GP and Bayesian Optimization.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "Cz9dvH4E1FO-"
   },
   "source": [
    "# Gaussian processes and Bayesian optimization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "1x24jKMW1FPA"
   },
   "source": [
    "In this assignment we will use <a href=\"http://sheffieldml.github.io/GPy/\">GPy</a> and <a href=\"http://sheffieldml.github.io/GPyOpt/\">GPyOpt</a> libraries to deal with gaussian processes. These libraries provide quite simple and inuitive interfaces for training and inference."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "NKHDJx6v1FPD"
   },
   "source": [
    "### Setup\n",
    "Load auxiliary files and then install and import the necessary libraries."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "gIHlN5WL1FPR"
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import GPy\n",
    "import GPyOpt\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.svm import SVR\n",
    "import sklearn.datasets\n",
    "from xgboost import XGBRegressor\n",
    "from sklearn.model_selection import cross_val_score\n",
    "import time"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "mwys3aRv1FPZ"
   },
   "source": [
    "## Gaussian processes: GPy (<a href=\"http://pythonhosted.org/GPy/\">documentation</a>)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "collapsed": true,
    "id": "uzd2Kbv71FPZ"
   },
   "source": [
    "We will start with a simple regression problem, for which we will try to fit a Gaussian Process with RBF kernel."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "A6wePT8v1FPa"
   },
   "outputs": [],
   "source": [
    "def generate_points(n=25, noise_variance=0.0036):\n",
    "    np.random.seed(777)\n",
    "    X = np.random.uniform(-3., 3., (n, 1))\n",
    "    y = np.sin(X) + np.random.randn(n, 1) * noise_variance**0.5\n",
    "    return X, y\n",
    "    \n",
    "def generate_noise(n=25, noise_variance=0.0036):\n",
    "    np.random.seed(777)\n",
    "    X = np.random.uniform(-3., 3., (n, 1))\n",
    "    y = np.random.randn(n, 1) * noise_variance**0.5\n",
    "    return X, y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "bzLjKc5-1FPp"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create data points\n",
    "X, y = generate_points()\n",
    "plt.plot(X, y, '.')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "AISpXJm-1FPr"
   },
   "source": [
    "To fit a Gaussian Process, we will need to define a kernel. For Gaussian (GBF) kernel we can use `GPy.kern.RBF` function."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "SuyEqz8z1FPs"
   },
   "source": [
    "We choose RBF kernel with variance 1.5 and length-scale parameter 2 for 1D samples and compute value of the kernel between points `X[5]` and `X[9]`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "573PCa0o1FPs"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0461813545396959"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kernel = GPy.kern.RBF(input_dim=1, variance=1.5, lengthscale=2.)\n",
    "kernel_59 = kernel.K(X)[5, 9]\n",
    "kernel_59"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "2vo9aW4F1FPu"
   },
   "source": [
    "Let's fit GP into generated data using the kernel above. Then we find the predicted mean and vairance at position $x=1$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "faKDVJNk1FPu"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([[0.66467749]]), array([[1.10014782]]))"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "position = np.array([[1]])\n",
    "model = GPy.models.GPRegression(X, y, kernel)\n",
    "mean = model.predict(position)[0]\n",
    "variance = model.predict(position)[1]\n",
    "mean, variance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "yPhBBZ921FPw"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "nMJb7qtA1FPy"
   },
   "source": [
    "We see that the model didn't fit the data quite well. Let's try to fit kernel and noise parameters automatically as discussed in the lecture! You can see the current parameters below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "uQf0yjdy1FPy"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       ".pd{\n",
       "    font-family: \"Courier New\", Courier, monospace !important;\n",
