MIT OCW, Machine Learning 06日目 宿題2

Rohit Singh, Tommi Jaakkola, and Ali Mohammad. 6.867 Machine Learning. Fall 2006. Massachusetts Institute of Technology: MIT OpenCourseWare, https://ocw.mit.edu. License: Creative Commons BY-NC-SA.

Assignment

Problem set 1 Section B

問

1.

パーセプトロンの実装.pythonを使う.

import numpy as np
import matplotlib.pyplot as plt

def sign(r):
    if r >= 1:
        return 1
    else:
        return -1

class PerceptronClassifier:
    def get_params(self):
        gamma = np.argmin(np.abs([np.dot(self.theta, x) for x in self.train_X]))
        gamma_geom = gamma / np.linalg.norm(self.theta)
        print("theta is: {0}, k till the convergence is {1}".format(self.theta, self.k))
        print("The angle with [1, 0] and theta is: {0} (rad)".format(np.arccos(self.theta[0]/np.linalg.norm(self.theta))))
        print("The geometric margin is {0}".format(gamma_geom))

    def perceptron_train(self, X, y):
        self.train_X = X
        self.train_y = y
        self.theta = np.zeros(len(X[0]))
        self.k = 0
        while True:
            cnt = 0
            for i in range(len(self.train_y)):
                if y[i] != sign(np.dot(self.theta, self.train_X[i])):
                    self.k += 1
                    self.theta = self.theta + y[i]*X[i]
                    cnt += 1
            if cnt == 0:
                break

    def perceptron_test(self, test_X, test_y):
        self.test_X = test_X
        self.test_y = test_y
        errors = 0
        for i in range(len(test_y)):
            if test_y[i] != sign(np.dot(self.theta, test_X[i])):
                errors += 1
        print("The error ratio is: {0}".format(errors/len(test_y)))

    def draw_graph(self, train=True):
        if train:
            X = self.train_X
            y = self.train_y
        else:
            X = self.test_X
            y = self.test_y

        plus = np.array([x for x in X if np.dot(self.theta, x)>=0 ])
        minus = np.array([x for x in X if np.dot(self.theta, x) < 0])

        plt.scatter(plus[:, 0], plus[:, 1], color='red', s=2)
        plt.scatter(minus[:, 0], minus[:, 1], color='blue', s=2)
        plt.show()

模範解答とはことなった結果を示すが,収束までの更新回数$k$や$\gamma_{geom}$は更新を行う前に定義する$\theta$の初期値にわりと鋭敏に反応するので,深く考えなくてもいいかもしれない(MATLABとPythonの精度も関係しているかも？).

X_a = np.loadtxt('p1_a_X.dat' )
y_a = np.loadtxt('p1_a_y.dat')
X_b = np.loadtxt('p1_b_X.dat')
y_b = np.loadtxt('p1_b_y.dat')

per_cla = PerceptronClassifier()
per_cla.perceptron_train(X_a, y_a)
per_cla.perceptron_test(X_a, y_a)
per_cla.draw_graph('Dataset A')
per_cla.get_params()

per_cla = PerceptronClassifier()
per_cla.perceptron_train(X_b, y_b)
per_cla.perceptron_test(X_b, y_b)
per_cla.draw_graph('Dataset B')
per_cla.get_params()

2, 3.

SVMの実装. quadratic programを解く関数を使っていいらしいがpythonだとpipにも入ってないから飛ばす