gp_process.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import tensorflow as tf\n",
    "import tensorflow_probability as tfp\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "sns.set()\n",
    "tf.enable_eager_execution()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "tfd = tfp.distributions\n",
    "tfk = tfp.positive_semidefinite_kernels\n",
    "tfe = tf.contrib.eager"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    return np.sin(3*x) + np.random.normal(loc=0, scale=0.2, size=(len(x), 1))\n",
    "\n",
    "def toy_data(num_obs_points, var_obs_noise):\n",
    "    \n",
    "    index_points = np.random.uniform(0., 5., size=(num_obs_points, 1)).astype(np.float32)\n",
    "    observations = f(index_points) + np.random.normal(loc=0,\n",
    "                                                      scale=np.sqrt(var_obs_noise),\n",
    "                                                      size=(num_obs_points, 1))\n",
    "    return index_points, observations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7fe3c1d47e80>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYcAAAEBCAYAAACT92m7AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvhp/UCwAAFNJJREFUeJzt3X9sVfX9x/FX7y3t96ttLb3fW7ildTXd+NLVGaNmBhdhKxcKsUJLUtBqdOjo12C2ZYuZzGWCHVu+JYuugy2OOBMJjrBmZUjlR8eMdQIhS9AFiybagCBtod5CCo7AvPd+/+Dbbt2ntL29555zz7nPx1/09tjz5k29r3M/n3M+n6x4PB4XAAD/wud0AQCA9EM4AAAMhAMAwEA4AAAMhAMAwEA4AAAMhAMAwEA4AAAMhAMAwEA4AAAMhAMAwEA4AAAMhAMAwJDtdAGJOn/+M8VimbOQbCCQp0jkktNlOIoe0AOJHkhT64HPl6Xp029M+FyuC4dYLJ5R4SAp4/6+Y6EH9ECiB5J9PWBYCQBgIBwAAAbCAQBgIBwAAAbCAQBgcN3dSgDgRoe7+9Xe1aPI0BUFCnK1fH6F5lbNdLqs6yIcACDFDnf365W9H+jq5zFJUmToil7Z+4EkpW1AMKwEACnW3tUzEgzDrn4eU3tXj0MVTYxwAIAUiwxdSej1dEA4AECKBQpyE3o9HWTEnIPbJoIAeMvy+RWj5hwkKSfbp+XzKxysanyeDwc3TgQB8Jbh9xo3XaRaFg4tLS3av3+/zpw5o927d2v27NnGMdFoVBs2bNBf/vIXZWVlqampSQ0NDVaVMKbxJoLS+R8GgLfMrZrpqvccy+YcFixYoFdffVWzZs267jG7d+/WqVOn1NnZqR07dmjTpk365JNPrCphTG6cCAIAp1kWDnfddZdCodC4x+zZs0cNDQ3y+XwqKipSOBzWvn37rCphTG6cCAIAp9k659DX16eSkpKRr0OhkPr7+xP6GYFAXkLHf7O2Spvb/qYr/4iOvJY7za9v1lYpGMxP6Gc5xS11phI9oAcSPZDs64HrJqQjkUsJbXZRdXOhHln838ZEUNXNhRoYuJjCSq0RDOa7os5Uogf0QKIH0tR64PNlJXxRLdkcDqFQSL29vbrtttskmZ8kUsVtE0FIL9wKjUxk60NwixcvVltbm2KxmAYHB3XgwAHV1NTYWQKQkOFboYdvYBi+Ffpwd2LDoYDbWBYOGzZs0Lx589Tf369Vq1bpvvvukyStXr1ax44dkyQtW7ZMpaWlWrRokVasWKEnn3xSZWVlVpUAWM6Na+IAVsiKx+Ou2rE70TkHt2Oc1dkePPa/b1z3ey+vrbatDn4PMrMH/z6k+c3aKlXdXJjQz5jqnANrKwHj4FZoOGWsIc3NbX+zbUiTcADGsXx+hXKyR/9vku5r4sAbxhrSvPKPqG1Dmq67lRWwkxvXxIE3OL26A+EATIBboeGEQEHumEFg15Am4QBMgOcc4ISxlvnOnea3bUiTcLAIbyDexJLvcMpYQ5pTuVtpqggHC/AG4l0s