{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Bagging and AdaBoost\n", "\n", "In this notebook, I will implement algorithms described in Sections 14.2 and 14.3 of the book PRML, i.e., bagging and adaboost for binary classifications." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib as mpl\n", "from matplotlib import pyplot as plt\n", "\n", "%matplotlib inline\n", "plt.rcParams['axes.labelsize'] = 14\n", "plt.rcParams['xtick.labelsize'] = 12\n", "plt.rcParams['ytick.labelsize'] = 12" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 1 Setting\n", "\n", "* $N \\in \\mathbb{N}$ : the number of observation data\n", "* $D \\in \\mathbb{N}$ : the dimension of observation data\n", "* $X = (x_0, x_1, \\dots, x_{N-1})$ : the set of observation data. $x_n \\in \\mathbb{R}^D$\n", "* $t = (t_0, t_1, \\dots, t_{N-1})$ : the target labels. $t_n \\in \\{ 1, -1 \\}$\n", "* $y : \\mathbb{R}^D \\times \\Theta \\rightarrow \\{1, -1\\}$ : a binary classifier parametrized by $\\theta \\in \\Theta$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 2 Theory \n", "\n", "In this notebook, we construct strong classifier from a given simple classifier, which we call a base classifier. \n", "\n", "## 2.1 Base classifier : decision stump\n", "\n", "First, let us consider an extremely simple classifier called decision stump. \n", "\n", "\n", "### 2.1.1 Definition \n", "\n", "A decision stump is characterized by parameter $\\theta = (d, a, s) \\in \\{ 0,1, \\dots, D-1 \\} \\times \\mathbb{R} \\times \\{ 1, -1 \\} $, whose prediction is given by\n", "$$\n", "\\begin{align}\n", " y(x, (d,a,s)) = \n", " \\begin{cases}\n", " s & (x^{(d)} \\geq a ) \\\\\n", " -s & (x^{(d)} < a)\n", " \\end{cases}\n", "\\end{align}\n", "$$\n", "where $x \\in \\mathbb{R}^D$ and $x^{(d)}$ stands for its $d$th component.\n", "In essence, the decision stump $y(\\cdot, (d,a,s))$ makes prediction according to whether the $d$ th coordinate of the input is smaller than $a$ or not. \n", "\n", "### 2.1.2 Training\n", "In training a decision stump, we choose a parameter $\\theta$ that minimizes\n", "$$\n", "\\begin{align}\n", " \\sum_{n=0}^{N-1} w_n I\\left[ y(x_n, \\theta) \\neq t_n \\right], \n", "\\end{align}\n", "$$\n", "where $w_n$ stands for sample weight, and will be specified later depending on the algorithm we consider.\n", "\n", "Given training data $x_0, \\dots, x_{N-1}$, we only consider $2D(N-1)$ possible decision stumps because\n", "* there are two ways of choosing the sign $s$, \n", "* there are $D$ possible ways of choosing the dimension $d$, and\n", "* although there are infinitely many ways of choosing $a$, here we limit the possible values of $a$ to be the average of two adjacent (in terms of $d$ the coordinate) training data points, which result in $N-1$ choices. \n", "\n", "As to the final point: The limitation does not affect the values of the error function, although it affects prediction error. Also, we assume that the training data is not single class (i.e., there are $n$ and $m$ such that $t_n \\neq t_m$ ).\n", "\n", "In the later implementation, we perform this exhaustive search." