import numpy as np import pandas as pd

计算代价函数J(θ)

def computeCost(X, y, theta): m = len(y) J = np.sum((X.dot(theta) - y) ** 2) / (2 * m) return J

批量梯度下降

返回参数 θ 的值和每次迭代后代价函数的值，梯度下降公式参考编程要求梯度下降公式

def gradientDescent(X, y, theta, alpha, epoch): m = len(y) cost = np.zeros(epoch) # 初始化一个 ndarray ，包含每次 epoch 的cost for i in range(epoch): theta = theta - alpha / m * X.T.dot(X.dot(theta) - y) cost[i] = computeCost(X, y, theta) return theta, cost

读取数据

data = pd.read_csv('ex1data1.txt', header=None, names=['Population', 'Profit'])

特征缩放

data = (data - data.mean()) / data.std()

添加一列全为1的列，对应θ0

data.insert(0, 'Ones', 1)

将X和y分别赋值

X = data.iloc[:, :-1].values y = data.iloc[:, -1].values.reshape(-1, 1)

初始化theta

theta = np.zeros((2, 1))

设置alpha和epoch

alpha = 0.01 epoch = 1000

进行梯度下降

theta, cost = gradientDescent(X, y, theta, alpha, epoch)

计算代价函数的值

J = computeCost(X, y, theta) print(J)