（斯坦福机器学习课程笔记）局部加权线性回归练习

代码使用PTHON3.x

题目如下

import numpy as npimport randomimport matplotlib.pyplot as pltF64='float64'def gen_sin_dot_sample(num_point):    x=np.linspace(0,10,num_point)    y=np.sin(x)+np.random.random(num_point)*0.05    return [x.tolist(),y.tolist()]def show_point(p_x,p_y):    plt.figure(1)    plt.plot(p_x,p_y,'ob')    plt.xlim(-5.2,15.2)    plt.ylim(-1.8,1.8)    plt.xlabel('x')    plt.ylabel('y')    plt.show()[x,y]=gen_sin_dot_sample(100)show_point(x,y)

得到下图样本点

要求用局部加权线性回归拟合该曲线

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代码如下

import numpy as npimport randomimport matplotlib.pyplot as pltF64='float64'def gen_sin_dot_sample(num_point):    x = np.linspace(0,10,num_point)    y = np.sin(x)+np.random.random(num_point)*0.5    return [x.tolist(),y.tolist()]def draw_point(p_x,p_y):    plt.figure(1)    plt.plot(p_x,p_y,'ob')    plt.xlim(-5.2,15.2)    plt.ylim(-2.2,2.2)    plt.xlabel('x')    plt.ylabel('y')    plt.show()def draw_point_and_line(p_x,p_y,l_x,l_y):    plt.figure(1)    plt.plot(p_x,p_y,'ob')    plt.plot(l_x,l_y,'r')    plt.xlim(-5.2,15.2)    plt.ylim(-2.2,2.2)    plt.xlabel('x')    plt.ylabel('y')    plt.show()def lwr(x,y,x_calculate,times_iteration,k,study_rate):# x,y,x_calculate is list    num_sample = len(x)    x = np.asarray(x,dtype=F64).reshape((num_sample,1))    y = np.asarray(y,dtype=F64).reshape((num_sample,1))    one_mat = np.ones((num_sample,1),dtype=F64)    x_add_one = np.hstack((one_mat,x))    theta = np.random.random((2))    theta = theta.astype(F64).reshape(2,1)    for i in xrange(times_iteration):        weight = np.exp(-np.square(np.hstack((x,x))-x_calculate)/(k**2))        diff_theta = ((np.dot(x_add_one,theta)-y)*x_add_one*weight).mean(0,dtype=F64,keepdims=True)        theta = theta-diff_theta.transpose()*study_rate    return theta.reshape((2)).tolist()[x,y] = gen_sin_dot_sample(100)x_calculate = np.linspace(0,10,50).tolist()point_list=[]for i in x_calculate:    theta = lwr(x,y,i,1000,0.3,0.1)    point_y = theta[0]+theta[1]*i    point_list.append(point_y)draw_point_and_line(x,y,x_calculate,point_list)

结果是，学习率选0.1、k选1.3时，欠拟合，下图

学习率选0.1、k选0.3时，合适，下图

学习率选0.1、k选0.03时，过拟合，下图

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总结，局部加权线性回归计算慢，但效果很好，补一张算法图，免忘

其中