789 lines
22 KiB
Plaintext
789 lines
22 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**Chapter 7 – Ensemble Learning and Random Forests**"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"_This notebook contains all the sample code and solutions to the exercices in chapter 7._"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Setup"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"First, let's make sure this notebook works well in both python 2 and 3, import a few common modules, ensure MatplotLib plots figures inline and prepare a function to save the figures:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"# To support both python 2 and python 3\n",
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"from __future__ import division, print_function, unicode_literals\n",
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"\n",
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"# Common imports\n",
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"import numpy as np\n",
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"import numpy.random as rnd\n",
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"import os\n",
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"\n",
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"# to make this notebook's output stable across runs\n",
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"rnd.seed(42)\n",
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"\n",
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"# To plot pretty figures\n",
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"%matplotlib inline\n",
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"import matplotlib\n",
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"import matplotlib.pyplot as plt\n",
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"plt.rcParams['axes.labelsize'] = 14\n",
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"plt.rcParams['xtick.labelsize'] = 12\n",
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"plt.rcParams['ytick.labelsize'] = 12\n",
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"\n",
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"# Where to save the figures\n",
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"PROJECT_ROOT_DIR = \".\"\n",
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"CHAPTER_ID = \"ensembles\"\n",
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"\n",
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"def image_path(fig_id):\n",
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" return os.path.join(PROJECT_ROOT_DIR, \"images\", CHAPTER_ID, fig_id)\n",
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"\n",
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"def save_fig(fig_id, tight_layout=True):\n",
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" print(\"Saving figure\", fig_id)\n",
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" if tight_layout:\n",
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" plt.tight_layout()\n",
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" plt.savefig(image_path(fig_id) + \".png\", format='png', dpi=300)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Voting classifiers"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"heads_proba = 0.51\n",
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"coin_tosses = (rnd.rand(10000, 10) < heads_proba).astype(np.int32)\n",
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"cumulative_heads_ratio = np.cumsum(coin_tosses, axis=0) / np.arange(1, 10001).reshape(-1, 1)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"plt.figure(figsize=(8,3.5))\n",
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"plt.plot(cumulative_heads_ratio)\n",
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"plt.plot([0, 10000], [0.51, 0.51], \"k--\", linewidth=2, label=\"51%\")\n",
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"plt.plot([0, 10000], [0.5, 0.5], \"k-\", label=\"50%\")\n",
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"plt.xlabel(\"Number of coin tosses\")\n",
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"plt.ylabel(\"Heads ratio\")\n",
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"plt.legend(loc=\"lower right\")\n",
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"plt.axis([0, 10000, 0.42, 0.58])\n",
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"save_fig(\"law_of_large_numbers_plot\")\n",
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"plt.show()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"from sklearn.cross_validation import train_test_split\n",
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"from sklearn.datasets import make_moons\n",
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"\n",
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"X, y = make_moons(n_samples=500, noise=0.30, random_state=42)\n",
