{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "import xlrd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import multivariate_normal as mvn\n",
    "import sklearn.neural_network as nn\n",
    "from scipy.stats import norm\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "hypnames = ['Even','Odd','Squares','Pow2', 'Pow4','Pow16','Mult5','Mult10','Num15to25','Num1to100']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "workbook = xlrd.open_workbook('/Users/chandola/Downloads/Class_03_08_2017__09_26_1Q_quickquestion20170308926.xlsx')\n",
    "worksheet = workbook.sheet_by_name(workbook.sheet_names()[0])\n",
    "num_rows = worksheet.nrows - 1\n",
    "curr_row = -1\n",
    "flag = False\n",
    "vals = []\n",
    "while curr_row < num_rows:\n",
    "    curr_row += 1\n",
    "    row = worksheet.row(curr_row)\n",
    "    cell_value = worksheet.cell_value(curr_row, 0)\n",
    "    if flag:\n",
    "        try:\n",
    "            cval = int(cell_value)\n",
    "            \n",
    "            vals.append(cval)\n",
    "        except ValueError:\n",
    "            continue\n",
    "    if('Student' in str(cell_value)):\n",
    "        flag = True\n",
    "vals = np.array(vals)\n",
    "#plt.hist(vals)\n",
    "nvals = np.bincount(vals,minlength=11)\n",
    "\n",
    "nvals = nvals[1:11]\n",
    "nvals = nvals/np.sum(nvals[1:11])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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sJEmSOjFYSZIkdWKwkiRJ6sRgJUmS1InBSpIkqRODlSRJUicGK0mSpE4MVpIkSZ0YrCRJ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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x119271518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=[10,6])\n",
    "plt.bar(range(1,11),list(nvals),alpha=0.6)\n",
    "xt = plt.xticks(range(1,11))\n",
    "ax = plt.gca()\n",
    "ax.set_xticklabels(hypnames,rotation=45,ha='right')\n",
    "plt.ylim([0,1])\n",
    "plt.title('Posterior Distribution, D = {16,4,64,32}')\n",
    "plt.savefig('/Users/chandola/cse574/slides/images/socrativeexp2017_posteriord2.png',dpi=240)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x10b641350>"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Uuwe5zaZr9LXHHCdkkNErrdPF64qIC3cNJxSRLZL0ev3six/4+10KPOjbdSve\n5N8cu2NSJ4cUxTJjlCHZDOVlAXTJ0U4Scmj16li6lFu2bp2xfXJyrij3U6ZDLxFLmEVkPvAj4Leq\nurFYk0qnTkqBiCmcocdv267pb9dqBfo6//g3J7yWOITaQ5frzTvck8egkyX+mbQaMexc7eXRJWUB\nhMbqk4YcOm0vInNS5/ol06GXiOsxbwV+Rlt1kevE+eMrOoc5pXh/2rf/GcA1eGGD94XZX5A9mSmj\nmjJj/LNJgknQqHX1Yp5vmkxefoGx+qNHWZGk17NRHF2FWUSeBZyHtyTTOwu3KF+aFJhtkbIHxCky\nKmvbBYuZeCeB47VX+N2bk/2nBN8UVIJeJ8IzL61/RgeqmvAtKsshTsihbUCYaN9+wQLYtCn5QDfI\nKW9FEcdj/jDwd8Dygm3JnbA/vtakU0AYN+H1lkgjEE26CH+IAN0KiIzKe5ndsP/BGNeTWTx8ez6J\n54U3fHsANpJjCXoMz7xJxkGzzPhnXucqKsuhW8ihQyhmVmOj9ub9ceinxkEuESnMInI+8KCq3iMi\nQxHbNQJvJ1SLX0cvA3Vme3JXA9tb/YGTCERMr6vJbAHaCAwxe2Xqa/EyZFrifRtwnGK8ySaeCM9n\nRjRfX3ZGQh4ea5nxz16ItUaFHDoMCENthSQkHXwsnS4+voYOxdm2m8f8MuACETkPr7BguYh8TlX/\nJriRupej2pFOjYCC3+d8vjCvfX5gkw/jNR0KeivHgf+ZZrCIa4+fftfiD522z7l8PPdQRZnxzzzO\n5XKWgz/4vN9voMTUFB9ybfDpZXyHdaL1XkRGOm0buyRbRF4J/Pf2rIxeLMmWMlfTmHvuVkn0B5ip\noLscr/nQ/2nZBBwjZtw3qXgmKcvOuXy8qkVny6XLCipVxGTjrpadtMx7kFe5zkqUdiYV5m2qekHc\ng7tI2X0x/HMGFyNdhRe+eDPwOryVuxvA5/GyX/C/f09cu0Ku6Wa88MzOwPfTophCyIeoaCDrSRzt\nC9JtQFi8WPatXs2aFSvg/PPh4YfjLUFlk3/pyKVXhqp+B/hOblZVR5Pyu8zVmR3XfjMzce0JGZXj\neLHud+B50R8GLo87WISEZ7YDHxCvTzN4E3yX4odUXC1B73kc76QXFYrxPd+zNvrPw9ddB+eck/24\nRjr6uvIvjCpEqVtcG/g68BO8CbkWhyB1SOCP/r+t8z1CjKyPMKpOa+sp3FpBJRH+JF5w1RN27uT4\nkSNuxL8i6fAWAAALy0lEQVQHjYET5iJJG1fVEX1ARqXOXAE85P/crex7jngCn8WLXQM0MghpE0f6\nWPcQTnXSy8C9FpaoBuvHnCOBWO8w8Fy8gpyNwJ/jpcS9DS8DYk5cO0rUu8V4W/syU9rdOl8r9/wR\nQvomVzFBN9CTgg5jk3jlY/2YSyIkZDEFvBDPg5oHHPK3meN1ZgmxBFLgWgPDDrywSKuU+xq8hkPt\n1Cl/rcMqzml0IUmetk32FU9fecwueGNt3m2QVNkMSbNIwrxriVinr4qMC8vy6F3Ms86PQfKY61To\njbXFes9iJk85C03Sx3jPklEBLx3v4uhNjTLodW/TKv3Koa+EuazOaRE0mRHABnAEuB64Aq+pfLz1\n8QIkCXFEDAyh96GKjIvAOV8PrGyd0/+6r2PNZfWV6HXxN/pMmKuiLYTygN9P+X8A9/uDxbfJ1lQ+\nLk1879r3lGNvD6VlXDSZGbzG8fK3V/o/OxlrzkvoyvA244p/2mtyuaS8n+grYa4w57bO7BDKJwgI\nXtmtLOPchy5ZIIXF6oNPABU/3cSi17qnxRH/rNd07Bj3j49zqiq/mZriKlfvRS/TV8JMRTm3Djaf\nbzLjOa/CC6s0g/sQHY8P++4yGZWBS3PL6uV264FchbeZ9ppCJv6WFGvp4NJXwjwApcZ1Ykxutt2H\nOp4w75dROZ1AVkenwSTsO7ymSrlNrA5CRWGcHsh5e5tFhhps4q88+kqYq6K0FpcpPPO8vPkCngqa\n9EBFYRahi9MDOW/i5CNbnNh9TJjzoUkPiEyQqMGk03d5nr9Xnm56oUF+O92aCqW9JhP08uirApM8\ncaFYJcSmxC1LO+2DH2dOMPn3NLxJzdLapfY6/ViMYal4+ZFLP+Y0B+9lqujbHMOmxINFt33iHtPF\ngaoQujS5T344EzIjHBPmlAxC6bCLA1Cl9GDLziKwAaV4orRzXtnGGPki/qrfgfdrfe82Fr4Atyb1\n7gQuGUhRFmn4ze09cZ69wPBAEcgmWTc8zLqlS7lFRNZXbdcgYcLcgbYJsFfhTYCtjd6rEup45d5b\nfA//q8AFScQ5K1kHBydQbUx7yqri0sojZVOrsW3zZi+bZMMG2LyZxS3v2SgHE+bONPEe6Sf8EIaT\nmRa+d9sAPobn8X7Af1+Ps39OA1AdL8d5KDA4xDq/g/RLk3ujh+kaYxaRRXhr/S0ETgS+pqrvDnzf\ntzHmXiGk1WjseHhek3qDEI8fFPoxm8RFMrX9VNXHReRVqvqoiCwA/llEzlbVf87dUiMxAY+3tZAr\neCtvT3TYfpYQM7PyCeBuPrFRHr2Yu91vxAplqOqj/o8n4q2M8XBhFjmKw3HUJl7o4j14oYjLgUZE\nOKJOxrBDyL3YBNyM+/F4IyaquufwYT338GE910S5fGJV/onIPOBu4HTg46r6s0KtcpM6Di6J5BeE\nfB34ie/tTsio3EuHeHhOpdV1Zt+Lq4HtrfBFL1Q+GobLJMpjFpGn4JV6vkvV/yP0UoyCEyYTre/6\njX6Jo+ZxHf1yLwyjLERkCLwGVj4juSwtpaqPiMg3gRcRiGHqAKcWJSVksu11ADqiN/vvC62oS9Jw\naWCq/QyjBHyHdaL1XkRGOm3bVZhF5GTgSVX9o4gsBtYxgClFOXaQqzM7DPBp//gPtY5LsSGSJvEb\nLrXbehNwsYxKnT5v2WkYVRInXe75wGfxJgrnAZ9X1f8V+H4g0uXy9B7bwwD+v06GBdpsfT1wiJlG\n+wR+Nk/aMBKQNV3uPmBN7lb1GFW0qXQwlNBam8/6ahhGgVg/5pJoiaz/9ia8tLZDwK3+Z2FhgToV\nZoKEhW/wMjCcXqfPMHodK8kujzpezvBK/PQyPGG+FLg0rPQ7pMHQcPCAYbnUOedbN5lbln4o5bEM\nw4iJecwlETd/uIsHuhIY7+JB18nJy24P3/iMY5N+hlEoJswOkyaUUPCK3U1mZ3RchreySdBemwQ0\njIyYMJdEynS7JnNT21YWamgEIR70g3jeeVmpfoYxEFiMuTyadGkj2h4fpq3BkE8rlBDak6LMPtLW\nZN8wisE85pKImW5XJzo+3KR7cUicbQzDcBhb888xeqkHha0XaBjpyVRgYhgRNDHv3DByx2LMDtFD\n6wy6WJVoGH2Decxu0aR3PNA6DvanNox+wGLMRmrC4uHmORtGPKK000IZRl6c1QcrZBuGE1gow0hF\nWzz8LGYWgrXGRg4gIutrNW8x1clJW0y11zBhNtLSxI+Hy6hFslxCRNYvXcotw8MsBhgb42wRucjE\nuXewGHOFdMhseAJY2CvZDpbL7B7Ll8ve4WHWbdjgvd+9G8bHuf3wYT23WsuMIJbH7C515mY2NIBG\nD2U7NOmdTBLD6AnMY66YDpkNcz6rwDSjR2mFMjZvng5lPDY1hYUyHCOTxywiq4DP4bV3VOAGVf1Y\nviYahpEXqrpHRC4aH/cm/6ambPKv14izGOtKYKWq3isiy4B9wGtV9X7/e/OYU9IhPtvwXxazNYw+\nJutirIfwlxNS1SMicj/wDOD+XK0cTJrMjc8+EfJZsyoDDcMon0QxZhGpA98BzlTVI/5n5jEbhmEk\nJJfKPz+M8RVga0uUDcMwjPyJlS4nIicANwNfUNVbQ75vBN5OqFoWgWEYRhARGQKGYm0bY/JPgM8C\nD6nqO0K+t1CGYRhGQqK0M44wnw18F/gJXrocwLtVdXe3gxuGYRjhZBLmLAc3DMMwwrG2nwYwdxVu\nGZW1fr8OwzAcwnplDBZ1bNURw3AeC2UMGNaHwzDcwEIZhmEYPYQJ8wDRS6twG8YgYzHmwaKJ9eEw\nDOexGLNhGEYFWIzZMAyjhzBhNgzDcAwTZsMwDMcwYTYMw3AME2bDMAzHMGE2DMNwDBNmwzAMxzBh\nNgzDcAwTZsMwDMcwYTYMw3AME2bDMAzHMGE2DMNwjK7CLCI3isjvReS+MgwyDMMYdOJ4zJ8BNhRt\nSFZEZKhqG1zB7sUMdi9msHsxg+v3oqswq+r3gP9Xgi1ZGaraAIcYqtoAhxiq2gCHGKraAIcYqtqA\nKCzGbBiG4RgmzIZhGI4RawUTEakDt6nq80O+y7YEimEYxoDSaQWTzGv+2bJShmEY+RInXe7LwF3A\nGSLygIi8pXizDMMwBpfMi7EahmEY+dLzk38iskpE7hSR/SLyUxG5vGqbqkRE5ovIPSJyW9W2VImI\nPFVEviIi94vIz0TkpVXbVBUi8m7/7+M+EfmSiCys2qayCCuQE5GTROR2EfmFiOwVkadWaWMYPS/M\nwFHgHap6JvBSYJOIPLdim6pkK/AzYNAfhT4K7FLV5wJ/DtxfsT2V4E/cvx1Y40/ezwfeWKVNJRNW\nIPcu4HZVPQP4tv/eKXpemFX1kKre6/98BO8P8BnVWlUNIvIs4DzgU8DATsqKyFOAtap6I4CqPqmq\nj1RsVlUcxnNelojIAmAJ8LtqTSqPDgVyFwCf9X/+LPDaUo2KQc8LcxDfO/gL4F+qtaQyPgz8HXC8\nakMq5jTgDyLyGRG5W0Q+KSJLqjaqClT1YeB64CDwr8AfVfWOaq2qnKer6u/9n38PPL1KY8LoG2EW\nkWXAV4Ctvuc8UIjI+cCDqnoPA+wt+ywA1gDjqroGmMLBx9UyEJHTgSuAOt6T5DIR+etKjXII9bIf\nnAv79YUwi8gJwM3AF1T11qrtqYiXAReIyK+BLwN/KSKfq9imqvgt8FtV/aH//it4Qj2IvAi4S1Uf\nUtUnga/i/V8ZZH4vIisBROTfAw9WbM8cel6YRUSATwM/U9WPVG1PVajqVaq6SlVPw5vc+SdV/Zuq\n7aoCVT0EPCAiZ/gfnQPsr9CkKvk58FIRWez/rZyDNzk8yHwdeLP/85sB55y5nhdm4OXAm4BX+Wli\n94iI821KS8C5x7OS2QJ8UUR+jJeVcW3F9lSCqv4Y+BzwI+An/sc3VGdRuQQK5P4sUCB3HbBORH4B\n/KX/3imswMQwDMMx+sFjNgzD6CtMmA3DMBzDhNkwDMMxTJgNwzAcw4TZMAzDMUyYDcMwHMOE2TAM\nwzFMmA3DMBzj/wMzbm9VMHGxnQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b565310>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# generate data\n",
    "\n",
    "n = 100\n",
    "data = np.random.multivariate_normal([6,6],[[1,0],[0,1]],n)\n",
    "labels = 0*np.ones([data.shape[0],1])\n",
    "\n",
    "n = 100\n",
    "data1 = np.random.multivariate_normal([4,4],[[1,0],[0,1]],n)\n",
    "labels1 = 1*np.ones([data1.shape[0],1])\n",
    "\n",
    "data = np.vstack([data1,data])\n",
    "labels = np.vstack([labels1,labels])\n",
    "\n",
    "n = 100\n",
    "data1 = np.random.multivariate_normal([8,5],[[1,0],[0,1]],n)\n",
    "labels1 = 2*np.ones([data1.shape[0],1])\n",
    "\n",
    "data = np.vstack([data1,data])\n",
    "labels = np.vstack([labels1,labels]).flatten()\n",
    "\n",
    "plt.scatter(data[labels == 0,0],data[labels == 0,1],c='r',marker='+')\n",
    "plt.scatter(data[labels == 1,0],data[labels == 1,1],c='g',marker='x')\n",
    "plt.scatter(data[labels == 2,0],data[labels == 2,1],c='y')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "mexico = [4.72, 4.15, 4.46, 4.23, 5.28, 4.07, 4.67, 4.87, 4.54, 3.75]\n",