+Q4n/fuQpp2383K3kgV4UMq7nJ4UBJxCOFiANxDv4jkHZCrCwQK8gXgXzzkgUxEOFuANxLvmVs3Uo0vmjAR9oCBXjy6Zw3wDPI8JaQvwoJS38ZwDMhHhYBHeQAB4CcNKAAAD4QAAMBAOAAAD4QAAMBAOAAADdysBwCRl0gKbhAMATEKmLbDJsBIATEKmLbBJOADAJGTaApuEAwBMQqYtsEk4AMAkZNoCm0xIA8AkZNoCm4QDAExSJi2wybASAMBAOAAADIQDAMBg2ZzDiRMntHbtWl24cEGFhYVqaWlReXn5qGM2bdqk3/3udyouLpYk3XHHHVq3bp1VJQAALGJZOKxbt06NjY1atmyZdu3apWeffVZbt241jqurq9PTTz9t1WkBAClgybBSJBLR8ePHVVtbK0mqra3V8ePHNTg4aMWPBwDYzJJw6Ovr04wZM+T3+yVJfr9fxcXF6uvrM459/fXXdf/99+uxxx7TO++8Y8XpAQAWs/U5hwceeEBPPPGEpk2bpoMHD2rNmjXas2ePpk+fPumfEQjkpbDC9BQM5jtdguPoAT2Q6IFkXw8sCYdQKKSzZ88qGo3K7/crGo3q3LlzCoVCo44LBoMjf/7a176mUCikDz/8UF/96lcnfa5I5JJisbgVZbtCMJivgYGLTpfhKHpADyR6IE2tBz5f1pQuqi0ZVgoEAqqsrFRHR4ckqaOjQ5WVlSoqKhp13NmzZ0f+/P777+vMmTO65ZZbrCgBAGAhy4aV1q9fr7Vr1+rXv/61CgoK1NLSIklavXq1vvOd7+grX/mKnn/+eXV3d8vn82natGnauHHjqE8TAID0kBWPx101RsOwUuZJtAde3MqR3wN6INk7rMTCe/CUTNvKEUgVls+Ap2TaVo5AqhAO8JRM28oRSBXCAZ6SaVs5AqlCOMBTMm0rRyBVmJCGp2TaVo5AqhAO8JxM2soRSBWGlQAABsIBAGAgHAAABuYcAHiSF5dRsRPhAMBzWEYleQwrAfAcllFJHuEAwHNYRiV5hAMAz2EZleQRDgA8h2VUkseENADPYRmV5BEOADyJZVSSw7ASAMBAOAAADIQDAMBAOAAADIQDAMBAOAAADNzK6lGsSAkgGYSDB7EiJYBkMazkQaxICSBZhIMHsSIlgGQRDh7EipQAkkU4eBArUgJIlmXhcOLECa1cuVI1NTVauXKlTp48aRwTjUb13HPPKRwOa+HChWpra7Pq9PgXc6tm6tElc0Y+KQQKcvXokjlMRgOYNMvuVlq3bp0aGxu1bNky7dq1S88++6y2bt066pjdu3fr1KlT6uzs1IULF1RXV6e5c+eqtLTUqjLw/1iREkAyLPnkEIlEdPz4cdXW1kqSamtrdfz4cQ0ODo46bs+ePWpoaJDP51NRUZHC4bD27dtnRQkAAAtZEg59fX2aMWOG/H6/JMnv96u4uFh9fX3GcSUlJSNfh0Ih9ff3W1ECAMBCrnsILhDIc7oE2wWD+U6X4Dh6QA8keiDZ1wNLwiEUCuns2bOKRqPy+/2KRqM6d+6cQqGQcVxvb69uu+02SeYnicmIRC4pFotbUbYrBIP5Ghi46HQZjqIH9ECiB9LUeuDzZU3potqSYaVAIKDKykp1dHRIkjo6OlRZWamioqJRxy1evFhtbW2KxWIaHBzUgQMHVFNTY0UJAAALWXYr6/r167Vt2zbV1NRo27Zteu655yRJq1ev1rFjxyRJy5YtU2lpqRYtWqQVK1boySefVFlZmVUlAAAskhWPx101RsOwUuahB/RAogeSC4eVAADeQjgAAAyEAwDAQDgAAAyEAwDAQDgAAAyEAwDA4Lq1lXB9h7v71d7Vo8jQFQUKcrV8fgXLdgOYEsLBIw539+uVvR/o6ucxSdf2i35l7weSREAASBjDSh7R3tUzEgzDrn4eU3tXj0MVAXAzwsEjIkNXEnodAMZDOHjE8H7Rk30dAMZDOHjE8vkVyske/c+Zk+3T8vkVDlUEwM2YkPaI4Uln7lYCYAXCwUPmVs0kDABYgmElAICBcAAAGBhWAlyGJ+FhB8IBcBGehIddGFYCXIQn4WEXwgFwEZ6Eh10IB8BFeBIediEcABfhSXjYhQlpwEV4Eh52IRwAl+FJeNiBYSUAgIFwAAAYGFZyCZ6KBWAnwsEFeCoWgN0YVnIBnooFYLekPzlcvnxZP/zhD9Xd3S2/36+nn35a3/jGN4zjjhw5oqamJpWXl0uScnJy1NbWluzpMwJPxQKwW9Lh8Nvf/lZ5eXn605/+pJMnT+qhhx5SZ2enbrzxRuPYiooKtbe3J3vKjBMoyB0zCHgqFkCqJD2stHfvXq1cuVKSVF5erltvvVVvvfVW0oXhn3gqFoDdkv7k0Nvbq1mzZo18HQqF1N/fP+axJ0+eVH19vbKzs9XY2Kj6+vqEzxcI5E25Vrda+vUvqSD/P7R17/v69Pxl/df0/9QjSyr19TvLnC7NNsFgvtMlOI4e0APJvh5MGA719fXq7e0d83uHDh2a9ImqqqrU1dWl/Px8nT59WqtWrdKMGTN0zz33TL5aSZHIJcVi8YT+GzcLBvM1MHBRVTcXquV/