       "    width: 100%;\n",
       "    padding: 3px;\n",
       "}\n",
       "</style>\n",
       "\n",
       "<p class=pd>\n",
       "<b>Model</b>: GP regression<br>\n",
       "<b>Objective</b>: 27.86687636693494<br>\n",
       "<b>Number of Parameters</b>: 3<br>\n",
       "<b>Number of Optimization Parameters</b>: 3<br>\n",
       "<b>Updates</b>: True<br>\n",
       "</p>\n",
       "<style type=\"text/css\">\n",
       ".tg  {font-family:\"Courier New\", Courier, monospace !important;padding:2px 3px;word-break:normal;border-collapse:collapse;border-spacing:0;border-color:#DCDCDC;margin:0px auto;width:100%;}\n",
       ".tg td{font-family:\"Courier New\", Courier, monospace !important;font-weight:bold;color:#444;background-color:#F7FDFA;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:#DCDCDC;}\n",
       ".tg th{font-family:\"Courier New\", Courier, monospace !important;font-weight:normal;color:#fff;background-color:#26ADE4;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:#DCDCDC;}\n",
       ".tg .tg-left{font-family:\"Courier New\", Courier, monospace !important;font-weight:normal;text-align:left;}\n",
       ".tg .tg-center{font-family:\"Courier New\", Courier, monospace !important;font-weight:normal;text-align:center;}\n",
       ".tg .tg-right{font-family:\"Courier New\", Courier, monospace !important;font-weight:normal;text-align:right;}\n",
       "</style>\n",
       "<table class=\"tg\"><tr><th><b>  GP_regression.         </b></th><th><b>value</b></th><th><b>constraints</b></th><th><b>priors</b></th></tr>\n",
       "<tr><td class=tg-left>  rbf.variance           </td><td class=tg-right>  1.5</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "<tr><td class=tg-left>  rbf.lengthscale        </td><td class=tg-right>  2.0</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "<tr><td class=tg-left>  Gaussian_noise.variance</td><td class=tg-right>  1.0</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<GPy.models.gp_regression.GPRegression at 0x12443c550>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "zMW6Zd6B1FP0"
   },
   "source": [
    "We optimize length-scale, variance and noise component of the model just by using the *optimize* method of the model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "X-z2RYE31FP0"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Name : GP regression\n",
      "Objective : -18.351767754167305\n",
      "Number of Parameters : 3\n",
      "Number of Optimization Parameters : 3\n",
      "Updates : True\n",
      "Parameters:\n",
      "  \u001b[1mGP_regression.         \u001b[0;0m  |                  value  |  constraints  |  priors\n",
      "  \u001b[1mrbf.variance           \u001b[0;0m  |     0.7099385903482573  |      +ve      |        \n",
      "  \u001b[1mrbf.lengthscale        \u001b[0;0m  |     1.6252681834583018  |      +ve      |        \n",
      "  \u001b[1mGaussian_noise.variance\u001b[0;0m  |  0.0038978707543180927  |      +ve      |        \n"
     ]
    }
   ],
   "source": [
    "model.optimize()\n",
    "print(model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can easily see the imporvement below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "rtxXBeQY1FP2"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "ae-T1iI21FP4"
   },
   "source": [
    "As we can see, the process generates outputs just right. Let's see if GP can distinguish noise and signal."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "YZAPIQNs1FP5"
   },
   "source": [
    "Generate two datasets: sinusoid wihout noise and samples from gaussian noise. Optimize kernel parameters and find the optimal values of noise component."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "42qb6mDN1FP5"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X, y = generate_noise(noise_variance=10) # data with noise\n",
    "k = GPy.kern.RBF(input_dim=1)\n",
    "model = GPy.models.GPRegression(X, y, k)\n",
    "\n",
    "model.optimize()\n",
    "\n",
    "model.plot()\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       ".pd{\n",
       "    font-family: \"Courier New\", Courier, monospace !important;\n",
       "    width: 100%;\n",
       "    padding: 3px;\n",
       "}\n",
       "</style>\n",
       "\n",
       "<p class=pd>\n",
