Model Interpretability with GPs.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"images/ublogo.png\"/>\n",
    "\n",
    "### CSE610 - Bayesian Non-parametric Machine Learning\n",
    "\n",
    "  - Lecture Notes\n",
    "  - Instructor - Varun Chandola\n",
    "  - Term - Fall 2020"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Objective\n",
    "The objective of this notebook is to discuss how to interpret (and explain) a GP model.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One of the key benefits of a GP based model (for classification or regression) is its ability to model the non-linear relationship between the input covariates and the target, without imposing strong assumptions on the nature of the relationship. However, as is true for any non-linear models, this flexibility results in the lack of interpretability of the GP model.\n",
    "\n",
    "For instance, consider the problem of predicting house prices, given various features about a house in the `Boston Housing Dataset`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [],
   "source": [
    "%run Utilities.ipynb\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "import time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "names = ['CRIM', 'ZN', 'INDUS', 'CHAS', 'NOX', 'RM', 'AGE', 'DIS', 'RAD',\n",
    "       'TAX', 'PTRATIO', 'B', 'LSTAT']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "boston_data = GPy.util.datasets.boston_housing()\n",
    "X,y = boston_data['X'],boston_data['Y']\n",
    "ss = StandardScaler()\n",
    "Xnorm = ss.fit_transform(X)\n",
    "inds = np.random.permutation(Xnorm.shape[0])\n",
    "train_size = 400\n",
    "Xtrain,ytrain,Xtest,ytest = Xnorm[inds[0:train_size],:],y[inds[0:train_size],:],Xnorm[inds[train_size:],:],y[inds[train_size:],:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "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": [
    "# this is the distribution of the target\n",
    "h = plt.hist(y,bins=20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will first train a linear regression model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RMSE = 4.51\n"
     ]
    }
   ],
   "source": [
    "md_lr = LinearRegression()\n",
    "md_lr.fit(Xtrain,ytrain)\n",
    "ypredict = md_lr.predict(Xtest)\n",
    "print('RMSE = {:.2f}'.format(np.sqrt(np.mean((ypredict - ytest)**2))))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "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": [
    "plt.scatter(ytest,ypredict)\n",
    "plt.xlabel('Actual House Price')\n",
    "plt.ylabel('Predicted House Price')\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Seems like a decent enough fit. An RMSE of 4.51 for a target that ranges between 0 - 50 could be considered reasonable.\n",
    "> The target corresponds to the price of the house divided by $1000.\n",
    "\n",
    "Now let us see if having a non-linear model has a better effect."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RMSE = 2.93\n",
      "Time taken = 0.86 seconds\n"
     ]
    }
   ],
   "source": [
    "st = time.time()\n",
    "md_gp = GPy.models.GPRegression(Xtrain,ytrain,kernel=GPy.kern.RBF(Xtrain.shape[1]))\n",
    "md_gp.optimize()\n",
    "ypredict = md_gp.predict(Xtest)\n",
    "en = time.time()\n",
    "print('RMSE = {:.2f}'.format(np.sqrt(np.mean((ypredict[0] - ytest)**2))))\n",
    "print('Time taken = {:.2f} seconds'.format(en-st))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "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>: 1085.9725270022936<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>511.28732378421313</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> 4.579718385079653</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> 6.130229589762804</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<GPy.models.gp_regression.GPRegression at 0x7fb6c16cbf28>"
      ]
     },
     "execution_count": 123,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "md_gp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "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": [
    "plt.scatter(ytest,ypredict[0],s=4*ypredict[1],alpha=0.7)\n",
    "plt.xlabel('Actual House Price')\n",
    "plt.ylabel('Predicted House Price')\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looks much better. Besides the significantly lower RMSE, the GP models offers an additional output - the variance associated with each output, denoted by the size of the circles in the scatter plot.\n",
    "\n",
    "But what about interpretability. It is very easy to interpret the linear model, as you can see below where we plot the model coefficients. Generally the model makes sense."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(14,6))\n",
    "ax = plt.subplot(111)\n",
    "ax.bar(np.array(np.arange(13)),md_lr.coef_.flatten())\n",
    "ax.set_xticks(np.array(np.arange(13)))\n",
    "xn = ax.set_xticklabels(names)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "k({\\bf x},{\\bf x}') = \\sigma^2_f\\exp{(-\\frac{1}{2\\ell}(\\Vert{\\bf x}-{\\bf x}')\\Vert_2^2)}\n",
    "$$\n",
    "$$\n",
    "k({\\bf x},{\\bf x}') = \\sigma^2_f\\exp{(-\\frac{1}{2\\ell}\\sum_{i=1}^D(x_i - x'_i)^2)}\n",
    "$$\n",
    "$$\n",
    "k({\\bf x},{\\bf x}') = \\sigma^2_f\\exp{(-\\frac{1}{2}\\sum_{i=1}^D\\frac{(x_i - x'_i)^2}{\\ell_i}})\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On the other hand, the GP model does not offer any such interpretability, in its present form.\n",
    "\n",
    "### Automatic Relevance Determination\n",