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"X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=42)\n",
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"\n",
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"from sklearn.ensemble import RandomForestClassifier\n",
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"from sklearn.ensemble import VotingClassifier\n",
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"from sklearn.linear_model import LogisticRegression\n",
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"from sklearn.svm import SVC\n",
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"\n",
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"log_clf = LogisticRegression(random_state=42)\n",
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"rnd_clf = RandomForestClassifier(random_state=42)\n",
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"svm_clf = SVC(probability=True, random_state=42)\n",
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"\n",
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"voting_clf = VotingClassifier(\n",
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" estimators=[('lr', log_clf), ('rf', rnd_clf), ('svc', svm_clf)],\n",
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" voting='soft'\n",
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" )\n",
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"voting_clf.fit(X_train, y_train)\n",
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"\n",
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"from sklearn.metrics import accuracy_score\n",
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"\n",
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"for clf in (log_clf, rnd_clf, svm_clf, voting_clf):\n",
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" clf.fit(X_train, y_train)\n",
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" y_pred = clf.predict(X_test)\n",
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" print(clf.__class__.__name__, accuracy_score(y_test, y_pred))"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Bagging ensembles"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"from sklearn.datasets import make_moons\n",
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"from sklearn.ensemble import BaggingClassifier\n",
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"from sklearn.metrics import accuracy_score\n",
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"from sklearn.tree import DecisionTreeClassifier\n",
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"\n",
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"bag_clf = BaggingClassifier(\n",
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" DecisionTreeClassifier(random_state=42), n_estimators=500,\n",
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" max_samples=100, bootstrap=True, n_jobs=-1, random_state=42\n",
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" )\n",
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"bag_clf.fit(X_train, y_train)\n",
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"y_pred = bag_clf.predict(X_test)\n",
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"print(accuracy_score(y_test, y_pred))"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"tree_clf = DecisionTreeClassifier(random_state=42)\n",
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"tree_clf.fit(X_train, y_train)\n",
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"y_pred_tree = tree_clf.predict(X_test)\n",
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"print(accuracy_score(y_test, y_pred_tree))"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"from matplotlib.colors import ListedColormap\n",
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"\n",
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"def plot_decision_boundary(clf, X, y, axes=[-1.5, 2.5, -1, 1.5], alpha=0.5, contour=True):\n",
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" x1s = np.linspace(axes[0], axes[1], 100)\n",
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" x2s = np.linspace(axes[2], axes[3], 100)\n",
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" x1, x2 = np.meshgrid(x1s, x2s)\n",
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" X_new = np.c_[x1.ravel(), x2.ravel()]\n",
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" y_pred = clf.predict(X_new).reshape(x1.shape)\n",
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" custom_cmap = ListedColormap(['#fafab0','#9898ff','#a0faa0'])\n",
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" plt.contourf(x1, x2, y_pred, alpha=0.3, cmap=custom_cmap, linewidth=10)\n",
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" if contour:\n",
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" custom_cmap2 = ListedColormap(['#7d7d58','#4c4c7f','#507d50'])\n",
