhwzFEUlH27ybwBWyIHcjlJaBMUk7JQ0DU+36GfLZ4iyw\nSN7ebu9nMxHxi2wqqoW4y+TzPSSdBEY7lncF77ik4218EXgFBDAs6XS7fon/V+JqA8ihODguAA82\nXXsIHCNfvjyV9AkYB+4B34E9kp60P6V6CXwDngOv2/p54ERbtwB8Bg63z3q+CY6I98D9cmke2C/p\nK3AV+NixdL1j/IN8jviFbLO+GxGrwDlgpu1zmgzMvvZotpmrw8zMCp8UzcwKh6KZWeFQNDMrHIpm\nZoVD0cyscCiamRUORTOzwqFoZlb8BnOVJQ2h9/+pAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x15a924a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "MLP = MLPClassifier(hidden_layer_sizes=(50, ), max_iter=10, alpha=.0001, \n",
    "                    solver='sgd', verbose=10, tol=.0001, random_state=42, learning_rate_init=.1)\n",
    "\n",
    "#Fit model & predict y\n",
    "MLP.fit(X_train, y_train)\n",
    "pred_y_train = MLP.predict(X_train)\n",
    "pred_y_test = MLP.predict(X_test)\n",
    "\n",
    "#Model accuracy - training data\n",
    "print\n",
    "print 'Precision:' + str(metrics.precision_score(y_train, pred_y_train, average = 'weighted', pos_label='high'))\n",
    "print 'Recall: ' + str(metrics.recall_score(y_train, pred_y_train, average = 'weighted', pos_label='high'))\n",
    "print 'Accuracy: ' + str(metrics.accuracy_score(y_train, pred_y_train))\n",
    "\n",
    "# Fancy boy confusion matrix - training data\n",
    "mat = metrics.confusion_matrix(y_train, pred_y_train)\n",
    "sns.heatmap(mat.T, square=True, annot=True, fmt='d', cbar=True)\n",
    "plt.xlabel('Actual Number')\n",
    "plt.ylabel('Predicted Number')\n",
    "plt.title('MLP - Training Performance')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Precision:0.980387484364\n",
      "Recall: 0.980290456432\n",
      "Accuracy: 0.980290456432\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x160cd518>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Kl6Zfj+c9jdesaROWLltOizbOoWj/3j08jRfu70JOIqUF6Mut7yPbiNA5UtU8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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x18983518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Model accuracy - training data\n",
    "print 'Precision:' + str(metrics.precision_score(y_test, pred_y_test, average = 'weighted', pos_label='high'))\n",
    "print 'Recall: ' + str(metrics.recall_score(y_test, pred_y_test, average = 'weighted', pos_label='high'))\n",
    "print 'Accuracy: ' + str(metrics.accuracy_score(y_test, pred_y_test))\n",
    "\n",
    "# Fancy boy confusion matrix - training data\n",
    "mat = metrics.confusion_matrix(y_test, pred_y_test)\n",
    "sns.heatmap(mat.T, square=True, annot=True, fmt='d', cbar=True)\n",
    "plt.xlabel('Actual Number')\n",
    "plt.ylabel('Predicted Number')\n",
    "plt.title('MLP - Test Performance')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 2 - Optimize MLP Parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 1, loss = 0.63780467\n",
      "Iteration 2, loss = 0.26993412\n",
      "Iteration 3, loss = 0.24531053\n",
      "Iteration 4, loss = 0.23249797\n",
      "Iteration 5, loss = 0.22329679\n",
      "Iteration 6, loss = 0.21626242\n",
      "Iteration 7, loss = 0.21060256\n",
      "Iteration 8, loss = 0.20636226\n",
      "Iteration 9, loss = 0.20275525\n",
      "Iteration 10, loss = 0.19956171\n",
      "Iteration 1, loss = 0.63829233\n",
      "Iteration 2, loss = 0.27025643\n",
      "Iteration 3, loss = 0.24654183\n",
      "Iteration 4, loss = 0.23410992\n",
      "Iteration 5, loss = 0.22552123\n",
      "Iteration 6, loss = 0.21804481\n",
      "Iteration 7, loss = 0.21292405\n",