    "boston = [5.76, 5.12, 5.64, 5.59, 5.54, 5.09, 5.46, 5.87, 5.71, 5.56]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "m_mean = np.mean(mexico)\n",
    "m_std = np.std(mexico)\n",
    "b_mean = np.mean(boston)\n",
    "b_std = np.std(boston)\n",
    "m_mle = norm(m_mean,m_std)\n",
    "b_mle = norm(b_mean,b_std)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "p_m_mean = 4.4\n",
    "p_m_std = 0.5\n",
    "p_b_mean = 5.0\n",
    "p_b_std = 0.7\n",
    "m_prior = norm(p_m_mean,p_m_std)\n",
    "b_prior = norm(p_b_mean,p_b_std)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prob that A is born in Mexico City according to prior estimates = 0.736540280607\n",
      "Prob that B is born in Mexico City according to prior estimates = 0.483941449038\n",
      "     Prob that A is born in Boston according to prior estimates = 0.484068479653\n",
      "     Prob that B is born in Boston according to prior estimates = 0.564131628472\n",
      "Prob that A is born in Mexico City according to MLE estimates = 0.908572570334\n",
      "Prob that B is born in Mexico City according to MLE estimates = 0.567880803477\n",
      "     Prob that A is born in Boston according to MLE estimates = 0.000942435640237\n",
      "     Prob that B is born in Boston according to MLE estimates = 0.0528698790113\n"
     ]
    }
   ],
   "source": [
    "a = 4.6\n",
    "b = 4.9\n",
    "print \"Prob that A is born in Mexico City according to prior estimates = \"+str(m_prior.pdf(a))\n",
    "print \"Prob that B is born in Mexico City according to prior estimates = \"+str(m_prior.pdf(b))\n",
    "\n",
    "print \"     Prob that A is born in Boston according to prior estimates = \"+str(b_prior.pdf(a))\n",
    "print \"     Prob that B is born in Boston according to prior estimates = \"+str(b_prior.pdf(b))\n",
    "\n",
    "\n",
    "print \"Prob that A is born in Mexico City according to MLE estimates = \"+str(m_mle.pdf(a))\n",
    "print \"Prob that B is born in Mexico City according to MLE estimates = \"+str(m_mle.pdf(b))\n",
    "\n",
    "print \"     Prob that A is born in Boston according to MLE estimates = \"+str(b_mle.pdf(a))\n",
    "print \"     Prob that B is born in Boston according to MLE estimates = \"+str(b_mle.pdf(b))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "X = np.array([[2,2],[7,5],[6,3],[3,1]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "y = np.array([1,1,-1,-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 8)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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PozyQxccmmotLkqcCLwc+BHT+lmwDND1fkscCJ1TVubD42FTLce7ZBdzaWpx77gMeAHb0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\nUqMMtCQ1ykBLUqMMtCQ1ykBLUqP+H7F51CdkLwrKAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11206f9d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[0:2,0],X[0:2,1],marker='x')\n",
    "plt.scatter(X[2:4,0],X[2:4,1],marker='o')\n",
    "a = 0.5\n",
    "c = 0\n",
    "p1 = [0,c+a*0]\n",
    "p2 = [(6.0-c)/a,6]\n",