5o763sDARYeqstdwDzIZPaAH0tR64PNlTemiesJw2Llz57jfLykp0ZkzZ1RUVCRJ6uvr0913320cl5f3z+LKysoUDod19OjRhMMBAJB6Sc85LF68WDt27JB0bdjo2LFjuvfee43jzp07p3j82hX/hQsXdPDgQc2ZMyfZ0wMAUiDpOYfHH39ca9eu1cKFC+Xz+dTc3DzyKaG1tVXFxcV68MEH1dnZqe3btys7O1vRaFR1dXUKh8NJ/wUAANbLig9fzrtEps45ZDJ6QA8keiDZO+fAE9IAAAPhAAAwEA4AAAPhAAAwEA4AAAPhAAAwEA4AAAPhAAAwsE0oAMexR3r6IRwAOIo90tMTw0oAHMUe6emJTw4AUmKyQ0XskZ6e+OQAwHLDQ0XDb/DDQ0WHu81dIq+3Fzp7pDuLcABguUSGitgjPT0xrIQJcScJEpXIUNHw7xK/Y+mFcMC4uJMEUxEoyB0zCK43VDS3aia/T2mGYSWMiztJMBUMFbkfnxwwLu4kwVQwVOR+hAPGlejwADCMoSJ3Y1gJ42J4AMhMfHLAuBgeADIT4YAJMTwAZB6GlQAABsIBAGAgHAAABsIBAGAgHAAABsIBAGAgHAAAhqTDYdeuXbr//vv15S9/Wdu2bRv32N///vdauHChwuGwmpubFYvFxj0eAOCMpMOhsrJSL7zwgmpra8c97vTp09q8ebN27Nihzs5Offzxx3rttdeSPT0AIAWSfkJ69uzZkiSfb/yc2b9/v8LhsIqKiiRJDQ0Nam9vV11dXbIlwCFsAgR4l23LZ/T19amkpGTk65KSEvX19dl1eliMTYAAb5swHOrr69Xb2zvm9w4dOiS/3295UeMJBPJsPV86CAbznS7B8Me3D4+5CdAf3z6hpV//kuXnS8ce2I0e0APJvh5MGA47d+605EShUGhUyPT29ioUCiX8cyKRS4rF4pbU5AbBYL4GBi46XYZh4Pzl675udb3p2gM70QN6IE2tBz5f1pQuqm27lbWmpkYHDhzQ4OCgYrGY2tratGTJErtOD4tdb7MfNgECvCHpcOjo6NC8efO0b98+tba2at68efroo48kSa2trdq+fbskqaysTGvWrNGKFSu0aNEilZaWaunSpcmeHg5hEyDA27Li8birxmgYVkofdt2tlM49sAs9oAeSvcNKbPaDKWMTIMC7CAcAjuJ5mfREOABwDM/LpC8W3gPgmPaunjGfl2nv6nGoIgwjHAA4JjJ0JaHXYR/CAYBjeF4mfREOABzD8zLpiwlpAI4ZnnTmbqX0QzgAcBTPy6QnhpUAAAbCAQBgIBwAAAbCAQBgIBwAAAbCAQBgIBwAAAbCAQBgIBwAAAbCAQBgIBwAAAbCAQBgIBwAAAbCAQBgYMluAGnhcHc/+zqkEcIBgOMOd/frlb0f6OrnMUnX9pB+Ze8HkkRAOIRwyABckSHdtXf1jATDsKufx9Te1cPvqkMIB4/jigxuEBm6ktDrSD0mpD1uvCsyIF0ECnITeh2pRzh4HFdkcIPl8yuUkz367Sgn26fl8yscqggMK3lcoCB3zCDgigzpZHiIk7mx9JF0OOzatUsvvfSSenp69Mwzz+jhhx8e87gjR46oqalJ5eXlkqScnBy1tbUle3pMYPn8ilFzDhJXZEhPc6tmEgZpJOlwqKys1AsvvKAtW7ZMeGxFRYXa29uTPSUSwBUZgKlIOhxmz54tSfL5mL5IV1yRAUiUre/oJ0+eVH19vRoaGrRz5047Tw0ASMCEnxzq6+vV29s75vcOHTokv98/qRNVVVWpq6tL+fn5On36tFatWqUZM2bonnvuSajgQCAvoeO9IBjMd7oEx9EDeiDRA8m+HkwYDlZd4efl/fNNvaysTOFwWEePHk04HCKRS4rF4pbU5AbBYL4GBi46XYaj6AE9kOiBNLUe+HxZU7qotm1Y6dy5c4rHr72pX7hwQQcPHtScOXPsOj0AIAFJT0h3dHRo48aNGhoa0p///Gdt2bJFL7/8sr74xS+qtbVVxcXFevDBB9XZ2ant27crOztb0WhUdXV1CofDVvwdAAAWy4oPX867xPnzn2XUsFIgkKdI5JLTZTiKHtADiR5IU+uBz5el6dNvTPhcrgsHAEDq8XACAMBAOAAADIQDAMBAOAAADIQDAMBAOAAADIQDAMBAOAAADIQDAMDAHtJpqqWlRfv379eZM2e0e/fukU2VMsn58+f1gx/8QKdOnVJOTo6+8IUvqLm5WUVFRU6XZps1a9bok08+kc/n0w033KAf//jHqqysdLosR2zevFmbNm3KyP8fqqurlZOTo9zca3u/P/XUU7r33ntTek7CIU0tWLBAjzzyiB566CGnS3FMVlaWvvWtb+nuu++WdC0wf/7zn+tnP/uZw5XZp6WlRfn519bvP3DggJ555pmM3Ciru7tb7777rmbNmuV0KY755S9/aWsoMqyUpu666y6FQiGny3BUYWHhSDBI0u23337djae8ajgYJOnSpUvKyspysBpnXL16Vc3NzVq/fr3TpWQUPjnAFWKxmLZv367q6mqnS7Hdj370Ix08eFDxeFwvvfSS0+XYrrW1