       "<b>Model</b>: GP regression<br>\n",
       "<b>Objective</b>: 67.9980411668395<br>\n",
       "<b>Number of Parameters</b>: 3<br>\n",
       "<b>Number of Optimization Parameters</b>: 3<br>\n",
       "<b>Updates</b>: True<br>\n",
       "</p>\n",
       "<style type=\"text/css\">\n",
       ".tg  {font-family:\"Courier New\", Courier, monospace !important;padding:2px 3px;word-break:normal;border-collapse:collapse;border-spacing:0;border-color:#DCDCDC;margin:0px auto;width:100%;}\n",
       ".tg td{font-family:\"Courier New\", Courier, monospace !important;font-weight:bold;color:#444;background-color:#F7FDFA;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:#DCDCDC;}\n",
       ".tg th{font-family:\"Courier New\", Courier, monospace !important;font-weight:normal;color:#fff;background-color:#26ADE4;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:#DCDCDC;}\n",
       ".tg .tg-left{font-family:\"Courier New\", Courier, monospace !important;font-weight:normal;text-align:left;}\n",
       ".tg .tg-center{font-family:\"Courier New\", Courier, monospace !important;font-weight:normal;text-align:center;}\n",
       ".tg .tg-right{font-family:\"Courier New\", Courier, monospace !important;font-weight:normal;text-align:right;}\n",
       "</style>\n",
       "<table class=\"tg\"><tr><th><b>  GP_regression.         </b></th><th><b>             value</b></th><th><b>constraints</b></th><th><b>priors</b></th></tr>\n",
       "<tr><td class=tg-left>  rbf.variance           </td><td class=tg-right> 4.840661337062973</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "<tr><td class=tg-left>  rbf.lengthscale        </td><td class=tg-right>0.4624141444416375</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "<tr><td class=tg-left>  Gaussian_noise.variance</td><td class=tg-right>10.143215047293625</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<GPy.models.gp_regression.GPRegression at 0x12421c860>"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       ".tg  {padding:2px 3px;word-break:normal;border-collapse:collapse;border-spacing:0;border-color:#DCDCDC;margin:0px auto;width:100%;}\n",
       ".tg td{font-family:\"Courier New\", Courier, monospace !important;font-weight:bold;color:#444;background-color:#F7FDFA;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:#DCDCDC;}\n",
       ".tg th{font-family:\"Courier New\", Courier, monospace !important;font-weight:normal;color:#fff;background-color:#26ADE4;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:#DCDCDC;}\n",
       ".tg .tg-left{font-family:\"Courier New\", Courier, monospace !important;font-weight:normal;text-align:left;}\n",
       ".tg .tg-right{font-family:\"Courier New\", Courier, monospace !important;font-weight:normal;text-align:right;}\n",
       "</style>\n",
       "<table class=\"tg\">\n",
       "\n",
       "<tr>\n",
       "  <th><b>index</b></th>\n",
       "  <th><b>GP_regression.Gaussian_noise.variance</b></th>\n",
       "  <th><b>constraints</b></th><th><b>priors</b></th>\n",
       "</tr>\n",
       "<tr><td class=tg-left>  [0]  </td><td class=tg-right>                          10.14321505</td><td class=tg-left>    +ve    </td><td class=tg-left>      </td></tr>"
      ],
      "text/plain": [
       "\u001b[1mGP_regression.Gaussian_noise.variance\u001b[0;0m:\n",
       "Param([10.14321505])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.Gaussian_noise.variance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "ename": "SyntaxError",
     "evalue": "invalid syntax (<ipython-input-41-17b3aa5c3518>, line 1)",
     "output_type": "error",
     "traceback": [
      "\u001b[0;36m  File \u001b[0;32m\"<ipython-input-41-17b3aa5c3518>\"\u001b[0;36m, line \u001b[0;32m1\u001b[0m\n\u001b[0;31m    So GP could find a good extimation of the noise variance.\u001b[0m\n\u001b[0m        ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n"
     ]
    }
   ],
   "source": [
    "So GP could find a good extimation of the noise variance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "ZFUOIU5U1FP7"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X, y = generate_points(noise_variance=0) # data without noise\n",
    "\n",
    "model = GPy.models.GPRegression(X, y, k)\n",
    "\n",
    "model.optimize()\n",
