3_pruning_crossval.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3. Pruning Cross-validation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Following the bias-variance trade-off we know:\n",
    "* when fitting a shallow tree (underfitting) we have a high bias and a low variance\n",
    "* when fitting a deep tree (overfitting) we have a low bias and a high variance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to find the right balance between between bias and variance we:\n",
    "* fit an overly complex deep tree\n",
    "* prune the tree to find the optimal subtree"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Look for the smallest subtree that minimizes a penalized loss function:\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "min{f_{loss}+\\alpha |T|}\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "* $f_{loss}$ represents the loss function\n",
    "* $\\alpha$ represents the complexity parameter\n",
    "* $|T|$ is the number of leaf nodes\n",
    "\n",
    "A shallow tree results when is large and a deep tree when is small. Perform cross-validation on the complexity parameter in order to select the most suitable balance between bias and variance. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import libraries\n",
    "import os\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from sklearn import tree\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.metrics import r2_score\n",
    "from sklearn.model_selection import cross_val_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [],
   "source": [
    "# generate synthetic data\n",
    "x = np.linspace(start = 0, stop = 2 * np.pi, num=500)\n",
    "m = 2 * np.sin(x)\n",
    "y = m + np.random.normal(loc = 0, scale = 1, size = len(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [],
   "source": [
    "# adding column name to array (and transforming it into pd.DataFrame)\n",
    "x = pd.DataFrame({'feature_1':x})\n",
    "y = pd.DataFrame({'y':y})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [],
   "source": [
    "# fit a very deep tree\n",
    "deep_tree = tree.DecisionTreeRegressor(max_depth = 20,\n",
    "                                      min_samples_split = 10,\n",
    "                                      min_samples_leaf = 10,\n",
    "                                      ccp_alpha = 0).fit(x, y)\n",
    "y_deep_tree = deep_tree.predict(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot deep_tree\n",
    "%matplotlib inline\n",
    "plt.scatter(x, y, s=20, edgecolor=\"black\", c=\"darkorange\", label=\"data\") # plot raw data (including stoch. desturbance)\n",
    "plt.plot(x, m, color=\"red\", label=\"m\", linewidth=2) # plot raw data (excluding stoch. desturbance)\n",
    "plt.plot(x, y_deep_tree, color=\"cornflowerblue\", label=\"max_depth = 1\", linewidth=2) # depth 1\n",
    "plt.xlabel(\"data\")\n",
    "plt.ylabel(\"target\")\n",
    "plt.title(\"Decision Tree Regression\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.1 Impurity of leaves vs effective alphas of pruned tree"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The tree above is oviously overfitting the data. We look at the ```cost_complexity_pruning_path```, ut provides another option to control the size of a tree. We show the effect of ccp_alpha on regularizing the trees and **how to choose a ccp_alpha based on the (validation) scores**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Minimal cost complexity pruning recursively finds the node with the “weakest link”. The weakest link is characterized by an effective alpha, where the nodes with the smallest effective alpha are pruned first. To get an idea of what values of ccp_alpha could be appropriate, scikit-learn provides ```DecisionTreeRegressor.cost_complexity_pruning_path``` that returns the effective alphas and the corresponding total leaf impurities at each step of the pruning process. \n",
    "\n",
    "**As alpha increases, more of the tree is pruned, which increases the total impurity of its leaves**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [],
   "source": [
    "path = deep_tree.cost_complexity_pruning_path(x, y)\n",
    "ccp_alphas, impurities = path.ccp_alphas, path.impurities"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the following plot, the maximum effective alpha value is removed, because it is the trivial tree with only one node."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Total Impurity vs effective alpha for training set')"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "fig, ax = plt.subplots()\n",
    "ax.plot(ccp_alphas[:-1], impurities[:-1], marker='o', drawstyle=\"steps-post\")\n",
    "ax.set_xlabel(\"effective alpha\")\n",
    "ax.set_ylabel(\"total impurity of leaves\")\n",
    "ax.set_title(\"Total Impurity vs effective alpha for training set\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we train a decision tree using the effective alphas. The last value in ```ccp_alphas``` is the alpha value that prunes the whole tree, leaving the tree, ```clfs[-1]```, with one node."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [],
   "source": [
    "clfs = []\n",
    "for ccp_alpha in ccp_alphas:\n",
    "    clf = tree.DecisionTreeRegressor(max_depth = 20,\n",
    "                                      min_samples_split = 10,\n",
    "                                      min_samples_leaf = 10,\n",
    "                                      ccp_alpha = ccp_alpha).fit(x, y)\n",
    "    clfs.append(clf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of nodes in the last tree is: 1 with ccp_alpha: 2.033153217381094\n"
     ]
    }
   ],
   "source": [