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" plt.contour(x1, x2, y_pred, cmap=custom_cmap2, alpha=0.8)\n",
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" plt.plot(X[:, 0][y==0], X[:, 1][y==0], \"yo\", alpha=alpha)\n",
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" plt.plot(X[:, 0][y==1], X[:, 1][y==1], \"bs\", alpha=alpha)\n",
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" plt.axis(axes)\n",
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" plt.xlabel(r\"$x_1$\", fontsize=18)\n",
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" plt.ylabel(r\"$x_2$\", fontsize=18, rotation=0)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 8,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"plt.figure(figsize=(11,4))\n",
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"plt.subplot(121)\n",
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"plot_decision_boundary(tree_clf, X, y)\n",
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"plt.title(\"Decision Tree\", fontsize=14)\n",
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"plt.subplot(122)\n",
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"plot_decision_boundary(bag_clf, X, y)\n",
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"plt.title(\"Decision Trees with Bagging\", fontsize=14)\n",
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"save_fig(\"decision_tree_without_and_with_bagging_plot\")\n",
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"plt.show()"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Random Forests"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 9,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"bag_clf = BaggingClassifier(\n",
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" DecisionTreeClassifier(splitter=\"random\", max_leaf_nodes=16, random_state=42),\n",
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" n_estimators=500, max_samples=1.0, bootstrap=True,\n",
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" n_jobs=-1, random_state=42\n",
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" )\n",
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"bag_clf.fit(X_train, y_train)\n",
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"y_pred = bag_clf.predict(X_test)"
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]
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},
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{
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||
"cell_type": "code",
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"execution_count": 10,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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||
"source": [
|
||
"from sklearn.ensemble import RandomForestClassifier\n",
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"\n",
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"rnd_clf = RandomForestClassifier(n_estimators=500, max_leaf_nodes=16, n_jobs=-1, random_state=42)\n",
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"rnd_clf.fit(X_train, y_train)\n",
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"\n",
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"y_pred_rf = rnd_clf.predict(X_test)"
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]
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||
},
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{
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"cell_type": "code",
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||
"execution_count": 11,
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||
"metadata": {
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||
"collapsed": false
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},
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"outputs": [],
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"source": [
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"np.sum(y_pred == y_pred_rf) / len(y_pred) # almost identical predictions"
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]
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},
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{
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||
"cell_type": "code",
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||
"execution_count": 12,
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||
"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
|
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"from sklearn.datasets import load_iris\n",
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"iris = load_iris()\n",
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"rnd_clf = RandomForestClassifier(n_estimators=500, n_jobs=-1, random_state=42)\n",
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"rnd_clf.fit(iris[\"data\"], iris[\"target\"])\n",
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"for name, importance in zip(iris[\"feature_names\"], rnd_clf.feature_importances_):\n",
