吴恩达《机器学习》第一次作业——多变量线性回归

旧城等待， 2022-02-13 09:43 185阅读 0赞

看这里 [https://github.com/fengdu78/Coursera-ML-AndrewNg-Notes/tree/master/code][https_github.com_fengdu78_Coursera-ML-AndrewNg-Notes_tree_master_code]  
这是一位大神整理的作业代码。我也就是照葫芦画瓢，慢慢来吧。

import numpy as np
    import pandas as pd
    import matplotlib.pyplot as plt
    path = 'ex1data2.txt'   #相对路径
    data = pd.read_csv(path, header=None, names=['Size', 'Bedrooms', 'Price'])
    
    '''记录目标变量的均值和和差值'''
    meanPrice = data['Price'].mean()
    stdPrice = data['Price'].std()
    
    '''操作数据，以便后续处理'''
    data = (data-data.mean())/data.std()        #特征缩放
    data.insert(0, 'Ones', 1)
    cols = data.shape[1]
    X = data.iloc[:, 0:cols-1]
    y = data.iloc[:, cols-1:cols]
    X = np.matrix(X.values)     #特征变量
    y = np.matrix(y.values)     #目标变量
    theta = np.matrix(np.array([0, 0, 0]))
    #————————————————————————————————————————————————————
    #cost function
    def computeCost(X, y, theta):
        '''损失函数'''
        inner = np.power((X*theta.T - y), 2)
        return np.sum(inner) / (2 * len(X))
    
    alpha = 0.01
    iters = 1000
    
    def gradientDescent(X, y, theta, alpha, iters):
        '''梯度下降算法'''
        temp = np.matrix(np.zeros(theta.shape))
        cost = np.zeros(iters)
    
        for i in range(iters):
            inner = X * theta.T - y
    
            for j in range(temp.shape[1]):
                term = np.multiply(inner, X[:, j])
                temp[0, j] = theta[0, j] - (alpha/len(X))*np.sum(term)
            theta = temp    #更新theta
            cost[i] = computeCost(X, y, theta)
        return theta, cost
    
    '''梯度下降'''
    theta, cost = gradientDescent(X, y, theta, alpha, iters)
    
    
    '''测试集'''
    testpath = 'testdata2.txt'
    testdata = pd.read_csv(testpath, header=None, names=['Size', 'Bedrooms'])
    testdata = (testdata-testdata.mean())/testdata.std()        #特征缩放
    testdata.insert(0, 'Ones', 1)
    Td = np.matrix(testdata)
    def h_theta_x(theta, Td):
        return Td*theta.T
    d1 = h_theta_x(theta, X)*stdPrice + meanPrice    #逆特征缩放
    d1 = d1.astype(np.int32)      #将矩阵元素类型转换为整数
    print('通过梯度下降')
    print(d1)
    
    '''绘图-cost function的收敛'''
    fig, ax = plt.subplots(figsize=(12,8))
    ax.plot(np.arange(iters), cost, 'r')
    ax.set_xlabel('Iterations')
    ax.set_ylabel('Cost')
    ax.set_title('Error vs. Training Epoch')
    plt.show()
    
    
    #—————————————————————————————————————————————
    def normalEqn(X, y):
        '''正规方程'''
        theta = np.linalg.inv(X.T@X)@X.T@y
        return theta
    
    nEtheta = normalEqn(X, y)
    
    '''测试集'''
    testpath = 'testdata2.txt'
    testdata = pd.read_csv(testpath, header=None, names=['Size', 'Bedrooms'])
    testdata = (testdata-testdata.mean())/testdata.std()        #特征均一化
    testdata.insert(0, 'Ones', 1)
    Td = np.matrix(testdata)
    def h_theta_x(theta, Td):
        return Td*theta.T
    d2 = h_theta_x(theta, X)*stdPrice + meanPrice    #逆特征缩放
    d2 = d2.astype(np.int32)      #将矩阵元素类型转换为整数
    print('通过正规方程')
    print(d2)
    
    print(theta - nEtheta)		#用梯度下降和正规方程求得的参数是不同的

[https_github.com_fengdu78_Coursera-ML-AndrewNg-Notes_tree_master_code]: https://github.com/fengdu78/Coursera-ML-AndrewNg-Notes/tree/master/code