gaussian_process_midterm.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "import seaborn as sns\n",
    "sns.set(color_codes=True)\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 275,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# ilk terimin covarianci hep 1 cikar -2 - -2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 298,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-2.  -1.   0.   3.5  4. ]\n",
      "[  4.1   0.9   2.   12.3  15.8]\n",
      "[ 0.  0.  0.  0.  0.]\n"
     ]
    }
   ],
   "source": [
    "x = np.array([-2, -1, 0, 3.5, 4,]);\n",
    "y = np.array([4.1, 0.9, 2, 12.3, 15.8])\n",
    "\n",
    "N = len(x)\n",
    "m = np.zeros((N))\n",
    "print(x)\n",
    "print(y)\n",
    "print(m)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[  7.3    16.39 ]\n",
      " [ 16.39   44.037]]\n"
     ]
    }
   ],
   "source": [
    "sigma = np.cov(x, y)\n",
    "print(sigma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 280,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def cov(x1, x2):\n",
    "    return np.exp(-1.0/2 * np.power(x1 - x2, 2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 299,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.]]\n",
      "[[  1.00000000e+00   6.06530660e-01   1.35335283e-01   2.69957850e-07\n",
      "    1.52299797e-08]\n",
      " [  6.06530660e-01   1.00000000e+00   6.06530660e-01   4.00652974e-05\n",
      "    3.72665317e-06]\n",
      " [  1.35335283e-01   6.06530660e-01   1.00000000e+00   2.18749112e-03\n",
      "    3.35462628e-04]\n",
      " [  2.69957850e-07   4.00652974e-05   2.18749112e-03   1.00000000e+00\n",
      "    8.82496903e-01]\n",
      " [  1.52299797e-08   3.72665317e-06   3.35462628e-04   8.82496903e-01\n",
      "    1.00000000e+00]]\n"
     ]
    }
   ],
   "source": [
    "K = np.zeros((N, N))\n",
    "print(K)\n",
    "for i in range(N):\n",
    "    for j in range(i, N):\n",
    "        K[i][j] = cov(x[i], x[j])\n",
    "        K[j][i] = K[i][j]\n",
    "print(K)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x107336eb8>"
      ]
     },
     "execution_count": 159,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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pnNIzAu8Fng48A3g+sCoiVhXehyRJKqRYEIiIJcCpwIsy8/rM/CJwHnBYqX1IkqSySp4a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\nQJKkihkEJEmqmEFAkqSK/X8JhQXK7Zy7MwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x107578470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 286,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 286,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cov(4, 4) # expected to be 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 297,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[  1.52299797e-08   3.72665317e-06   3.35462628e-04   8.82496903e-01\n",
      "   1.00000000e+00]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(matrix([[ 15.8]]), 1.0)"
      ]
     },
     "execution_count": 297,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def pred(xp):\n",
    "    K2 = np.zeros((N+1, N+1))\n",
    "    N2 = N + 1\n",
    "    \n",
    "    sigma22 = cov(xp, xp)\n",
    "    K2[N2-1][N2-1] = sigma22\n",
    "    \n",
    "    for i in range(N):\n",
    "        for j in range(i, N):\n",
    "            K2[i][j] = cov(x[i], y[j])\n",
    "            K2[j][i] = K2[i][j]\n",
    "    \n",
    "    for i in range(N):\n",
    "        K2[N2-1][i]= cov(xp, x[i])\n",
    "        K2[i][N2-1]= cov(xp, x[i])\n",
    "\n",
    "    sigma12 = np.array(K2[:N2-1,N2-1])\n",
    "    sigma11 = np.mat(K)\n",
    "    sigma21 = K[N-1:]\n",
    "    print(sigma12)\n",
    "    mp = (sigma12.T * sigma11.I) * np.mat(y).T\n",
    "#     sigmap = sigma22 - np.mat(sigma12).T * sigma11.I * np.mat(sigma12)\n",
    "#     return mp, sigmap\n",
    "    return mp, sigma22\n",
    "\n",