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" print(name, \"=\", importance)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 13,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"rnd_clf.feature_importances_"
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]
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},
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{
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||
"cell_type": "code",
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"execution_count": 14,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"plt.figure(figsize=(6, 4))\n",
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"\n",
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"for i in range(15):\n",
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" tree_clf = DecisionTreeClassifier(max_leaf_nodes=16, random_state=42+i)\n",
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" indices_with_replacement = rnd.randint(0, len(X_train), len(X_train))\n",
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" tree_clf.fit(X[indices_with_replacement], y[indices_with_replacement])\n",
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" plot_decision_boundary(tree_clf, X, y, axes=[-1.5, 2.5, -1, 1.5], alpha=0.02, contour=False)\n",
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"\n",
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"plt.show()"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Out-of-Bag evaluation"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 15,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"bag_clf = BaggingClassifier(\n",
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" DecisionTreeClassifier(random_state=42), n_estimators=500,\n",
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" bootstrap=True, n_jobs=-1, oob_score=True, random_state=40\n",
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")\n",
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"bag_clf.fit(X_train, y_train)\n",
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"bag_clf.oob_score_"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 16,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"bag_clf.oob_decision_function_[:10]"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 17,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"from sklearn.metrics import accuracy_score\n",
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"y_pred = bag_clf.predict(X_test)\n",
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"accuracy_score(y_test, y_pred)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Feature importance"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 18,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
|
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"from sklearn.datasets import fetch_mldata\n",
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"mnist = fetch_mldata('MNIST original')\n",
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"rnd_clf = RandomForestClassifier(random_state=42)\n",
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"rnd_clf.fit(mnist[\"data\"], mnist[\"target\"])"
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]
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},
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{
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||
"cell_type": "code",
|
||
"execution_count": 19,
|
||
"metadata": {
|
||
"collapsed": true
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||
},
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||
"outputs": [],
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||
"source": [
|
||
"def plot_digit(data):\n",
|
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" image = data.reshape(28, 28)\n",
|
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" plt.imshow(image, cmap = matplotlib.cm.hot,\n",
|
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" interpolation=\"nearest\")\n",
|
||
" plt.axis(\"off\")"
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]
|
||
},
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{
|
||
"cell_type": "code",
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||
"execution_count": 20,
|
||
"metadata": {
|
||
"collapsed": false
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||
},
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||
"outputs": [],
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||
"source": [
|
||
"plot_digit(rnd_clf.feature_importances_)\n",
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"\n",
|
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"cbar = plt.colorbar(ticks=[rnd_clf.feature_importances_.min(), rnd_clf.feature_importances_.max()])\n",
|
||
"cbar.ax.set_yticklabels(['Not important', 'Very important'])\n",
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||
"\n",
|
||