      "Iteration 8, loss = 0.20858724\n",
      "Iteration 9, loss = 0.20470124\n",
      "Iteration 10, loss = 0.20241500\n",
      "Iteration 1, loss = 0.63081829\n",
      "Iteration 2, loss = 0.26626237\n",
      "Iteration 3, loss = 0.24312374\n",
      "Iteration 4, loss = 0.22986850\n",
      "Iteration 5, loss = 0.22091677\n",
      "Iteration 6, loss = 0.21371822\n",
      "Iteration 7, loss = 0.20887361\n",
      "Iteration 8, loss = 0.20509427\n",
      "Iteration 9, loss = 0.20130855\n",
      "Iteration 10, loss = 0.19839854\n",
      "Iteration 1, loss = 0.60657526\n",
      "Iteration 2, loss = 0.22005063\n",
      "Iteration 3, loss = 0.18682238\n",
      "Iteration 4, loss = 0.16716691\n",
      "Iteration 5, loss = 0.15196110\n",
      "Iteration 6, loss = 0.13962892\n",
      "Iteration 7, loss = 0.12912051\n",
      "Iteration 8, loss = 0.12056776\n",
      "Iteration 9, loss = 0.11294147\n",
      "Iteration 10, loss = 0.10638375\n",
      "Iteration 1, loss = 0.60690770\n",
      "Iteration 2, loss = 0.22004360\n",
      "Iteration 3, loss = 0.18788125\n",
      "Iteration 4, loss = 0.16889224\n",
      "Iteration 5, loss = 0.15457528\n",
      "Iteration 6, loss = 0.14202926\n",
      "Iteration 7, loss = 0.13243389\n",
      "Iteration 8, loss = 0.12403781\n",
      "Iteration 9, loss = 0.11650343\n",
      "Iteration 10, loss = 0.11071412\n",
      "Iteration 1, loss = 0.59941831\n",
      "Iteration 2, loss = 0.21620908\n",
      "Iteration 3, loss = 0.18488508\n",
      "Iteration 4, loss = 0.16496688\n",
      "Iteration 5, loss = 0.15008771\n",
      "Iteration 6, loss = 0.13782905\n",
      "Iteration 7, loss = 0.12843622\n",
      "Iteration 8, loss = 0.12048553\n",
      "Iteration 9, loss = 0.11278761\n",
      "Iteration 10, loss = 0.10651958\n",
      "Iteration 1, loss = 0.60334773\n",
      "Iteration 2, loss = 0.21464833\n",
      "Iteration 3, loss = 0.18020430\n",
      "Iteration 4, loss = 0.15948147\n",
      "Iteration 5, loss = 0.14328362\n",
      "Iteration 6, loss = 0.13001486\n",
      "Iteration 7, loss = 0.11860901\n",
      "Iteration 8, loss = 0.10920139\n",
      "Iteration 9, loss = 0.10075090\n",
      "Iteration 10, loss = 0.09343127\n",
      "Iteration 1, loss = 0.60366405\n",
      "Iteration 2, loss = 0.21460377\n",
      "Iteration 3, loss = 0.18124167\n",
      "Iteration 4, loss = 0.16122386\n",
      "Iteration 5, loss = 0.14594845\n",
      "Iteration 6, loss = 0.13250119\n",
      "Iteration 7, loss = 0.12205182\n",
      "Iteration 8, loss = 0.11283304\n",
      "Iteration 9, loss = 0.10451663\n",
      "Iteration 10, loss = 0.09794638\n",
      "Iteration 1, loss = 0.59617305\n",
      "Iteration 2, loss = 0.21078484\n",
      "Iteration 3, loss = 0.17828764\n",
      "Iteration 4, loss = 0.15732605\n",
      "Iteration 5, loss = 0.14145815\n",
      "Iteration 6, loss = 0.12829625\n",
      "Iteration 7, loss = 0.11803868\n",
      "Iteration 8, loss = 0.10926194\n",
      "Iteration 9, loss = 0.10074601\n",
      "Iteration 10, loss = 0.09373623\n",
      "Iteration 1, loss = 0.32769650\n",
      "Iteration 2, loss = 0.16996961\n",
      "Iteration 3, loss = 0.13890580\n",
      "Iteration 4, loss = 0.12263480\n",
      "Iteration 5, loss = 0.11061077\n",
      "Iteration 6, loss = 0.10305921\n",
      "Iteration 7, loss = 0.09770082\n",
      "Iteration 8, loss = 0.09333071\n",
      "Iteration 9, loss = 0.08909739\n",
      "Iteration 10, loss = 0.08707868\n",