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2.2 Bagging \n", "\n", "The idea of bagging, or bootstrap aggregation, is to train $M$ base classifiers using different \"training data\" for each classifier, where we obtain the \"training data\" by resampling from the original training data. \n", "\n", "### 2.2.1 Training \n", "\n", "For $m = 0,1, \\dots, M-1$, \n", "1. randomly sample $N$ data points from $(X,T)$ with replacement, and\n", "2. train the $m$ th classifier $y(\\cdot, \\theta_m)$ using the resampled data. \n", "\n", "### 2.2.2 Prediction \n", "\n", "Output the prediction for input $x$ by \n", "$$\n", "\\begin{align}\n", " y_{bag}(x) = \\mathrm{sign} \\left[ \\sum_{m=0}^{M-1} y(x, \\theta_m) \\right]\n", "\\end{align}\n", "$$\n", "\n", "NOTE : Eq. (14.7) in the book is for regression, and for classification, we have to take sign to obtain meaningful result. We ommitted $1/M$ factor, because here we only care about sign." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2.3 AdaBoost\n", "\n", "NOTE : Formally, we can use other classifiers than decision stump for AdaBoost. However, in that case, the error function to be minimized by each base classifier is not necessarily $\\sum_{n=0}^{N-1} w^{(m)}_{n} I \\left[ y(x_n, \\theta_m) \\neq t_n \\right]$, and I am not sure whether it is theoretically sound or not.\n", "\n", "### 2.3.1 Training\n", "\n", "In AdaBoost, we train the classifier following the algorithm shown below: \n", "\n", "0. input : training data $(X, T)$, base classifier $y$, the number of boosting $M$. \n", "1. Initialize data weights $(w_0, w_1, \\dots, w_{N-1})$ as $w^{(0)}_{n} = 1/N$. \n", "2. For $m = 0, \\dots, M-1$: \n", " 1. Choose $\\theta_m \\in \\Theta$ such that\n", " $$\n", " \\begin{align}\n", " \\sum_{n=0}^{N-1} w^{(m)}_{n} I \\left[ y(x_n, \\theta_m) \\neq t_n \\right]\n", " \\end{align}\n", " $$\n", " is minimized.\n", " 2. Evalute \n", " $$\n", " \\begin{align}\n", " \\varepsilon_m &:= \\sum_{n=0}^{N-1} w^{(m)}_{n} I \\left[ y(x_n, \\theta_m) \\neq t_n \\right] \\\\ \n", " \\alpha_m &:= \\log \\left(\\frac{1 - \\varepsilon_m}{\\varepsilon_m} \\right)\n", " \\end{align}\n", " $$\n", " 3. Update the data weight by \n", " $$\n", " \\begin{align}\n", " \\tilde{w}^{(m+1)}_{n} &= w^{(m)}_{n} \\exp\\left\\{ \\alpha_m I \\left[ y(x_n, \\theta_m) \\neq t_n \\right] \\right\\} \\\\\n", " w^{(m+1)}_{n} &= \\frac{\\tilde{w}^{(m+1)}_{n}}{ \\sum_{n'=0}^{N-1} \\tilde{w}^{(m+1)}_{n'} }\n", " \\end{align}\n", " $$\n", " \n", "NOTE :\n", "* We normalize the weight here, which results in apprently different (but intrinsically the same) definition of $\\varepsilon_m$ from (14.16) of the book.\n", "* It is implicitly assumed that the base classifier is better than random in the sense that $\\varepsilon_m < \\frac{1}{2}$ for all $m$. As far as I understand, the algorithm does not work when $\\varepsilon_m > \\frac{1}{2}$.