VUuXLlVpaanTpTjqqaeeUjwe15133qnvf//7KigoSOn5+OQAV/jJT36iG264QQ8//LDTpdjupz/9qd58801973vf08aNG50ux1bvvPOO3nvvPTU2NjpdiqNeffVVvfbaa/rDH/6geDyu5ubmlJ+TcEDaa2lp0ccff6xf/OIX8vky91e2rq5OR44c0fnz550uxTZ//etf1dPTowULFqi6ulr9/f16/PHH9fbbbztdmq2Gh5hzcnLU2Nioo0ePpvycDCshrT3//PN67733tGXLFuXk5Dhdjq0+++wzDQ0NjbwxvPHGG7rppptUWFjocGX2aWpqUlNT08jX1dXVevHFFzPqbqW///3vikajys/PVzwe1549e2y5Y41wSFMbNmxQZ2enPv30U61atUqFhYV6/fXXnS7LVh9++KF+85vfqLy8XA888IAkqbS0VL/61a8crswely9f1ne/+11dvnxZPp9PN910k1588cWMnJTOZJFIRN/+9rcVjUYVi8VUUVGhdevWpfy87AQHADBk7gAuAOC6CAcAgIFwAAAYCAcAgIFwAAAYCAcAgIFwAAAYCAcAgOH/AFVqaSxYJ8WHAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "NUM_OBS_POINTS = 20\n",
    "index_points, observations = toy_data(NUM_OBS_POINTS, 0.1)\n",
    "plt.scatter(index_points, observations)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "amplitude = tf.nn.softplus(tfe.Variable(initial_value=5.,\n",
    "                                        name='amplitude',\n",
    "                                        dtype=np.float64))\n",
    "length_scale = tf.nn.softplus(tfe.Variable(initial_value=10.,\n",
    "                                           name='length_scale',\n",
    "                                           dtype=np.float64))\n",
    "noise_variance = tf.nn.softplus(tfe.Variable(initial_value=1.,\n",
    "                                             name='noise_variance',\n",
    "                                             dtype=np.float64))\n",
    "\n",
    "kernel = tfk.ExponentiatedQuadratic(amplitude, length_scale)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "ename": "AttributeError",
     "evalue": "module 'tensorflow_probability.python.distributions' has no attribute 'GaussianProcess'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-7-441b41a9273d>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m gp = tfd.GaussianProcess(kernel=kernel,\n\u001b[0m\u001b[1;32m      2\u001b[0m                          \u001b[0mindex_points\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mindex_points\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m                          observation_noise_variance=noise_variance)\n",
      "\u001b[0;31mAttributeError\u001b[0m: module 'tensorflow_probability.python.distributions' has no attribute 'GaussianProcess'"
     ]
    }
   ],
   "source": [
    "gp = tfd.GaussianProcess(kernel=kernel,\n",
    "                         index_points=index_points,\n",
    "                         observation_noise_variance=noise_variance)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}