"save_fig(\"mnist_feature_importance_plot\")\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"# AdaBoost"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 21,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"from sklearn.ensemble import AdaBoostClassifier\n",
|
||
"\n",
|
||
"ada_clf = AdaBoostClassifier(\n",
|
||
" DecisionTreeClassifier(max_depth=2), n_estimators=200,\n",
|
||
" algorithm=\"SAMME.R\", learning_rate=0.5, random_state=42\n",
|
||
" )\n",
|
||
"ada_clf.fit(X_train, y_train)\n",
|
||
"plot_decision_boundary(ada_clf, X, y)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 22,
|
||
"metadata": {
|
||
"collapsed": false
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||
},
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||
"outputs": [],
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||
"source": [
|
||
"m = len(X_train)\n",
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"\n",
|
||
"plt.figure(figsize=(11, 4))\n",
|
||
"for subplot, learning_rate in ((121, 1), (122, 0.5)):\n",
|
||
" sample_weights = np.ones(m)\n",
|
||
" for i in range(5):\n",
|
||
" plt.subplot(subplot)\n",
|
||
" svm_clf = SVC(kernel=\"rbf\", C=0.05)\n",
|
||
" svm_clf.fit(X_train, y_train, sample_weight=sample_weights)\n",
|
||
" y_pred = svm_clf.predict(X_train)\n",
|
||
" sample_weights[y_pred != y_train] *= (1 + learning_rate)\n",
|
||
" plot_decision_boundary(svm_clf, X, y, alpha=0.2)\n",
|
||
" plt.title(\"learning_rate = {}\".format(learning_rate - 1), fontsize=16)\n",
|
||
"\n",
|
||
"plt.subplot(121)\n",
|
||
"plt.text(-0.7, -0.65, \"1\", fontsize=14)\n",
|
||
"plt.text(-0.6, -0.10, \"2\", fontsize=14)\n",
|
||
"plt.text(-0.5, 0.10, \"3\", fontsize=14)\n",
|
||
"plt.text(-0.4, 0.55, \"4\", fontsize=14)\n",
|
||
"plt.text(-0.3, 0.90, \"5\", fontsize=14)\n",
|
||
"save_fig(\"boosting_plot\")\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 23,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"list(m for m in dir(ada_clf) if not m.startswith(\"_\") and m.endswith(\"_\"))"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"# Gradient Boosting"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 24,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"from sklearn.tree import DecisionTreeRegressor\n",
|
||
"\n",
|
||
"rnd.seed(42)\n",
|
||
"X = rnd.rand(100, 1) - 0.5\n",
|
||
"y = 3*X[:, 0]**2 + 0.05 * rnd.randn(100)\n",
|
||
"\n",
|
||
"tree_reg1 = DecisionTreeRegressor(max_depth=2, random_state=42)\n",
|
||
"tree_reg1.fit(X, y)\n",
|
||
"\n",
|
||
"y2 = y - tree_reg1.predict(X)\n",
|
||
"tree_reg2 = DecisionTreeRegressor(max_depth=2, random_state=42)\n",
|
||
"tree_reg2.fit(X, y2)\n",
|
||
"\n",
|
||
"y3 = y2 - tree_reg2.predict(X)\n",
|
||
"tree_reg3 = DecisionTreeRegressor(max_depth=2, random_state=42)\n",
|
||
"tree_reg3.fit(X, y3)\n",
|
||
"\n",
|
||
"X_new = np.array([[0.8]])\n",
|
||
"y_pred = sum(tree.predict(X_new) for tree in (tree_reg1, tree_reg2, tree_reg3))\n",
|
||
"print(y_pred)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 25,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"def plot_predictions(regressors, X, y, axes, label=None, style=\"r-\", data_style=\"b.\", data_label=None):\n",
|
||
" x1 = np.linspace(axes[0], axes[1], 500)\n",
|
||
" y_pred = sum(regressor.predict(x1.reshape(-1, 1)) for regressor in regressors)\n",
|
||
" plt.plot(X[:, 0], y, data_style, label=data_label)\n",
|
||
" plt.plot(x1, y_pred, style, linewidth=2, label=label)\n",
|
||
" if label or data_label:\n",
|
||
" plt.legend(loc=\"upper center\", fontsize=16)\n",
|
||
" plt.axis(axes)\n",
|
||
"\n",
|
||
"plt.figure(figsize=(11,11))\n",
|
||
"\n",
|
||
"plt.subplot(321)\n",
|
||
"plot_predictions([tree_reg1], X, y, axes=[-0.5, 0.5, -0.1, 0.8], label=\"$h_1(x_1)$\", style=\"g-\", data_label=\"Training set\")\n",
|
||
"plt.ylabel(\"$y$\", fontsize=16, rotation=0)\n",
|
||
"plt.title(\"Residuals and tree predictions\", fontsize=16)\n",
|
||
"\n",
|
||
"plt.subplot(322)\n",
|
||
"plot_predictions([tree_reg1], X, y, axes=[-0.5, 0.5, -0.1, 0.8], label=\"$h(x_1) = h_1(x_1)$\", data_label=\"Training set\")\n",
|
||
"plt.ylabel(\"$y$\", fontsize=16, rotation=0)\n",
|
||
"plt.title(\"Ensemble predictions\", fontsize=16)\n",
|
||
"\n",
|
||
"plt.subplot(323)\n",
|
||
"plot_predictions([tree_reg2], X, y2, axes=[-0.5, 0.5, -0.5, 0.5], label=\"$h_2(x_1)$\", style=\"g-\", data_style=\"k+\", data_label=\"Residuals\")\n",
|
||
"plt.ylabel(\"$y - h_1(x_1)$\", fontsize=16)\n",
|
||
"\n",
|
||
"plt.subplot(324)\n",
|
||
"plot_predictions([tree_reg1, tree_reg2], X, y, axes=[-0.5, 0.5, -0.1, 0.8], label=\"$h(x_1) = h_1(x_1) + h_2(x_1)$\")\n",
|
||
"plt.ylabel(\"$y$\", fontsize=16, rotation=0)\n",
|
||
"\n",
|
||
"plt.subplot(325)\n",
|
||
"plot_predictions([tree_reg3], X, y3, axes=[-0.5, 0.5, -0.5, 0.5], label=\"$h_3(x_1)$\", style=\"g-\", data_style=\"k+\")\n",
|
||
"plt.ylabel(\"$y - h_1(x_1) - h_2(x_1)$\", fontsize=16)\n",
|
||
"plt.xlabel(\"$x_1$\", fontsize=16)\n",