\n", "\n", "### 2.3.2 Prediction \n", "\n", "Having obtained the classifier, the predicted label for input $x$ is given by \n", "$$\n", "\\begin{align}\n", " \\textrm{sign} \\left[ \\sum_{m=0}^{M-1} \\alpha_m y(x, \\theta_m) \\right]\n", "\\end{align}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 3 From math to code\n", "\n", "Here we define three classes, namely, `DecisionStump`, `Bagging`, and `AdaBoost`. \n", "\n", "We let `Bagging` and `AdaBoost` classes have `fit` and `precit` methods, and the following properties\n", "* `BaseClassifierClass` : the class from which base classifiers are generated (class, rather than instance should be given), which is assumed to implement `fit` and `predict` methods. For `AdaBoost` class, it is also assumed that the `fit` method of `BaseClassifierClass` can handle `sample_weight`.\n", "* `num_clfs` : $M$, i.e., the number of base classifiers used.\n", "* `clfs` : list for storing base classifiers\n", "\n", "\n", "\n", "## 3.1 Decision stump\n", "\n", "We let our `DecisionStump` class to have the following properties\n", "* `axis` : $d$, i.e., the axis used for prediction\n", "* `sign` : $s$\n", "* `threshold` : $a$\n", "\n", "In fitting a decision stump, we \n", "* first perform the exhaustive search over $s$ and $a$ for each dimension using `fit_onedim` method (where the axis $d$ is given), and \n", "* then compare the result for each dimension $d$. \n", "\n", "In `fit_onedim`, we use the folowoing arrays, assuming that $X, T$ and $w$ are sorted according the value of the $d$th component of the input data $X$: \n", "* `pred` : $(N-1, N)$ array, where `pred[m,n]` = $y\\left(x_n, \\left(d, \\frac{x_m + x_{m+1}}{2}, 1 \\right) \\right)$. Note that it can be generated easily by using np.tri (Although it is inefficient in terms of memory. ).\n", "* `mistakes` : $(N-1, N)$ array, where `mistakes[m,n]` = $I \\left[ y\\left(x_n, \\left(d, \\frac{x_m + x_{m+1}}{2}, 1 \\right) \\right) \\neq t_n\\right] $\n", "* `errs` : $(2, N-1)$ array, where \n", " * `errs[0,m]` = $\\sum_{n=0}^{N-1} w_n I \\left[ y\\left(x_n, \\left(d, \\frac{x_m + x_{m+1}}{2}, 1 \\right) \\right) \\neq t_n\\right] $\n", " * `errs[1,m]` = $\\sum_{n=0}^{N-1} w_n I \\left[ y\\left(x_n, \\left(d, \\frac{x_m + x_{m+1}}{2}, -1 \\right) \\right) \\neq t_n\\right] $" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "class DecisionStump:\n", " \n", " def __init__(self, axis=None, sign=None, threshold=None):\n", " self.axis = axis\n", " self.sign = sign\n", " self.threshold = threshold\n", " \n", " def fit_onedim(self, X, y, sample_weight, axis):\n", " '''\n", " Performing exhaustive search on threshold and sign, where the axis to consider is given.\n", " \n", " Parameters\n", " ----------\n", " X : 2D numpy array\n", " 2D numpy array representing input data, where X[n, i] represents the i-th element of n-th point in X.\n", " y : 1D numpy array\n", " (len(X),) numpy array representing labels, where y[n] represents the label corresponding to n-th point in X.\n", " Each element should be either 1 or -1\n", " sample_weight : 1D numpy array\n", " (len(X), ) numpy array representing the sample weights.\n", " The elements should be non-negative.\n", " axis : integer\n", " A non-negative integer the axis to be considered.