      "Iteration 1, loss = 0.33041193\n",
      "Iteration 2, loss = 0.17399560\n",
      "Iteration 3, loss = 0.14429026\n",
      "Iteration 4, loss = 0.12604185\n",
      "Iteration 5, loss = 0.11450893\n",
      "Iteration 6, loss = 0.10691431\n",
      "Iteration 7, loss = 0.09997780\n",
      "Iteration 8, loss = 0.09515561\n",
      "Iteration 9, loss = 0.09154212\n",
      "Iteration 10, loss = 0.08872786\n",
      "Iteration 1, loss = 0.32565014\n",
      "Iteration 2, loss = 0.17308850\n",
      "Iteration 3, loss = 0.13977370\n",
      "Iteration 4, loss = 0.12101251\n",
      "Iteration 5, loss = 0.11011633\n",
      "Iteration 6, loss = 0.10172117\n",
      "Iteration 7, loss = 0.09610960\n",
      "Iteration 8, loss = 0.09152365\n",
      "Iteration 9, loss = 0.08826406\n",
      "Iteration 10, loss = 0.08494918\n",
      "Iteration 1, loss = 0.29506389\n",
      "Iteration 2, loss = 0.13183500\n",
      "Iteration 3, loss = 0.09719699\n",
      "Iteration 4, loss = 0.07892097\n",
      "Iteration 5, loss = 0.06479694\n",
      "Iteration 6, loss = 0.05513066\n",
      "Iteration 7, loss = 0.04824435\n",
      "Iteration 8, loss = 0.04313394\n",
      "Iteration 9, loss = 0.03800487\n",
      "Iteration 10, loss = 0.03420222\n",
      "Iteration 1, loss = 0.29803052\n",
      "Iteration 2, loss = 0.13659130\n",
      "Iteration 3, loss = 0.10373084\n",
      "Iteration 4, loss = 0.08280233\n",
      "Iteration 5, loss = 0.06962321\n",
      "Iteration 6, loss = 0.05968517\n",
      "Iteration 7, loss = 0.05172204\n",
      "Iteration 8, loss = 0.04527722\n",
      "Iteration 9, loss = 0.04006127\n",
      "Iteration 10, loss = 0.03624973\n",
      "Iteration 1, loss = 0.29314425\n",
      "Iteration 2, loss = 0.13566467\n",
      "Iteration 3, loss = 0.09934579\n",
      "Iteration 4, loss = 0.07841785\n",
      "Iteration 5, loss = 0.06605170\n",
      "Iteration 6, loss = 0.05505128\n",
      "Iteration 7, loss = 0.04789957\n",
      "Iteration 8, loss = 0.04135617\n",
      "Iteration 9, loss = 0.03697052\n",
      "Iteration 10, loss = 0.03309285\n",
      "Iteration 1, loss = 0.29155400\n",
      "Iteration 2, loss = 0.12737423\n",
      "Iteration 3, loss = 0.09213668\n",
      "Iteration 4, loss = 0.07330185\n",
      "Iteration 5, loss = 0.05840143\n",
      "Iteration 6, loss = 0.04824502\n",
      "Iteration 7, loss = 0.04122594\n",
      "Iteration 8, loss = 0.03527789\n",
      "Iteration 9, loss = 0.02975104\n",
      "Iteration 10, loss = 0.02537422\n",
      "Iteration 1, loss = 0.29462037\n",
      "Iteration 2, loss = 0.13244832\n",
      "Iteration 3, loss = 0.09886417\n",
      "Iteration 4, loss = 0.07707905\n",
      "Iteration 5, loss = 0.06322731\n",
      "Iteration 6, loss = 0.05288853\n",
      "Iteration 7, loss = 0.04449314\n",
      "Iteration 8, loss = 0.03735601\n",
      "Iteration 9, loss = 0.03142793\n",
      "Iteration 10, loss = 0.02733370\n",
      "Iteration 1, loss = 0.28980615\n",
      "Iteration 2, loss = 0.13125853\n",
      "Iteration 3, loss = 0.09404097\n",
      "Iteration 4, loss = 0.07291184\n",
      "Iteration 5, loss = 0.05977777\n",
      "Iteration 6, loss = 0.04829043\n",
      "Iteration 7, loss = 0.04096340\n",
      "Iteration 8, loss = 0.03387250\n",
      "Iteration 9, loss = 0.02931666\n",
      "Iteration 10, loss = 0.02473635\n",
      "Iteration 1, loss = 0.24919265\n",
      "Iteration 2, loss = 0.11119727\n",