    "*Automatic Relevance Determination* or ARD, is a way to infer relevance of the different features in a GP based model. There are several ways to do ARD. For stationary kernels, where the covariance function depends only on the difference between the two vectors, once can perform ARD by choosing a different lengthscale for each feature in the input vector. For instance, the SE kernel with ARD can be calculated as:\n",
    "$$\n",
    "k({\\bf x},{\\bf x}') = \\sigma^2_f\\exp{(-\\frac{1}{2}({\\bf x}-{\\bf x}')^\\top M ({\\bf x}-{\\bf x}'))}\n",
    "$$\n",
    "where $M$ is a diagonal matrix, i.e., $M = diag(\\frac{1}{\\bf l})$. The $D$-length vector ${\\bf l}$ can be used to determine the relevance of each feature, as:\n",
    "$$\n",
    "r_i = \\frac{1}{{\\bf l}[i]}\n",
    "$$\n",
    "> The above result can be obtained from the fact that if the lengthscale for any feature is small, then the covariance along the corresponding dimension will change very fast. On the other hand a larger lengthscale would mean that the covariance is not very sensitive to that feature.\n",
    "\n",
    "In `GPy` a stationary kernel (RBF, Matern32, etc.) can be turned into an ARD kernel, by using `ARD = True` flag."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RMSE = 3.12\n",
      "Time taken = 6.53 seconds\n"
     ]
    }
   ],
   "source": [
    "st = time.time()\n",
    "md_gp_ard = GPy.models.GPRegression(Xtrain,ytrain,kernel=GPy.kern.RBF(Xtrain.shape[1],ARD=True))\n",
    "md_gp_ard.optimize()\n",
    "ypredict = md_gp_ard.predict(Xtest)\n",
    "en = time.time()\n",
    "print('RMSE = {:.2f}'.format(np.sqrt(np.mean((ypredict[0] - ytest)**2))))\n",
    "print('Time taken = {:.2f} seconds'.format(en-st))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "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>: 1037.2613484549481<br>\n",
       "<b>Number of Parameters</b>: 16<br>\n",
       "<b>Number of Optimization Parameters</b>: 16<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>699.2961921616991</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>            (14,)</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>4.287432213596658</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<GPy.models.gp_regression.GPRegression at 0x7fb6c5850748>"
      ]
     },
     "execution_count": 124,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "md_gp_ard"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The RMSE is not very worse than the regular GPR, and can be improved with using more data, a better kernel, etc. The time is much longer, since now there are many more hyper-parameters to be trained. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [],
   "source": [
    "relvec = 1/np.array(md_gp_ard.kern.lengthscale)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(14,6))\n",
    "ax = plt.subplot(111)\n",
    "ax.bar(np.array(np.arange(13)),relvec)\n",
    "ax.set_xticks(np.array(np.arange(13)))\n",
    "xn = ax.set_xticklabels(names)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> Notice that the relevance vector obtained from ARD does not give us the \"direction\" of the relevance.\n",
    "\n",
    "Additionally, the relevance vector values are _uncalibrated_. We do not know if a value of 0.3 is low or high. One \"hack\" to handle that could be to add a completely random vector as a dummy feature and use its relevance as the baseline to find the significance of the relevance values.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [],
   "source": [
    "Xaug = np.hstack((X,np.random.normal(0,1,(X.shape[0],1))))\n",
    "ss = StandardScaler()\n",
    "Xnorm = ss.fit_transform(Xaug)\n",
    "inds = np.random.permutation(Xnorm.shape[0])\n",
    "train_size = 400\n",
    "Xtrain,ytrain,Xtest,ytest = Xnorm[inds[0:train_size],:],y[inds[0:train_size],:],Xnorm[inds[train_size:],:],y[inds[train_size:],:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RMSE = 2.83\n",
      "Time taken = 13.30 seconds\n"
     ]
    }
   ],
   "source": [
    "st = time.time()\n",
    "md_gp_ard = GPy.models.GPRegression(Xtrain,ytrain,kernel=GPy.kern.RBF(Xtrain.shape[1],ARD=True))\n",
    "md_gp_ard.optimize()\n",
    "ypredict = md_gp_ard.predict(Xtest)\n",
    "en = time.time()\n",
    "print('RMSE = {:.2f}'.format(np.sqrt(np.mean((ypredict[0] - ytest)**2))))\n",
    "print('Time taken = {:.2f} seconds'.format(en-st))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [],
   "source": [
    "relvec = 1/np.array(md_gp_ard.kern.lengthscale)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [],
   "source": [
    "relvec_adj = relvec[0:13]/relvec[-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(14,6))\n",
    "ax = plt.subplot(111)\n",
    "ax.bar(np.array(np.arange(13)),relvec_adj)\n",
    "ax.set_xticks(np.array(np.arange(13)))\n",
    "xn = ax.set_xticklabels(names)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "k({\\bf x},{\\bf x}') = \\sum_{i=1}^D k_i(x_i,x_i^i)\n",
    "$$\n",
    "$$\n",
    "f({\\bf  x}) = \\sum_{i=1}^Df_i(x_i)\n",
    "$$"
   ]
  }
 ],
 "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": "3.6.10"
  },
  "latex_envs": {
   "LaTeX_envs_menu_present": true,
   "autoclose": false,
   "autocomplete": true,
   "bibliofile": "biblio.bib",
   "cite_by": "apalike",
   "current_citInitial": 1,
   "eqLabelWithNumbers": true,
   "eqNumInitial": 1,
   "hotkeys": {
    "equation": "Ctrl-E",
    "itemize": "Ctrl-I"
   },
   "labels_anchors": false,
   "latex_user_defs": false,
   "report_style_numbering": false,
   "user_envs_cfg": true
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}