\n", " Must be between 0 and X.shape(1)-1\n", " \n", " Returns\n", " ----------\n", " sign : int, 1 or -1\n", " Integer representing the sign s for the (candidate) decision stump\n", " threshold : float\n", " Threshold a for the (candidate) decision stump\n", " err : float\n", " Training error for the (candidate) decision stump\n", " '''\n", " N = len(X)\n", " \n", " # Here we sort everything according the axis-th coordinate of X\n", " sort_ind = np.argsort(X[:, axis])\n", " sorted_label = y[sort_ind]\n", " sorted_input = X[sort_ind]\n", " sorted_sample_weight = sample_weight[sort_ind]\n", " \n", " pred = -2*np.tri(N-1, N, k=0, dtype='int') + 1 \n", " mistakes = (pred != sorted_label ).astype('int')\n", " \n", " # The (weighted) error is calculated for each classifier\n", " errs = np.zeros((2, N-1))\n", " errs[0] = mistakes @ sorted_sample_weight\n", " errs[1] = (1 - mistakes) @ sorted_sample_weight\n", " \n", " # Here, we select the best threshold and sign\n", " ind = np.unravel_index(np.argmin(errs, axis=None), errs.shape)\n", " sign = -2*ind[0] + 1\n", " threshold = ( sorted_input[ind[1], axis] + sorted_input[ind[1] + 1, axis] ) / 2\n", " err = errs[ind]\n", " return sign, threshold, err\n", "\n", " \n", " def fit(self, X, y, sample_weight=None):\n", " '''\n", " Performing fitting by exhaustive search on threshold, sign, and axis.\n", " \n", " Parameters\n", " ----------\n", " X : 2D numpy array\n", " 2D numpy array representing input data, where X[n, i] represents the i-th element of n-th point in X.\n", " y : 1D numpy array\n", " (len(X),) numpy array representing labels, where y[n] represents the label corresponding to n-th point in X.\n", " Each element should be either 1 or -1\n", " sample_weight : 1D numpy array\n", " (len(X), ) numpy array representing the sample weights.\n", " The elements should be non-negative.\n", " If None, the sample_weight is assumed to be uniform.\n", " '''\n", " N, D = X.shape\n", " \n", " if sample_weight is None:\n", " sample_weight = np.ones(N)/N\n", " \n", " signs = np.zeros(D)\n", " threshs = np.zeros(D)\n", " errs = np.zeros(D)\n", " for axis in range(D):\n", " signs[axis], threshs[axis], errs[axis] = self.fit_onedim(X, y, sample_weight, axis)\n", " self.axis = np.argmin(errs)\n", " self.sign = signs[self.axis]\n", " self.threshold = threshs[self.axis]\n", "\n", " def predict(self, X):\n", " '''\n", " The method predicts the labels for the given input data X.\n", " \n", " Parameters\n", " ----------\n", " X : 2D numpy array\n", " 2D numpy array representing input data, where X[n, i] represents the i-th element of n-th point in X.\n", " \n", " Returns\n", " ----------\n", " y : 1D numpy array\n", " (len(X),) numpy array representing the predicted labels, where y[n] represents the label corresponding to n-th point in X.\n", " '''\n", " return self.sign*( 2*(X[:, self.axis] >= self.threshold) - 1 )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3.2 Bagging \n", "\n", "The implementation is rather straightforward. \n", "\n", "The code is written in a way that it can be used for other base classifiers, assuming that the base classifier class has `fit` and `predict` method." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "class Bagging:\n", " def __init__(self, BaseClassifierClass, num_clfs):\n", " self.BaseClassifierClass = BaseClassifierClass # base classifier class\n", " self.num_clfs = num_clfs\n", " self.clfs = [self.BaseClassifierClass() for _ in range(self.num_clfs)]\n", "\n", " def fit(self, X, y):\n", " '''\n", " The method performs fitting by bagging using the given base classifier.