    "print(f\"Number of nodes in the last tree is: {clfs[-1].tree_.node_count} with ccp_alpha: {ccp_alphas[-1]}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the remainder of this example, we remove the last element in ```clfs``` and ```ccp_alphas```, because it is the trivial tree with only one node. Here **we show that the number of nodes and tree depth decreases as alpha increases**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "clfs = clfs[:-1]\n",
    "ccp_alphas = ccp_alphas[:-1]\n",
    "\n",
    "node_counts = [clf.tree_.node_count for clf in clfs]\n",
    "score = [clf.score(y, clf.predict(x)) for clf in clfs]\n",
    "depth = [clf.tree_.max_depth for clf in clfs]\n",
    "\n",
    "fig, ax = plt.subplots(2, 1)\n",
    "ax[0].plot(ccp_alphas, node_counts, marker='o', drawstyle=\"steps-post\")\n",
    "ax[0].set_xlabel(\"alpha\")\n",
    "ax[0].set_ylabel(\"number of nodes\")\n",
    "ax[0].set_title(\"Number of nodes vs alpha\")\n",
    "ax[1].plot(ccp_alphas, depth, marker='o', drawstyle=\"steps-post\")\n",
    "ax[1].set_xlabel(\"alpha\")\n",
    "ax[1].set_ylabel(\"depth of tree\")\n",
    "ax[1].set_title(\"Depth vs alpha\")\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.2 Selecting optimal alpha via cross-validation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import mean_absolute_error, mean_squared_error, r2_score\n",
    "from sklearn.model_selection import cross_val_score\n",
    "\n",
    "alpha_loop_values = []\n",
    "for ccp_alpha in ccp_alphas:\n",
    "    regr_dt = tree.DecisionTreeRegressor(max_depth = 30,\n",
    "                                      min_samples_split = 10,\n",
    "                                      min_samples_leaf = 10,\n",
    "                                      ccp_alpha = ccp_alpha).fit(x, y)\n",
    "    \n",
    "    predictions = regr_dt.predict(x)\n",
    "    cvs = np.mean(cross_val_score(regr_dt, x, y, cv = 10, scoring='r2'))\n",
    "    node_counts = regr_dt.tree_.node_count\n",
    "    depth = regr_dt.tree_.max_depth\n",
    "    \n",
    "    alpha_loop_values.append([ccp_alpha, node_counts, depth,\n",
    "                              cvs])\n",
    "#best_alpha = float(alpha_results[alpha_results.cvs == alpha_results.cvs.max()].alpha)\n",
    "#print(f'best alpha: {best_alpha}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note:** The unified scoring API always maximizes the score, so scores which need to be minimized are negated in order for the unified scoring API to work correctly. The score that is returned is therefore negated when it is a score that should be minimized and left positive if it is a score that should be maximized."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>alpha</th>\n",
       "      <th>node_counts</th>\n",
       "      <th>depth</th>\n",
       "      <th>cvs</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>75</td>\n",
       "      <td>11</td>\n",
       "      <td>0.102596</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.000191</td>\n",
       "      <td>73</td>\n",
       "      <td>10</td>\n",
       "      <td>0.101899</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.000938</td>\n",
       "      <td>71</td>\n",
       "      <td>10</td>\n",
       "      <td>0.101198</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.001017</td>\n",
       "      <td>69</td>\n",
       "      <td>10</td>\n",
       "      <td>0.101198</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.001414</td>\n",
       "      <td>65</td>\n",
       "      <td>10</td>\n",
       "      <td>0.105515</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.002700</td>\n",
       "      <td>63</td>\n",
       "      <td>10</td>\n",
       "      <td>0.123278</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.003199</td>\n",
       "      <td>61</td>\n",
       "      <td>10</td>\n",
       "      <td>0.119021</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.003206</td>\n",
       "      <td>55</td>\n",
       "      <td>7</td>\n",
       "      <td>0.119021</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.003629</td>\n",
       "      <td>51</td>\n",
       "      <td>7</td>\n",
       "      <td>0.119021</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.003741</td>\n",
       "      <td>49</td>\n",
       "      <td>7</td>\n",
       "      <td>0.113199</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.003965</td>\n",
       "      <td>45</td>\n",
       "      <td>7</td>\n",
       "      <td>0.114436</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0.004518</td>\n",
       "      <td>43</td>\n",
       "      <td>7</td>\n",
       "      <td>0.114436</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.004803</td>\n",
       "      <td>41</td>\n",
       "      <td>7</td>\n",
       "      <td>0.114436</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>0.005393</td>\n",
       "      <td>39</td>\n",
       "      <td>7</td>\n",
       "      <td>0.114436</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>0.005472</td>\n",
       "      <td>37</td>\n",
       "      <td>7</td>\n",
       "      <td>0.114436</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>0.005821</td>\n",
       "      <td>35</td>\n",
       "      <td>7</td>\n",
       "      <td>0.140929</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>0.006179</td>\n",
       "      <td>33</td>\n",
       "      <td>7</td>\n",
       "      <td>0.143605</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>0.006445</td>\n",
       "      <td>29</td>\n",
       "      <td>7</td>\n",
       "      <td>0.144702</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>0.007397</td>\n",