      "Iteration 3, loss = 0.08101890\n",
      "Iteration 4, loss = 0.06582402\n",
      "Iteration 5, loss = 0.05551116\n",
      "Iteration 6, loss = 0.04768295\n",
      "Iteration 7, loss = 0.04212951\n",
      "Iteration 8, loss = 0.03863674\n",
      "Iteration 9, loss = 0.03435591\n",
      "Iteration 10, loss = 0.03156028\n",
      "Best parameters:{'alpha': 0.01, 'activation': 'relu'}\n",
      "Best score:0.976947902259\n"
     ]
    }
   ],
   "source": [
    "#cross validate\n",
    "param_grid = { 'alpha' : [0.1,0.01,0.001], 'activation' : ['logistic', 'relu'] }\n",
    "clf = GridSearchCV(MLP, param_grid)\n",
    "clf.fit(X_train,y_train)\n",
    "\n",
    "print \"{}:{}\".format(\"Best parameters\", clf.best_params_)\n",
    "print \"{}{}\".format(\"Best score:\",clf.best_score_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Conclusion:\n",
    "The \"optimal\" paramaters selected perform worse then the original parameters provided (???)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 3 - Display Misclassifications"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sample Missclassifications:\n"
     ]
    },
    {
     "data": {
      "image/png": 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DvEuqh3M14CNgjLsvzuVnqyVfHYCl7l5n9G9m6wA3AluT6lm8xd0vauj7Flsh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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x16d66908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Plot missclasified images\n",
    "#NOTE - Using parameters from Part 1 for now. Will need to change once we figure out whats going on with Part 2.\n",
    "\n",
    "misclass_idx = np.where(y_test != pred_y_test)\n",
    "\n",
    "misclass_act = y_test[misclass_idx]\n",
    "misclass_pred = pred_y_test[misclass_idx]\n",
    "misclass_img = X_test[misclass_idx]*255\n",
    "misclass_img = misclass_img.astype(int)\n",
    "\n",
    "misclass_list = zip(misclass_act,misclass_pred,misclass_img)\n",
    "\n",
    "print \"Sample Missclassifications:\"\n",
    "for index, missclass in enumerate(misclass_list[:9]):\n",
    "    plt.subplot(3, 3, index+1)\n",
    "    plt.axis('off')\n",
    "    plt.imshow(missclass[2].reshape((28,28)), cmap=plt.cm.gray_r, interpolation='nearest')\n",
    "    plt.title('Act: %i | Pred: %i' % (missclass[0], missclass[1]))\n",
    "    \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Question 2: Regression Trees (10 points)\n",
    "\n",
    "In this question, we will be exploring the application of regression tree (RT) using sklearn package in Python. You will be using the same Hitters.csv dataset (available on Canvas) used in HW2 Q5 to predict a baseball player’s Salary using all the 16 performance variables. Use a random state of 42 and a test size of 1/3 to split the data into training and test.\n",
    "\n",
    "1. Build a regression using [DecisionTreeRegressor](http://scikit-learn.org/stable/modules/generated/sklearn.tree.DecisionTreeRegressor.html) with max_depth = 5. Report the mean squared errors on both training and test datasets. (4)\n",
    "2. Repeat Part-1 with max_depth = 2. (4)\n",
    "3. Briefly explain what you observe from these MSE values obtained by using maximum tree depths 5 and 2? Which tree is better and why? (2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Question 3 - Support Vector Regression vs. Linear Regression (10pts)\n",