\n", " \n", " Parameters\n", " ----------\n", " X : 2D numpy array\n", " 2D numpy array representing input data, where X[n, i] represents the i-th element of n-th point in X.\n", " y : 1D numpy array\n", " (len(X),) numpy array representing labels, where y[n] represents the label corresponding to n-th point in X.\n", " Each element should be either 1 or -1\n", " '''\n", " N = len(X)\n", " for m in range(self.num_clfs):\n", " \n", " # resampling is performed here\n", " sample_ind = np.random.randint(0, N, N)\n", " X_resampled = X[sample_ind] \n", " y_resampled = y[sample_ind]\n", " # traing the classifier using the resampled training data\n", " self.clfs[m].fit(X_resampled, y_resampled)\n", " \n", " def predict(self, X):\n", " '''\n", " The method predicts the labels for the given input data X.\n", " \n", " Parameters\n", " ----------\n", " X : 2D numpy array\n", " 2D numpy array representing input data, where X[n, i] represents the i-th element of n-th point in X.\n", " y : 1D numpy array\n", " (len(X),) numpy array representing the predicted labels, where y[n] represents the label corresponding to n-th point in X.\n", " '''\n", " base_pred = np.zeros((self.num_clfs, len(X)))\n", " for m in range(self.num_clfs):\n", " base_pred[m] = self.clfs[m].predict(X)\n", " return np.sign( np.sum(base_pred, axis = 0 ) )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3.3 AdaBoost\n", "\n", "Just like the `Bagging` class, the code is written in a way that it can be used for other base classifiers, asuming that the base classifier class has \n", "* `fit` method which takes input data, label, and sample weight, and \n", "* `predict` method." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "class AdaBoost:\n", " def __init__(self, BaseClassifierClass, num_clfs):\n", " self.BaseClassifierClass = BaseClassifierClass # base classifier class\n", " self.num_clfs = num_clfs\n", " self.alpha = np.zeros(self.num_clfs)\n", " self.clfs = [self.BaseClassifierClass() for _ in range(self.num_clfs)]\n", " \n", " def fit(self, X, y):\n", " '''\n", " The method performs fitting by AdaBoost using the given base classifier.\n", " \n", " Parameters\n", " ----------\n", " X : 2D numpy array\n", " 2D numpy array representing input data, where X[n, i] represents the i-th element of n-th point in X.\n", " y : 1D numpy array\n", " (len(X),) numpy array representing labels, where y[n] represents the label corresponding to n-th point in X.\n", " Each element should be either 1 or -1\n", " '''\n", " N = len(X)\n", " w = np.ones(N)/N # initialize the weight\n", " for m in range(self.num_clfs):\n", " self.clfs[m].fit(X, y, sample_weight = w)\n", " mistakes = (self.clfs[m].predict(X) != y)\n", " \n", " # calculate the epsilon and alpha\n", " ep = np.sum ( w * mistakes)\n", " self.alpha[m] = np.log(1.0/ep - 1)\n", " \n", " # update the weight\n", " w = w * np.exp( self.alpha[m] * mistakes )\n", " w = w/np.sum(w)\n", " \n", " def predict(self, X):\n", " '''\n", " The method predicts the labels for the given input data X.\n", " \n", " Parameters\n", " ----------\n", " X : 2D numpy array\n", " 2D numpy array representing input data, where X[n, i] represents the i-th element of n-th point in X.