explain_gbt_toydata.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Demonstration of applying weighted shap value technique to decision tree based ML models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "_cell_guid": "b1076dfc-b9ad-4769-8c92-a6c4dae69d19",
    "_uuid": "8f2839f25d086af736a60e9eeb907d3b93b6e0e5",
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Importing Required Libraries\n",
    "import numpy as np\n",
    "import numpy.random as npr\n",
    "from sklearn.ensemble import RandomForestRegressor, HistGradientBoostingRegressor\n",
    "from sklearn.multioutput import MultiOutputRegressor\n",
    "from sklearn.metrics import r2_score\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create the coefficients for the (non)linear model underlying the data generation process"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "npr.seed(10)\n",
    "X = npr.multivariate_normal(np.zeros(10), np.eye(10), size=int(1e5))\n",
    "\n",
    "# Method 1\n",
    "scatter = npr.multivariate_normal(mean=np.zeros(2), cov=[[1,0.6],[0.6,1]], size=10000)\n",
    "\n",
    "# Optionally, plot scatter on which method 1 is based\n",
    "# plt.figure()\n",
    "# plt.scatter(scatter[:,0], scatter[:,1], s=1)\n",
    "\n",
    "hist = np.histogram2d(scatter[:,0], scatter[:,1], range=([-2,2],[-2,2]), bins=10)\n",
    "coefs = hist[0]\n",
    "\n",
    "# Method 2\n",
    "# coefs = sum([np.eye(10, k=k)*(10-abs(k)) for k in range(-10,10)])\n",
    "\n",
    "plt.figure()\n",
    "plt.imshow(coefs)\n",
    "plt.title('Coefficients')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Apply linear transform and optionally nonlinear one"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100000, 10)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Apply linear and optionally a non-linear transform to x data\n",
    "\n",
    "# linear transform\n",
    "Y = X @ coefs\n",
    "\n",
    "# optionally, add non-linear transform\n",
    "Y = np.exp(Y/Y.max())\n",
    "# Y = Y**3\n",
    "\n",
    "Y.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Define and fit ML model: GBT or RF"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R2 score:  0.9918578253100157\n"
     ]
    }
   ],
   "source": [
    "# For GBT\n",
    "model = MultiOutputRegressor(HistGradientBoostingRegressor(), n_jobs=4)\n",
    "# For RF\n",
    "# model = RandomForestRegressor()\n",
    "\n",
    "model.fit(X, Y)\n",
    "\n",
    "print('R2 score: ', r2_score(Y, model.predict(X)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calculate SHAP values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from shap import TreeExplainer, KernelExplainer, Explainer\n",
    "from convection_param.shap_values.ShapMultiOutputRegressor import MultiOutputTreeExplainer, build_tree_explainer\n",
    "\n",
    "# This class can be used for MultiOutputRegressors\n",
    "class MultiOutputTreeExplainer(Explainer):\n",
    "    \"\"\" Abstraction of Explainer for MultiOutputRegressor model\n",
    "    \"\"\"\n",
    "    def __init__(self, model, *args, **kwargs):\n",
    "        assert isinstance(model, MultiOutputRegressor)\n",
    "        self.explainers = []\n",
    "        self.expected_value = []\n",
    "        for estimator in model.estimators_:\n",
    "            explainer = TreeExplainer(estimator, *args, **kwargs)\n",
    "            self.explainers.append(explainer)\n",
    "            self.expected_value.append(explainer.expected_value)\n",
    "\n",
    "    def shap_values(self, *args, **kwargs):\n",
    "        shap_values = []\n",
    "        for explainer in self.explainers:\n",
    "            shap_values.append(explainer.shap_values(*args, **kwargs))\n",
    "        return np.array(shap_values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 1.8 s, sys: 4.02 ms, total: 1.8 s\n",
      "Wall time: 1.82 s\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "((10, 300, 10), (300, 10))"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%time\n",
    "# Calculate shap values for a subset of 300 samples\n",
    "npr.seed(745)\n",
    "random_idx = npr.choice(X.shape[0], size=300, replace=False)\n",
    "X_explain = X[random_idx]\n",
    "\n",
    "# For GBT\n",
    "explainer = MultiOutputTreeExplainer(model)\n",
    "# For RF\n",
    "# explainer = TreeExplainer(model)\n",
    "\n",
    "shap_values = np.array(explainer.shap_values(X_explain))\n",
    "shap_values.shape, X_explain.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Apply weighted averaging"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10, 10)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "multiplier = X_explain - np.mean(X_explain, axis=0)\n",
    "multiplier /= np.maximum(np.max(np.abs(multiplier), axis=0), 0)\n",
    "mean_shap_values3d = np.mean(multiplier * shap_values, axis=1)\n",
    "mean_shap_values3d.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot found weights as well as Original weights of linear transform of the data generation process"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(mean_shap_values3d)\n",
    "plt.title('Weighted Shap Values of Model')\n",
    "plt.figure()\n",
    "plt.imshow(coefs)\n",
    "plt.title('Original Weights of Linear Transform')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Py3.8 (conda)",
   "language": "python",
   "name": "py3.8"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.15"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}