    "\n",
    "model.plot()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Name : GP regression\n",
      "Objective : -140.28957451789958\n",
      "Number of Parameters : 3\n",
      "Number of Optimization Parameters : 3\n",
      "Updates : True\n",
      "Parameters:\n",
      "  \u001b[1mGP_regression.         \u001b[0;0m  |                   value  |  constraints  |  priors\n",
      "  \u001b[1mrbf.variance           \u001b[0;0m  |       4.025037839763786  |      +ve      |        \n",
      "  \u001b[1mrbf.lengthscale        \u001b[0;0m  |      2.6455878696286192  |      +ve      |        \n",
      "  \u001b[1mGaussian_noise.variance\u001b[0;0m  |  1.5071540413599144e-14  |      +ve      |        \n"
     ]
    }
   ],
   "source": [
    "print(model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       ".tg  {padding:2px 3px;word-break:normal;border-collapse:collapse;border-spacing:0;border-color:#DCDCDC;margin:0px auto;width:100%;}\n",
       ".tg td{font-family:\"Courier New\", Courier, monospace !important;font-weight:bold;color:#444;background-color:#F7FDFA;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:#DCDCDC;}\n",
       ".tg th{font-family:\"Courier New\", Courier, monospace !important;font-weight:normal;color:#fff;background-color:#26ADE4;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:#DCDCDC;}\n",
       ".tg .tg-left{font-family:\"Courier New\", Courier, monospace !important;font-weight:normal;text-align:left;}\n",
       ".tg .tg-right{font-family:\"Courier New\", Courier, monospace !important;font-weight:normal;text-align:right;}\n",
       "</style>\n",
       "<table class=\"tg\">\n",
       "\n",
       "<tr>\n",
       "  <th><b>index</b></th>\n",
       "  <th><b>GP_regression.Gaussian_noise.variance</b></th>\n",
       "  <th><b>constraints</b></th><th><b>priors</b></th>\n",
       "</tr>\n",
       "<tr><td class=tg-left>  [0]  </td><td class=tg-right>                           0.00000000</td><td class=tg-left>    +ve    </td><td class=tg-left>      </td></tr>"
      ],
      "text/plain": [
       "\u001b[1mGP_regression.Gaussian_noise.variance\u001b[0;0m:\n",
       "Param([1.50715404e-14])"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.Gaussian_noise.variance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "which shows GP recognizes that this is data without noise!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "qkoXcwya1FP-"
   },
   "source": [
    "## Sparse GP\n",
    "Now let's consider the speed of GP. We will generate a dataset of 3000 points and measure the time that is consumed for prediction of mean and variance for each point. We will then try to use inducing inputs and find the optimal number of points according to quality-time tradeoff. We know that GP sparse should be faster because it only uses afew points to find the fitting curve whithout sacrificing too much of the quality of prediction.\n",
    "\n",
    "For the sparse model with inducing points, we should use ```GPy.models.SparseGPRegression``` class. we can set the number of inducing inputs with parameter ```num_inducing``` and optimize their positions and values with ```.optimize()``` call."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "Dhw8o4gF1FP_"
   },
   "source": [
    "Create a dataset of 1000 points and fit GPRegression. Measure time for predicting mean and variance at position $x=1$. Then fit `SparseGPRegression` with 10 inducing inputs and repeat the experiment. Report speedup as a ratio between consumed time without and with inducing inputs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "LwOLB96R1FP_"
   },
   "outputs": [],
   "source": [
    "X, y = generate_points(1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "xmfP8GNn1FQB"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.19282793998718262"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "start = time.time()\n",
    "model = GPy.models.GPRegression(X, y, k)\n",
    "mean = model.predict(position)[0] \n",
    "variance = model.predict(position)[1]\n",
    "time_gp = time.time()-start\n",
    "time_gp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "bzAJoe8v1FQD"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.028563261032104492"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "start = time.time()\n",