\n", " y : 1D numpy array\n", " (len(X),) numpy array representing the predicted labels, where y[n] represents the label corresponding to n-th point in X.\n", " '''\n", " base_pred = np.zeros((self.num_clfs, len(X)))\n", " for m in range(self.num_clfs):\n", " base_pred[m] = self.clfs[m].predict(X)\n", " return np.sign( base_pred.T @ self.alpha )" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "# 4 Experiment\n", "\n", "## 4.1 Data and preparation" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def get_meshgrid(x, y, nx, ny, margin=0.1):\n", " x_min, x_max = (1 + margin) * x.min() - margin * x.max(), (1 + margin) * x.max() - margin * x.min()\n", " y_min, y_max = (1 + margin) * y.min() - margin * y.max(), (1 + margin) * y.max() - margin * y.min()\n", " xx, yy = np.meshgrid(np.linspace(x_min, x_max, nx),\n", " np.linspace(y_min, y_max, ny))\n", " return xx, yy\n", "\n", "\n", "def plot_result(ax, clf, xx, yy, X, y):\n", " pred = clf.predict(np.c_[xx.ravel(), yy.ravel()]).reshape(xx.shape)\n", " ax.contourf(xx, yy, pred, alpha=0.7)\n", " ax.scatter(X[:,0], X[:,1], c=y, edgecolor='k')\n" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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HJJPI5aRoqlWr5pB1lGS//Po7cydWztbWvaMvDw7eTVpaWp4XEIwZ8ywDBw5i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\naMFQSillFy0YSiml7KIFQymllF1K1BC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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from sklearn import datasets\n", "\n", "X, y = datasets.make_moons(n_samples = 50, noise = 0.1, random_state=1)\n", "y = 2*y-1\n", "plt.scatter(X[:,0], X[:,1], c=y, edgecolor='k')\n", "\n", "xx, yy = get_meshgrid(X[:, 0], X[:, 1], nx=100, ny=100, margin=0.1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 4.2 Results\n", "\n", "Let us compare the results for \n", "* single decision stump\n", "* bagging\n", "* Adaboost\n" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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LTGThtBsZkzbB6rCUUgGuz9nLtsJ3KCzeDSJMHTub+ZOvJcgRbHVoyo/pE0E14t7a/iLv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\nC5x0253t6d7Tn9nfJ1NcVMqosbGMvCwCna7pDbv6R1i4G33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ENgcMO+g6abLa0aQGptEo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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "clfs = [DecisionStump(), Bagging(DecisionStump, 100), AdaBoost(DecisionStump, 100)]\n", "clf_names = ['Decision Stump', 'Bagging', 'AdaBoost']\n", "\n", "fig, axes = plt.subplots(1, 3, figsize=(15,5))\n", "\n", "for i in range(len(clfs)):\n", " clfs[i].fit(X, y)\n", " plot_result(ax=axes[i], clf=clfs[i], xx=xx, yy=yy, X=X, y=y)\n", " axes[i].set_title(clf_names[i])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* For decision stump, as is trivial from the definition, the decision boundary is a straight line parallel to an axis.\n", "* For the bagging, we can see that it can express slightly more flexible decision boundary (However, in many cases, it does not show any visible differences from the decision stump case).