    "pred(4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 285,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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d3jw4zNlro2shEpHypmBQIYLZCE311XSvbY/02CnH4Zx1HTz58iG27uzDdV2c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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1076ac748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x, y)\n",
    "def p():\n",
    "    x = np.linspace(-5, 20, 200)\n",
    "    y = np.zeros(200)\n",
    "    yu = np.zeros(200)\n",
    "    yb = np.zeros(200)\n",
    "    for i in range(len(x)):\n",
    "        yp, sigmap = pred(x[i])\n",
    "        \n",
    "        yp = np.asarray(yp)[0][0]\n",
    "        yu[i] = yp - np.sqrt(sigmap)\n",
    "        y[i] = yp\n",
    "#     plt.plot(x, yu)\n",
    "    plt.plot(x, y)\n",
    "p()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9.1176530400000005e+27"
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.asarray(np.mat([[  9.11765304e+27]]))[0][0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 238,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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m4C1r7dhTQ14JfZ2ISFLZe/T0NsJVi8pi8hjhkYjegVE3hIgku4jXGFhrHwx/bIwZ+6k5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\nEZeCgYiIiLj+fx8fRMj8Ah1DAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106e61ef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def cov(x1, x2):\n",
    "    return np.exp(-1.0/2 * np.abs(x1 - x2))\n",
    "\n",
    "def pred(xp):\n",
    "    K2 = np.zeros((N+1, N+1))\n",
    "    N2 = N + 1\n",
    "    \n",
    "    sigma22 = cov(xp, xp)\n",
    "    K2[N2-1][N2-1] = sigma22\n",
    "    \n",
    "    for i in range(N):\n",
    "        for j in range(i, N):\n",
    "            K2[i][j] = cov(x[i], y[j])\n",
    "            K2[j][i] = K2[i][j]\n",
    "    \n",
    "    for i in range(N):\n",
    "        K2[N2-1][i]= cov(xp, x[i])\n",
    "        K2[i][N2-1]= cov(xp, x[i])\n",
    "    \n",
    "    sigma12 = np.array(K2[:N2-1,N2-1])\n",
    "    sigma11 = np.mat(K)\n",
    "    sigma21 = K[N-1:]\n",
    "#     print(sigma12)\n",
    "#     print(sigma11)\n",
    "    mp = (sigma12.T * sigma11.I) * np.mat(y).T\n",
    "#     sigmap = sigma11 - np.mat(sigma12) * sigma21.T\n",
    "    return mp, sigma22\n",
    "\n",
    "plt.scatter(x, y)\n",
    "def p():\n",
    "    x = np.linspace(-10, 10, 200)\n",
    "    y = np.zeros(200)\n",
    "    yu = np.zeros(200)\n",
    "    yb = np.zeros(200)\n",
    "    for i in range(len(x)):\n",
    "        yp, sigmap = pred(x[i])\n",
    "        \n",
    "        yp = np.asarray(yp)[0][0]\n",
    "        yu[i] = yp - np.sqrt(sigmap) * 3\n",
    "        y[i] = yp\n",
    "#     plt.plot(x, yu)\n",
    "    plt.plot(x, y)\n",
    "p()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  1.00000000e+00,   6.06530660e-01,   1.35335283e-01,\n",
       "          2.69957850e-07,   1.52299797e-08],\n",
       "       [  6.06530660e-01,   1.00000000e+00,   6.06530660e-01,\n",
       "          4.00652974e-05,   3.72665317e-06],\n",
       "       [  1.35335283e-01,   6.06530660e-01,   1.00000000e+00,\n",
       "          2.18749112e-03,   3.35462628e-04],\n",
       "       [  2.69957850e-07,   4.00652974e-05,   2.18749112e-03,\n",
       "          1.00000000e+00,   8.82496903e-01],\n",
       "       [  1.52299797e-08,   3.72665317e-06,   3.35462628e-04,\n",
       "          8.82496903e-01,   1.00000000e+00]])"
      ]
     },
     "execution_count": 189,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "K"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 209,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  1.52299797e-08,   3.72665317e-06,   3.35462628e-04,\n",
       "          8.82496903e-01,   1.00000000e+00]])"
      ]
     },
     "execution_count": 209,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "K[N-1:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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