    "plt.plot([p1[0],p2[0]],[p1[1],p2[1]])\n",
    "plt.xlim([0,8])\n",
    "plt.ylim([0,8])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 2.  1.]\n",
      " [ 1.  1.]\n",
      " [ 4.  1.]\n",
      " [ 3.  1.]]\n",
      "[[2]\n",
      " [3]\n",
      " [1]\n",
      " [4]]\n"
     ]
    }
   ],
   "source": [
    "X = np.array([[2],[1],[4],[3]])\n",
    "y = np.array([2,3,1,4])\n",
    "y = y[:,np.newaxis]\n",
    "X = np.hstack([X,np.ones([X.shape[0],1])])\n",
    "print X\n",
    "print y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 3.5]]\n",
      "[[ 11.375]]\n",
      "[[ 6.5]]\n",
      "[[ 4.875]]\n"
     ]
    }
   ],
   "source": [
    "ws = [np.array([[.5],[1.5]]),np.array([[.5],[3.0]]),np.array([[1.5],[0.5]]),np.array([[.5],[2.0]])]\n",
    "\n",
    "for w in ws:\n",
    "    alpha = 1\n",
    "    J2 = 0.5*np.sum((np.dot(X,w) - y)**2) +0.5*alpha*np.dot(np.transpose(w),w)\n",
    "\n",
    "    print J2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5.25\n",
      "3.75\n",
      "18.25\n",
      "52.5\n"
     ]
    }
   ],
   "source": [
    "ws = [np.array([[.5],[1.5]]),np.array([[.0],[2.5]]),np.array([[1.5],[0.5]]),np.array([[2.5],[.0]])]\n",
    "\n",
    "for w in ws:\n",
    "    alpha = 1\n",
    "    J3 = 0.5*np.sum((np.dot(X,w) - y)**2) + 0.5*alpha*np.sum(np.abs(w))\n",
    "    print J3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.25"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w = ws[0]\n",
    "0.5*np.sum((np.dot(X,w) - y)**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 2.  1.]\n",
      " [ 1.  1.]\n",
      " [ 2.  1.]\n",
      " [ 3.  1.]]\n"
     ]
    }
   ],
   "source": [
    "print X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "from sklearn import linear_model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "model = linear_model.Ridge(fit_intercept=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ridge(alpha=1.0, copy_X=True, fit_intercept=False, max_iter=None,\n",
       "   normalize=False, random_state=None, solver='auto', tol=0.001)"
      ]
     },
     "execution_count": 150,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.fit(X,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.80645161  0.70967742]\n",
      "0.0\n"
     ]
    }
   ],
   "source": [
    "print model.coef_\n",
    "print model.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.5\n",
      "[ 0.]\n"
     ]
    }
   ],
   "source": [
    "model1 = linear_model.Lasso()\n",
    "model1.fit(X,y)\n",
    "print model1.intercept_\n",
    "print model1.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.   0. ]\n",
      " [ 0.4  0.6]\n",
      " [ 0.   1. ]]\n"
     ]
    }
   ],
   "source": [
    "R = np.array([[1,0],[0.4,0.6],[0,1]])\n",
    "print R"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "X = [1,10,20]\n",
    "X2 = [x**2 for x in X]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.46666667  0.53333333]\n"