\n", "* For AdaBoost, it can be seen that the model is much more flexible compared with the others, and fits the training data well.\n", "\n", "Let us take a look on how AdaBoost behaves when we increase the number of base classifiers." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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Mn7rcJccUvkUaQR+mlIVpabOZljbbLcdLjknn2Xu/ycEz22hqa2BKTA5zpj5D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V69o30WvzGGUaO7MWq07y5+BbgOkZt03iQAy5cV8LsfJzdrmzQuDI/X8r0fjuTjT/ZQU+1mxsUD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LRylyisB/NW7gwlsTivaI4Lmzyfwy/QhRJxOoVt2fXn3L4+Ulq2YJUVwcPRLH0J7OedqcnQ3U\nru7MsaMJRbYQNJstLPnjJGv/Oo27uxM9+5Sneo2CvxtVCFG0RB5LoGY155wi8F9NGjjzzcw4G0V1\new4dvMycmYe5HJfOQ41D6NwtHJPJwdZh3Rdkaqgodnx9ndEaDh/LyNO+YUsq5St6FajP5CQzfyw8\nyfy5x4mLTbdGmNfZtfMSj7ZeREbcaR5ulMrBnUd5tPUizp1LuSf7E0IUvgoVfVi/JS1PW2qqhZ17\n0yhX3vOO+9Nas33rRebMOsbuXTFora0Vag6z2cKQ/n8y/YedtKidQimfGAY/vpJfph22+r6EELZR\nrrwneyLSSEmx5GlfvyWNchV9CtTnxehU5v0aydI/TpGakmmNMK+zcP5x+nZfRoDLRVrVS2HB7D08\n3nM5qan3Zn/FjRSCotgxGg0MG/kAfYZHs3VXGunpFhYsS+KV/4tlxHN3vmz6X6vO0LDuXH6fuZNV\nC/fQ9MF5zJpxxOpxv/vGZj5515cvx/kzuI8XMyeVoFcHE198vMvq+xJC2MaAwZWZOS+ZSVMvk5Rs\n4UhkBn1GRNOkWfAdjwbGx2fQu+syRj+/hh1r9/Ps0FUM7LOSlGSzVWNeOP8EGSmJ/D0vmGEDvXhr\nlC9/zw/hvbHbSUjIyL8DIUSRF1bSnRatQ+kzIprDxzJITrHw7f8u8/OcJAYOrnzH/f30/QFaNv6d\nNUv2MnvqDhrVnWv1dRpSUzN5+/V/WPZLMGNf8eOp/l78OScIb9d0Zs84atV9FVdSCIpiadjIavTs\nV40+I2LwKBfJuK/SeHL4A0z76QC9uyxh/LjtXIxOzbef+PgMXnhmHYt+DmTJjCDmTQnknyWhfPh/\n24k8lmC1eOPjM9i/P54+XfNeCD49wJOVy6Ksth8hhG2FhLox49d2/L7KAf8qkTTtco6AsGCCQ93o\n3WUJzwz9iw3rzt1WXx+M2UrVMmb2rw3j568COLyxJCW8Uvl0gnVvHq1eeZIhfdxxdMx98XyFsk5U\nrWjkn00XrLovIYTtjP+0MWWrlKJ5t3P4VY7ktxWKp555gLdf20Sfbkv5dmLEbd1o2rsnhklf7mbn\nyjB++yGQFbODmPlNAM8M/duqI4N7dscQEuRArQdMOW0Gg+Lp/h4sXRRpEP3c5QAAD/lJREFUtf0U\nZ1IIimJJKcWgJ6uwbksPTpzrT98BlZg2JYJHGmcwdpQzmQln6fLIYqIv3LoYXLE0iuYNXWhYzyWn\nrUJZJ/r1cGPBvONWi9fJaMCSpUlKzjslI/ayBbNZlpUXojipUs2HqTPbEnmmP8vXdGbViigsiecY\n86IzjzbJYPTza/Oddqm15vd5Jxn3mi8GQ3aB5uCg+L9XfJj3q3UvgOLiMoiJvT4PxcRmcjoq2ar7\nEkLYjsnkwCtv1mF7xGNEnulPhYo+/DHvIIN7wOsjnNj7zxH69VpBevqtr0sWzI3kqf4elC5pzGlr\n3dSVapWNrPnrrNXiNRoNXIoxXzclPiYuiwv5XN+JbFIIimIvPT2LCe/tYPH0IIYN9KJVE1cmfhBA\n53bOfP9txC23TUvLwtNDXdfu6a6Y88thkpKsMwXLxdURo5Pi7fExWCz6yr4tvD3+EgmJWWRlWfLp\nQQhxP/rxu/082trEpA8DaN3UlacHeLFkRhAT3t9xy3cLag3pGRY83PL+Gff0MBCfYGbtGutdbPn4\nOPP55MucPpub72b9nkhMbNY9eSZRCGF7UaeS+G3OMdbMDaZPVw8eae3GvCmBuJky+GPByVtum5aW\niZf79SWGyaj54duInOucu+XjYyIlRTN5Wu4MrehLmXw0MY60dLluuh1SCIpiKSEhg7VrzrJ7VwxH\nj8Tj5+vAA5VNeT7Tu5MbWzfdegpWi1Yh/LEymXMXcqcyJCVb+GV+EpXKGPj6sz1Wizk4yJX1W1Kp\n0uQkjz19jrINTmA0KoICTTg4yK+qEMWB1ppdOy+xds1ZEhMz2LL5HL07ueX5TNVKJgJLOHLk8OWb\n9mMwKFq2DOLbn+PztH/3czwtGrrwn2fW5XvX/nbVfyiQ4EBHarY6RddBZ2ncMYrXx10iKNCJ8DJ3\nvsCNEKJounAhhTWrz3L0SDxb/4mmdVM3vL1yV99UStGrkwtb8rl2atW2FD/NSSYtLbcYOxllZsuO\nNFITk1n4+wmrxFuihAtZWvHRxFgatD9F98FnqdLkJNWrOFGlirdV9lHcWe31EUopX+BHoB1wCXhd\naz3zJp99F3gTuHr5xRpa68grP691pa8qwAHgSa21rJghbsvUHw/w8Ye7qFHVmXMXMjE4OhIdbSY1\n1YKLS25BdfyUGT9/l1v0BCVLuTPoySrUaBHB80954+JsYMrMeNo0c2XYQE+6Dz3Ba2/VtUrcw56t\nzvdf7+Cdl31wcFA80duT/46PY9jI6lbp315JbhJFxfHIBIYN/ovMjAwCAxzZdzCN0qXdOB6VSfOr\nPpeWZuH8BTN+fs437QvgzTH16fzwYnbsSaPxgy6s3ZTK5m1p/DU/jH4jL/LPpgs0axFy13F361mW\niV/sYfRIH0qHOuLqauCfHWksWJlJ85bBd92