    "Download datasets 'summer_gpa_test.csv' and 'summer_gpa_train.csv' from Canvas. With this toy dataset, we want to predict GPA in Summer 2016 for students using 5 different features. So, target variable will be 'GPA_summer2016' in this problem.\n",
    "\n",
    "1. Fit a support vector regression using the default options on [sklearn's SVR](http://scikit-learn.org/stable/modules/generated/sklearn.svm.SVR.html) on training data. Note that the default kernel is \"rbf\".  Report the root MSE for both train and test data. (2)\n",
    "\n",
    "2. Fit SVR with 'linear' kernel and Linear Regression (for other options, use default parameter settings). Report RMSE of prediction on train and test data for the two methods. (3)\n",
    "\n",
    "3. Now, compare the results of three different methods, then provide a possible reason for SVR with RBF kernel not working well on test set. (1)\n",
    "\n",
    "4.  Provide simple residual plots on Train and Test set for all three methods. Specifically, submit a scatter plot wherein y-axis shows the residuals and x-axis the predicted values. What can you learn about the effect of outliers on different models from this problem? (4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "from sklearn.svm import SVR\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "d_train = pd.read_csv('summer_gpa_train.csv',index_col='student')\n",
    "d_test = pd.read_csv('summer_gpa_test.csv',index_col='student')\n",
    "\n",
    "y_train = d_train['GPA_summer2016']\n",
    "y_test = d_test['GPA_summer2016']\n",
    "x_train = d_train.drop('GPA_summer2016',axis=1)\n",
    "x_test = d_test.drop('GPA_summer2016',axis=1)"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Question 4: Bayesian Networks (10 pts)\n",
    "#### Part (a) (5 points)\n",
    "Consider the following Bayesian network of binary (True/False) variables.\n",
    "\n",
    "<img src=\"hw4q4pic1.png\">\n",
    "\n",
    "This is equivalent to saying that X and Y are conditionally independent given C, or P(X,Y|C) = P(X|C)P(Y|C). This happens to be the assumption used by the Naive Bayes classifier.\n",
    "\n",
    "The exact probabilities are given:  \n",
    "P(X = True | C = True) = .75  \n",
    "P(X = True | C = False) = .5  \n",
    "P(Y = True | C = True) = .25  \n",
    "P(Y = True | C = False) = .5  \n",
    "P(C = True) = .5\n",
    "\n",
    "Find P(C = True | X = True, Y = True). The easiest method is to use Bayes rule, along with the conditional independence equation given above.\n",
    "\n",
    "#### (b) (5 points)\n",
    "A new feature Z is added, and based on prior knowledge, we believe that one of the two networks given below properly captures the dependencies among the variables. Our goal is to determine P(C|X,Y,Z). For each of these two different networks:\n",
    "\n",
    "<img src=\"hw4q4pic2.png\">\n",
    "\n",
    "will P(C|X,Y,Z) be the same as P(C|X,Y) (the inference from part a)? Or will it be different? Give a separate answer for each network."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Question 5: Mulitclass Classification (5 points)\n",
    "\n",
    "One way of using a binary classifier for addressing a multiclass classification problem is to use a One-vs.-All (or One-vs.-Rest)  strategy.\n",
    "\n",
    "1. Briefly describe the  One-vs.-All method.  (2pts)\n",
    "\n",
    "2. What are two disadvantages of using the One-vs.-All method in situations where the number of classes $N$ is very large? (3pts)"
   ]
  }
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