     ]
    }
   ],
   "source": [
    "pi = np.sum(R,axis=0)/3\n",
    "print pi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.57142857143\n",
      "16.25\n"
     ]
    }
   ],
   "source": [
    "mu_1 = np.sum(R[:,0]*X)/np.sum(R[:,0])\n",
    "mu_2 = np.sum(R[:,1]*X)/np.sum(R[:,1])\n",
    "print mu_1\n",
    "print mu_2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "sigma_1 = (np.sum(R[:,0]*X2)/np.sum(R[:,0])) - mu_1**2\n",
    "sigma_2 = (np.sum(R[:,1]*X2)/np.sum(R[:,1])) - mu_2**2\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "16.5306122449\n",
      "23.4375\n"
     ]
    }
   ],
   "source": [
    "print sigma_1\n",
    "print sigma_2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "X = np.array([[0,0],[0,10],[10,0],[10,10],[4,4],[4,6],[6,4],[6,6]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x11173cb50>"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/chandola/anaconda/lib/python2.7/site-packages/matplotlib/collections.py:590: FutureWarning: elementwise comparison failed; returning scalar instead, but in the future will perform elementwise comparison\n",
      "  if self._edgecolors == str('face'):\n"
     ]
    },
    {
     "data": {
      "image/png": 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dzeTDt/8YUcipqgeAe5M8Y7rq+cAdA47UxV3A+Um2TZ9Hz2fyIfTYfAa4bPr7ZcCoTmjm\naea6fM98jDcYJXkhcA2TT/M/VFXvGnikmSW5APgi8B1+9/byqqr67HBTzSfJLmC5qi4eepYukpzL\n5MPbk4AfAK8dy4egSf6GSQAfAb4JvH76RYANKcnHgF3Ak5hcH38H8GngE8DTgHuAl1XVg0PNuJbj\nzP9OJt9e6dRMbxqSpAb4v42TpAYYc0lqgDGXpAYYc0lqgDGXpAYYc0lqgDGXpAYYc0lqwP8BW/jz\nqkuSczwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111459250>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[:,0],X[:,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "import scipy.stats as st"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "X = np.array([[-2,-4,-6],[-1,-3,-5],[0,0,0],[1,3,5],[2,4,6]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "e,v = np.linalg.eig(np.cov(np.transpose(X)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  4.53677475e+01,   1.32252544e-01,   3.81059486e-19])"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "e"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "36.294197965093666"
      ]
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.var(np.dot(X,v[:,0:1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.10580203490632742"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.var(np.dot(X,v[:,1:2]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6.3108872417680948e-31"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.var(np.dot(X,v[:,2:3]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.23, -0.88,  0.41],\n",
       "       [-0.52, -0.24, -0.82],\n",
       "       [-0.82,  0.4 ,  0.41]])"
      ]
     },
     "execution_count": 124,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.round(v,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.,  0.,  0.])"