/vZLcJIoKi0Uz9q0t/DYnkjo1nDlwOJ2gYHccuH7W\n0/FTmfleO7VoFcLUH7yo3uIUIwZ5kZBo4fvp8Yx91Q8vTwOzFkbStXuZu47bzd1I337liTxwmiF9\n3DEYoH9PT154K4ZPv37grvu3B9YcZpgIZACBQD/gG6VUtVt8frbW2v2qr3+TmROwAJgO+AD/AxZc\naRfiljZvusDkr/ewbXkYa+YFc3B9GE8/7oKTUfHKuBjSr0wVOHo8gzGfXKbfoCr59jl0eFVSUjUx\nsVmcOmPmqw9KMPHDgOzncqw4Lap333IMGFqDV8ZdZsQrF3nypUt06lmFQUPvfLUukYfkJmFzWmue\nHrSa4f1NHFgXxt/zg/lnSShRUcmM+TiOI5HZq2+mp1t4dVwstesGEBLqdss+y5X3olnzYMxm2L0v\nnUb1XNi5qhThJY0orJeevLycmPlbe5auNfD0yxfp/8wF9hxzZdqcdjJb4e5IbhJFws8/HWLfjtMc\n21yKP+cEc2JraWpXyeL4qQwm/nQ5Zyrn+n9SmToriV59y9+yP4NB8ex/amDBQORJMympFhbPCGXk\nEG8MBqteOvH62/WoXLMUI9+IYdjoS7z6fgJv/9+DNG4qN6luh1VGBJVSbkAP4AGtdRKwXim1EBgA\nvHaH3bW4EtfnOvvhgy+VUi8DrYBl1ohXFF+zZxzipRFelC2d/YCyUor/PO3F11Pi2XHAkZJ1ThIW\n4sSpM2ZefLkmrdqE5tunh4cTDR4KoFSYZtTw7KkGWms+/iaehzuGWy12pRRPDKlM/ycqkpBgxtPT\nKBdZd0lykygqdu24hCXTzMjBgSiV/dxx+TJOvP6cN3OWahp2PEupUCNnzpmpWduPz75uelv9du5e\njq8+3sKGhYG4XXkR9MatqRyJNPNgw0CrxV+hohe/zHuYpCQzDgaFi6vVJhTZJclNoiiZM/MQn7/r\ng4939jRQo1Hx8Tv+zFlwgu9/yWDCxFN4uDtwOcHCx182oUzZ/KeE16kXQIZZ0eVhN9o2z76plZZm\n4csfE+n/ZG2rxW40GnjtrXq89FodkpPNeHk55eRYkT9rZfKKQJbW+uplznZDntku1+qklIoFzgFf\na62/udJeDdij8z6BvudK+3UJTSn1NPA0gJebb8H/BaJYSLicTkigQ542pRShwU6MHFWLMmU9uHgx\njUqVvHB1M96kl+uNG9+Qx3uu4K+NadSqZmTF32lYlInpH975ewnz4+BgwMfHlP8Hxe0oErkpNOzW\nIzui+Lscn0FIkON1FyjBgY4EBBiYPrsHhw7F4+/vTMlS7rfdb/tHSrLmzyiqtzhNr86uRF+ysGhF\nMl9Maoazs0P+Hdwhd/fbz5vilopEbpLrJgEQf9lMSGDeksDL04DRycD/fmlDfLyZlJRMqlbzwdHx\n9m5QOzoa+HxiUx5/cg3tWyRTMsTA3MUpVK8VSJfu4Vb/NxiNBry95drpTlmrEHQH4q9piwdu9nbc\nOcBk4ALwIDBXKXVZa/3LnfaltZ58pS9C/ErL8mV2rnGzMKb9dojuHdxzLriOHs8g4lAatev64+5u\nJKzk7V9k/atMWU9Wr+/K4kUniTqVxDOjfGnVJlRG7Iq+IpGbatTyk9xk5+rUDeC5vWmciDITfmVJ\nda010+cm07RdFVzdjNSu43/H/RoMig8/bcSunTH8/ddZyoUYWf12OP4Bt36GR9hckchNct0kAJo0\nC+bnXy8z7jW/nLbFfyYTHOyCf4ALASVcC9Rvw8ZBrNnYjQXzT3A5Lp2PvgyiXoMAGbErQm6rEFRK\nreHmd6k2AM8B144TewKJN9pAa73/qm83KqW+AHoCvwBJd9KXEFfr06888347StfBF+jfw40z5zL5\n9LsEXnmj9l3fyXZxdaTnY+WsFKmwBslN4n7h5eXES6/UokW3PYwa7kVQCQd+/jWZ6DhHet1lXlFK\nUbuOf4EKSXFvSG4S95PnRtWkR6elXIyx8HBLF3bvT+ebqYl89V3zuy7afHxNDHqykpUiFdZ2W8MZ\nWusWWmt1k68mwGHAUSlV4arNagK3fknbVbsA/j3TIoAaKu+ZV+MO+hJ2zNXNyJz5D9OgWSV+mqfY\ncsCDL79tyYBBsuBKcSS5SdxPBj9VhU8ntWBThBtT5ysat6nMrHkPy/N2xZDkJnE/CSvpzuKVHfEM\nLsn3c+D0ZX/mLHiEJs1kwZXizip/fbTWyUqpecBYpdRQoBbQBWh0o88rpboAa4HLQH3geeCNKz9e\nA2QBzyulvgW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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "num_clf_list = [2, 4, 8, 16, 32, 64]\n", "clfs = [AdaBoost(DecisionStump, M) for M in num_clf_list]\n", "\n", "fig, axes = plt.subplots(2, 3, figsize=(15,10))\n", "\n", "for i in range(len(clfs)):\n", " clfs[i].fit(X, y)\n", " plot_result(ax=np.ravel(axes)[i], clf=clfs[i], xx=xx, yy=yy, X=X, y=y)\n", " np.ravel(axes)[i].set_title(f'M = {num_clf_list[i]}')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Roughly speaking, the larger the number of base classifiers is, the more complex the decision boundary becames. It seems to be intuitively natural, because in AdaBoost, a base classifier \"tries\" to correct the mistakes that its previous base classifier made." ] } ], "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": "3.6.6" } }, "nbformat": 4, "nbformat_minor": 2 }