    "model = GPy.models.SparseGPRegression(X, y, k)\n",
    "mean = model.predict(position)[0] \n",
    "variance = model.predict(position)[1]\n",
    "time_sgp = time.time()-start\n",
    "time_sgp"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "which is faster with good quality as shown below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "7TFk8mE11FQF"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "b-bMd1bK1FQJ"
   },
   "source": [
    "## Bayesian optimization: GPyOpt (<a href=\"http://pythonhosted.org/GPyOpt/\">documentation</a>, <a href=\"http://nbviewer.jupyter.org/github/SheffieldML/GPyOpt/blob/master/manual/index.ipynb\">tutorials</a>)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "zdGV3wpX1FQJ"
   },
   "source": [
    "In this part of the assignment, we will try to find optimal hyperparameters to XGBoost model! We will use data from a small competition to speed things up, but keep in mind that the approach works even for large datasets.\n",
    "\n",
    "We will use diabetes dataset provided in sklearn package."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "kmaBiv6b1FQJ"
   },
   "outputs": [],
   "source": [
    "dataset = sklearn.datasets.load_diabetes()\n",
    "X = dataset['data']\n",
    "y = dataset['target']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "h26vMkWU1FQL"
   },
   "source": [
    "We will use cross-validation score to estimate accuracy and our goal will be to tune: ```max_depth```, ```learning_rate```, ```n_estimators``` parameters of XGBoost model. The baseline MSE with default XGBoost parameters is $0.2$. Let's see if we can do better. First, we have to define optimization function and domains."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "Bwc2H7U21FQL"
   },
   "outputs": [],
   "source": [
    "# Score. Optimizer will try to find minimum, so we will add a \"-\" sign.\n",
    "def f(parameters):\n",
    "    parameters = parameters[0]\n",
    "    score = -cross_val_score(\n",
    "        XGBRegressor(learning_rate=parameters[0],\n",
    "                     max_depth=int(parameters[2]),\n",
    "                     n_estimators=int(parameters[3]),\n",
    "                     gamma=int(parameters[1]),\n",
    "                     min_child_weight = parameters[4]), \n",
    "        X, y, scoring='neg_mean_squared_error'\n",
    "    ).mean()\n",
    "    score = np.array(score)\n",
    "    return score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "pYssOmHx1FQM"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4217.028096646883"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "baseline = -cross_val_score(\n",
    "    XGBRegressor(), X, y, scoring='neg_mean_squared_error'\n",
    ").mean()\n",
    "baseline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "_4VaYZIA1FQO"
   },
   "outputs": [],
   "source": [
    "# Bounds (NOTE: define continuous variables first, then discrete!)\n",
    "bounds = [\n",
    "    {'name': 'learning_rate',\n",
    "     'type': 'continuous',\n",
    "     'domain': (0, 1)},\n",
    "\n",
    "    {'name': 'gamma',\n",
    "     'type': 'continuous',\n",
    "     'domain': (0, 5)},\n",
    "\n",
    "    {'name': 'max_depth',\n",
    "     'type': 'discrete',\n",
    "     'domain': (1, 50)},\n",
    "\n",
    "    {'name': 'n_estimators',\n",
    "     'type': 'discrete',\n",
    "     'domain': (1, 300)},\n",
    "\n",
    "    {'name': 'min_child_weight',\n",
    "     'type': 'discrete',\n",
    "     'domain': (1, 10)}\n",
    "]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "VSTcdZx21FQP"
   },
   "outputs": [],
   "source": [
    "np.random.seed(777)\n",
    "optimizer = GPyOpt.methods.BayesianOptimization(\n",
    "    f=f, domain=bounds,\n",
    "    acquisition_type ='MPI',\n",
    "    acquisition_par = 0.1,\n",
    "    exact_eval=True\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "R1sFMkhM1FQR"
   },
   "outputs": [],
   "source": [
    "max_iter = 50\n",
    "max_time = 60\n",
    "optimizer.run_optimization(max_iter, max_time)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "BRDahTLP1FQS"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "optimizer.plot_convergence()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "YbcUtQsB1FQT"
