题目：给定数据集dataSet，每一行代表一组数据记录,每组数据记录中，第一个值为房屋面积（单位：平方英尺），第二个值为房屋中的房间数，第三个值为房价（单位：千美元），试用梯度下降法，构造损失函数，在函数gradientDescent中实现房价price关于房屋面积area和房间数rooms的线性回归，返回值为线性方程𝑝𝑟𝑖𝑐𝑒=𝜃0+𝜃1∗𝑎𝑟𝑒𝑎+𝜃2∗𝑟𝑜𝑜𝑚𝑠中系数𝜃𝑖(𝑖=0,1,2)的列表。

%matplotlib inlineimport numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from numpy import genfromtxt
dataPath = r"./Input/data1.csv"
dataSet = pd.read_csv(dataPath,header=None)
print(dataSet)
price = []
rooms = []
area = []
for data in range(0,len(dataSet)):area.append(dataSet[0][data])rooms.append(dataSet[1][data])price.append(dataSet[2][data])
print(area)

执行结果：

def gradientDescent(rooms, price, area):epochs = 500alpha = 0.00000001theta_gradient = [0,0,0]const = [1,1,1,1,1]theta = [1,2,1]loss = []for i in range(epochs):theta0 = np.dot(theta[0],const)theta1 = np.dot(theta[1],area)theat2 = np.dot(theta[2],rooms) predict_tmp = np.add(theta0,theta1)predict = np.add(predict_tmp,theat2) loss_ = predict - pricetheta_gradient[0] = (theta_gradient[0] + np.dot(const,loss_.transpose()))/5theta_gradient[1] = (theta_gradient[1] + np.dot(area,loss_.transpose()))/5theta_gradient[2] = (theta_gradient[2] + np.dot(rooms,loss_.transpose()))/5loss_t = np.sum(np.divide(np.square(loss_),2))/5if i%50==0:print("loss_t:",loss_t)loss.append(loss_t)theta[0] = theta[0] - alpha * theta_gradient[0]theta[1] = theta[1] - alpha * theta_gradient[1]theta[2] = theta[2] - alpha * theta_gradient[2]plt.plot(loss,c='b')plt.show()return theta

def demo_GD():theta_list = gradientDescent(rooms, price, area)
demo_GD()

j结果展示：