       "      <td>27</td>\n",
       "      <td>7</td>\n",
       "      <td>0.142104</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>0.008830</td>\n",
       "      <td>25</td>\n",
       "      <td>7</td>\n",
       "      <td>0.138226</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>0.011045</td>\n",
       "      <td>23</td>\n",
       "      <td>6</td>\n",
       "      <td>0.252027</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>0.011402</td>\n",
       "      <td>21</td>\n",
       "      <td>6</td>\n",
       "      <td>0.252027</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>0.016308</td>\n",
       "      <td>19</td>\n",
       "      <td>5</td>\n",
       "      <td>0.325485</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>0.016550</td>\n",
       "      <td>15</td>\n",
       "      <td>4</td>\n",
       "      <td>0.325485</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>0.017258</td>\n",
       "      <td>13</td>\n",
       "      <td>3</td>\n",
       "      <td>0.325485</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>0.023243</td>\n",
       "      <td>11</td>\n",
       "      <td>3</td>\n",
       "      <td>0.446283</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>0.085259</td>\n",
       "      <td>9</td>\n",
       "      <td>3</td>\n",
       "      <td>0.574288</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>0.089529</td>\n",
       "      <td>7</td>\n",
       "      <td>2</td>\n",
       "      <td>0.574288</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>0.089691</td>\n",
       "      <td>5</td>\n",
       "      <td>2</td>\n",
       "      <td>0.574288</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       alpha  node_counts  depth       cvs\n",
       "0   0.000000           75     11  0.102596\n",
       "1   0.000191           73     10  0.101899\n",
       "2   0.000938           71     10  0.101198\n",
       "3   0.001017           69     10  0.101198\n",
       "4   0.001414           65     10  0.105515\n",
       "5   0.002700           63     10  0.123278\n",
       "6   0.003199           61     10  0.119021\n",
       "7   0.003206           55      7  0.119021\n",
       "8   0.003629           51      7  0.119021\n",
       "9   0.003741           49      7  0.113199\n",
       "10  0.003965           45      7  0.114436\n",
       "11  0.004518           43      7  0.114436\n",
       "12  0.004803           41      7  0.114436\n",
       "13  0.005393           39      7  0.114436\n",
       "14  0.005472           37      7  0.114436\n",
       "15  0.005821           35      7  0.140929\n",
       "16  0.006179           33      7  0.143605\n",
       "17  0.006445           29      7  0.144702\n",
       "18  0.007397           27      7  0.142104\n",
       "19  0.008830           25      7  0.138226\n",
       "20  0.011045           23      6  0.252027\n",
       "21  0.011402           21      6  0.252027\n",
       "22  0.016308           19      5  0.325485\n",
       "23  0.016550           15      4  0.325485\n",
       "24  0.017258           13      3  0.325485\n",
       "25  0.023243           11      3  0.446283\n",
       "26  0.085259            9      3  0.574288\n",
       "27  0.089529            7      2  0.574288\n",
       "28  0.089691            5      2  0.574288"
      ]
     },
     "execution_count": 134,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alpha_results = pd.DataFrame(alpha_loop_values, \n",
    "                         columns=['alpha', 'node_counts', 'depth','cvs'])\n",
    "\n",
    "# taking absolute value of cvs\n",
    "alpha_results['cvs'] = np.abs(alpha_results.cvs)\n",
    "alpha_results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha_results = alpha_results.loc[(alpha_results['cvs']==np.max(alpha_results['cvs']))]\n",
    "best_alpha = alpha_results.loc[(alpha_results['depth']==np.max(alpha_results['depth']))]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "metadata": {},
   "outputs": [],
   "source": [
    "regr_dt = tree.DecisionTreeRegressor(max_depth = int(best_alpha.depth),\n",
    "                                      min_samples_split = 10,\n",
    "                                      min_samples_leaf = 10,\n",
    "                                      ccp_alpha = float(best_alpha.alpha)).fit(x, y)\n",
    "y_deep_tree = regr_dt.predict(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "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": [
    "# Plot deep_tree\n",
    "plt.figure()\n",
    "plt.scatter(x, y, s=20, edgecolor=\"black\", c=\"darkorange\", label=\"data\") # plot raw data (including stoch. desturbance)\n",
    "plt.plot(x, m, color=\"red\", label=\"m\", linewidth=2) # plot raw data (excluding stoch. desturbance)\n",
    "plt.plot(x, y_deep_tree, color=\"cornflowerblue\", label=\"max_depth = 1\", linewidth=2) # depth 1\n",
    "plt.xlabel(\"data\")\n",
    "plt.ylabel(\"target\")\n",
    "plt.title(\"Decision Tree Regression\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```train_scores = [clf.score(x, y) for clf in clfs]\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.set_xlabel(\"alpha\")\n",
    "ax.set_ylabel(\"r2\")\n",
    "ax.set_title(\"r2 vs alpha for training set\")\n",
    "ax.plot(ccp_alphas, train_scores, marker='o', label=\"train\",\n",
    "        drawstyle=\"steps-post\")\n",
    "#ax.plot(ccp_alphas, test_scores, marker='o', label=\"test\",\n",
    "#        drawstyle=\"steps-post\")\n",
    "ax.legend()\n",
    "plt.show()```"
   ]
  }
 ],
 "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": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}