Coursera ML(3)-Multivariate Linear Regression python实现
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Coursera ML(3)-Multivariate Linear Regression python实现

in Coursera ML with 0 comment
Multivariate Linear Regression and Programming Exercise 1

Gradient Descent for Multiple Variables


Get every feature into approximately [-1, 1]. Just normalize all the parameters :)

Programming Exercise 1

下载程序及相关数据

Stanford coursera Andrew Ng 机器学习课程编程作业(Exercise 1),作业下载链接貌似被墙了,下载链接放这。
http://home.ustc.edu.cn/~mmmwhy/machine-learning-ex1.zip

重新推导一下:

其实这里一共就两个式子:

$$h_\theta (x) = \theta_0 + \theta_1 x_1 + \theta_2 x_2 + \theta_3 x_3 + \cdots + \theta_n x_n$$
$$J(\theta_0,\theta_1 )=\frac1{wm} \sum_{i=1}^{m}(h_{\theta}(x^{(i)})-y^{(i)})^w$$

python拟合实现代码

原本用的是matlab代码,我用python实现了一下,结果是一样的:

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt


def readfile(path):
    X=[]
    y=[]
    with open(path,'r') as f:
        for line in f:
            X.append([1,float(line.split(',')[0])])
            y.append(float(line.split(',')[1]))
    return X,y


def dataplot(x,theta,y):
    plt.plot(x, y, 'rx', markersize=10)
    plt.ylabel('Profit in $10,000s')
    plt.xlabel('Population of City in 10,000s')
    plt.plot(X[:,1],X*theta,'-')
    plt.show()


def computeCost(X,y,theta):
    m = len(y)
    J = 0
    for i in range(m):
        J = J + float((X[i]*theta-y[i])**2)
    return J/(2*m)

def gradientDescent(X, y, theta, alpha, num_iters):
    m = len(y)
    num_iters = 1500
    J_history = np.zeros(num_iters)
    for i in range(num_iters):
        S =X.T * (X * theta - np.mat(y).T) / m
        theta = theta - alpha * S;
        J_history[i] = computeCost(X,y,theta)
    return theta

if __name__=="__main__":
    theta = np.mat([[0],[0]])
    iterations = 1500
    alpha = 0.01
    iterations = 1500
    path = "C:\Users\wing\Documents\MATLAB\ex1\ex1data1.txt"
    
    x,y = readfile(path)# 小写的X不是矩阵,是list,大写的X是矩阵。
    X = np.mat(x)
    J = computeCost(X, y, theta)
    theta = gradientDescent(X, y, theta, alpha, iterations)
    dataplot(X[:,1],theta,y)


输出的图有点小,就这样吧。

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