   },
   "source": [
    "Best values of parameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "Boepvj1D1FQU"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4.00490607e-02, 1.28080648e+00, 1.00000000e+00, 3.00000000e+02,\n",
       "       1.00000000e+00])"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "optimizer.X[np.argmin(optimizer.Y)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "AEME98_k1FQV"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MSE: 3193.5261235600055 Gain: 24.270693712017284\n"
     ]
    }
   ],
   "source": [
    "print('MSE:', np.min(optimizer.Y),\n",
    "      'Gain:', np.abs(baseline - np.min(optimizer.Y))/baseline*100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "jx8HH47g1FQW"
   },
   "source": [
    "We were able to get 9% boost without tuning parameters by hand! Let's try this on SVR. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "JaGhj8U41FQW"
   },
   "source": [
    "We try to find optimal values for three parameters: `C`, `epsilon` and `gamma`. We use range (1e-5, 1000) for `C`, (1e-5, 10) for `epsilon` and `gamma`. We use MPI as an acquisition function with weight 0.1. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.svm import SVR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "-pNEw2m41FQX"
   },
   "outputs": [],
   "source": [
    "domains = [\n",
    "    {'name': 'C',\n",
    "     'type': 'continuous',\n",
    "     'domain': (1e-5, 1000)},\n",
    "\n",
    "    {'name': 'epsilon',\n",
    "     'type': 'continuous',\n",
    "     'domain': (1e-5, 10)},\n",
    "\n",
    "    {'name': 'gamma',\n",
    "     'type': 'continuous',\n",
    "     'domain': (1e-5, 10)}]\n",
    "\n",
    "def f(parameters):\n",
    "    parameters = parameters[0]\n",
    "    score = -cross_val_score(\n",
    "        SVR(C=parameters[0],\n",
    "                     epsilon=parameters[1],\n",
    "                     gamma=parameters[2]),\n",
    "        X, y, scoring='neg_mean_squared_error'\n",
    "    ).mean()\n",
    "    score = np.array(score)\n",
    "    return score\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4976.655882526393"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "baseline = -cross_val_score(\n",
    "    SVR(), X, y, scoring='neg_mean_squared_error'\n",
    ").mean()\n",
    "baseline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(777)\n",
    "optimizer = GPyOpt.methods.BayesianOptimization(\n",
    "    f=f, domain=domains,\n",
    "    acquisition_type ='MPI',\n",
    "    acquisition_par = 0.1,\n",
    "    exact_eval=True\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [],
   "source": [
    "max_iter = 100\n",
    "max_time = 400\n",
    "optimizer.run_optimization(max_iter, max_time)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "optimizer.plot_convergence()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([41.20854258,  2.44201122, 10.        ])"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "optimizer.X[np.argmin(optimizer.Y)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2904.220046387097"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.min(optimizer.Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "240.13558324668415"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "baseline / (baseline - np.min(optimizer.Y))*100"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "tOG3JnVt1FQY"
   },
   "source": [
    "The boost in improvement that you got after tuning hyperparameters is 240%."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Bayesian optimization is very useful when we can not find the true value of a function for example, in the case we dont havea formula for the function. An example of this is when we want to tune hyperparameters of neural network. But when it we can easilt find the value of the function, it is better to do random search as training a bayesian model could be time-consuming anyways. For wxample, we would use random search for a simple regression on a small data set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "colab": {
   "name": "gp_assignment.ipynb",
   "provenance": [],
   "version": "0.3.2"
  },
  "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}