|
||
"\n",
|
||
"plt.subplot(326)\n",
|
||
"plot_predictions([tree_reg1, tree_reg2, tree_reg3], X, y, axes=[-0.5, 0.5, -0.1, 0.8], label=\"$h(x_1) = h_1(x_1) + h_2(x_1) + h_3(x_1)$\")\n",
|
||
"plt.xlabel(\"$x_1$\", fontsize=16)\n",
|
||
"plt.ylabel(\"$y$\", fontsize=16, rotation=0)\n",
|
||
"\n",
|
||
"save_fig(\"gradient_boosting_plot\")\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 26,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"from sklearn.ensemble import GradientBoostingRegressor\n",
|
||
"\n",
|
||
"gbrt = GradientBoostingRegressor(max_depth=2, n_estimators=3, learning_rate=0.1, random_state=42)\n",
|
||
"gbrt.fit(X, y)\n",
|
||
"\n",
|
||
"gbrt_slow = GradientBoostingRegressor(max_depth=2, n_estimators=200, learning_rate=0.1, random_state=42)\n",
|
||
"gbrt_slow.fit(X, y)\n",
|
||
"\n",
|
||
"plt.figure(figsize=(11,4))\n",
|
||
"\n",
|
||
"plt.subplot(121)\n",
|
||
"plot_predictions([gbrt], X, y, axes=[-0.5, 0.5, -0.1, 0.8], label=\"Ensemble predictions\")\n",
|
||
"plt.title(\"learning_rate={}, n_estimators={}\".format(gbrt.learning_rate, gbrt.n_estimators), fontsize=14)\n",
|
||
"\n",
|
||
"plt.subplot(122)\n",
|
||
"plot_predictions([gbrt_slow], X, y, axes=[-0.5, 0.5, -0.1, 0.8])\n",
|
||
"plt.title(\"learning_rate={}, n_estimators={}\".format(gbrt_slow.learning_rate, gbrt_slow.n_estimators), fontsize=14)\n",
|
||
"\n",
|
||
"save_fig(\"gbrt_learning_rate_plot\")\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Gradient Boosting with Early stopping"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 27,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"from sklearn.cross_validation import train_test_split\n",
|
||
"from sklearn.metrics import mean_squared_error\n",
|
||
"\n",
|
||
"X_train, X_val, y_train, y_val = train_test_split(X, y)\n",
|
||
"\n",
|
||
"gbrt = GradientBoostingRegressor(max_depth=2, n_estimators=120, learning_rate=0.1, random_state=42)\n",
|
||
"gbrt.fit(X_train, y_train)\n",
|
||
"\n",
|
||
"errors = [mean_squared_error(y_val, y_pred) for y_pred in gbrt.staged_predict(X_val)]"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 28,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"best_n_estimators = np.argmin(errors)\n",
|
||
"min_error = errors[best_n_estimators]\n",
|
||
"\n",
|
||
"gbrt_best = GradientBoostingRegressor(max_depth=2, n_estimators=best_n_estimators, learning_rate=0.1, random_state=42)\n",
|
||
"gbrt_best.fit(X_train, y_train)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 29,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"plt.figure(figsize=(11, 4))\n",
|
||
"\n",
|
||
"plt.subplot(121)\n",
|
||
"plt.plot(errors, \"b.-\")\n",
|
||
"plt.plot([best_n_estimators, best_n_estimators], [0, min_error], \"k--\")\n",
|
||
"plt.plot([0, 120], [min_error, min_error], \"k--\")\n",
|
||
"plt.plot(best_n_estimators, min_error, \"ko\")\n",
|
||
"plt.text(best_n_estimators, min_error*1.2, \"Minimum\", ha=\"center\", fontsize=14)\n",
|
||
"plt.axis([0, 120, 0, 0.01])\n",
|
||
"plt.xlabel(\"Number of trees\")\n",
|
||
"plt.title(\"Validation error\", fontsize=14)\n",
|
||
"\n",
|
||
"plt.subplot(122)\n",
|
||
"plot_predictions([gbrt_best], X, y, axes=[-0.5, 0.5, -0.1, 0.8])\n",
|
||
"plt.title(\"Best model (55 trees)\", fontsize=14)\n",
|
||
"\n",
|
||
"save_fig(\"early_stopping_gbrt_plot\")\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 30,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"gbrt = GradientBoostingRegressor(max_depth=2, n_estimators=1, learning_rate=0.1, random_state=42, warm_start=True)\n",
|
||
"\n",
|
||
"min_val_error = float(\"inf\")\n",
|
||
"error_going_up = 0\n",
|
||
"for n_estimators in range(1, 120):\n",
|
||
" gbrt.n_estimators = n_estimators\n",
|
||
" gbrt.fit(X_train, y_train)\n",
|
||
" y_pred = gbrt.predict(X_val)\n",
|
||
" val_error = mean_squared_error(y_val, y_pred)\n",
|
||
" if val_error < min_val_error:\n",
|
||
" min_val_error = val_error\n",
|
||
" error_going_up = 0\n",
|
||
" else:\n",
|
||
" error_going_up += 1\n",
|
||
" if error_going_up == 5:\n",
|
||
" break # early stopping"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 31,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"print(gbrt.n_estimators)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {
|
||
"collapsed": true
|
||
},
|
||
"source": [
|
||
"# Exercise solutions"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"**Coming soon**"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"metadata": {
|
||
"collapsed": true
|
||
},
|
||
"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": "3.5.1"
|
||
},
|
||
"nav_menu": {
|
||
"height": "252px",
|
||
"width": "333px"
|
||
},
|
||
"toc": {
|
||
"navigate_menu": true,
|
||
"number_sections": true,
|
||
"sideBar": true,
|
||
"threshold": 6,
|
||
"toc_cell": false,
|
||
"toc_section_display": "block",
|
||
"toc_window_display": false
|
||
}
|
||
},
|
||
"nbformat": 4,
|
||
"nbformat_minor": 0
|
||
}
|