      ]
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(X,axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.23 & -0.88 &  0.41\\\\\n",
      "-0.52 & -0.24 & -0.82\\\\\n",
      "-0.82 &  0.40 &  0.41\\\\\n"
     ]
    }
   ],
   "source": [
    "for i in range(3):\n",
    "    print \" & \".join([\"%5.2f\"%x for x in v[i,:]])+\"\\\\\\\\\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "20526.0517019\n"
     ]
    }
   ],
   "source": [
    "h = np.exp(10*np.log(3))\n",
    "m = (1/0.05)*(1024 + np.log(1/0.1))\n",
    "print m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6603260869565217"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(18.0/125)/((18.0/125) + (2.0/27))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "## COPIED FROM SVD NOTEBOOK\n",
    "# ignore from here on\n",
    "X = np.array([[1,1,1,0,0,0],\n",
    " [1,1,1,0,0,0],\n",
    " [0,0 ,0 ,1 ,1 ,1],\n",
    " [0,0 ,0 ,1 ,1 ,1],\n",
    " [1,1 ,0 ,0 ,0 ,0]])\n",
    "print X\n",
    "U, s, Vh = svd(X)\n",
    "#plot the elbow plot\n",
    "plt.plot(s**2)\n",
    "plt.xlabel(\"K\")\n",
    "plt.ylabel('$s^2$')\n",
    "plt.title('Elbow plot for SVD')\n",
    "plt.show()\n",
    "#truncate to 2 \n",
    "s[1:]=0\n",
    "#calculate estimate using truncated S\n",
    "outX = np.round(np.dot(np.dot(U,diagsvd(s,5,6)),Vh))\n",
    "\n",
    "outX1 = np.round(np.dot(U[:,0:1],Vh[0:1,:])*s[0])\n",
    "#show results\n",
    "print \"X=\\n\"+str(X)\n",
    "print \"U=\\n\"+str(U[:1,:].round(2))\n",
    "print \"S=\\n\"+str(diagsvd(s,5,6).round(2))\n",
    "print \"V=\\n\"+str(Vh[:,:1].round(2))\n",
    "print \"X'=\\n\"+str(outX)\n",
    "print \"X'=\\n\"+str(outX1)\n",
    "\n",
    "foods = ['Chocolate','Peanuts','Crisps','Wine','Beer','Champagne']\n",
    "names = ['Annie','Brian','Chuck','Dave','Emma']\n",
    "print \"& \"+\" & \".join(foods)+\"\\\\\\\\\\hline\"\n",
    "for i in range(len(names)):\n",
    "    print names[i]+\" & \"+\" & \".join([str(x) for x in X[i,:]])+\"\\\\\\\\\"\n",
    "U,s,V = svd(X)\n",
    "S = np.zeros(X.shape)\n",
    "for i in range(X.shape[0]):\n",
    "    S[i,i] = s[i]\n",
    "print U\n",
    "print S\n",
    "print V\n",
    "\n",
    "for i in range(len(names)):\n",
    "    print \" & \".join([\"%.2f\"%x for x in U[i,:]])+\"\\\\\\\\\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "for i in range(6):\n",
    "    print \" & \".join([\"%.2f\"%x for x in V[i,:]])+\"\\\\\\\\\"\n",
    "    \n",
    "for i in range(5):\n",
    "    print \" & \".join([\"%.2f\"%x for x in S[i,:]])+\"\\\\\\\\\"\n",
    "    \n",
    "np.round(np.dot(np.dot(U,S),V)) - X\n",
    "\n",
    "U1 = np.round(U[:,0:1],2)\n",
    "V1 = np.round(V[0:1,:],2)\n",
    "S1 = np.round(S[0,0],2)\n",
    "np.round(np.dot(U1,V1)*S1)\n",
    "X = np.array([[-2,-4,-6],[-1,-3,-5],[0,0,0],[1,3,5],[2,4,6]])\n",
    "\n",
    "np.round(np.linalg.eig(np.cov(np.transpose(X)))[1],2)"
   ]
  }
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