[机器学习]多变量线性回归代码实现

dataset

2104,3,399900
1600,3,329900 
2400,3,369000
1416,2,232000 
3000,4,539900 
1985,4,299900 
1534,3,314900 
1427,3,198999 
1380,3,212000 
1494,3,242500 
1940,4,239999 
2000,3,347000 
1890,3,329999 
4478,5,699900
1268,3,259900 
2300,4,449900 
1320,2,299900 
1236,3,199900 
2609,4,499998 
3031,4,599000 
1767,3,252900 
1888,2,255000 
1604,3,242900 
1962,4,259900 
3898,3,573900 
1100,3,249900 
1458,3,464500 
2526,3,469000 
2200,3,475000 
2637,3,299900

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

data = pd.read_csv("ex1data2.txt",names = ["size","bedrooms","price"])
print(data.head())

def normalize_feature(data):
    return (data - data.mean())/data.std()

data = normalize_feature(data)

print(data.head())

plt.scatter(data["size"],data["price"],label = "size")

plt.scatter(data["bedrooms"],data["price"],label = "bedrooms")

plt.legend()


data.insert(0,"ones",1)

X = data.iloc[:,0:-1]
y = data.iloc[:,-1]

X = X.values
y = y.values

print(X.shape)

y = y.reshape(30,1)
print(y.shape)

def costFunction(X, y, theta):
    inner = np.power(X @ theta - y, 2)
    return np.sum(inner) / (2 * len(X))

theta = np.zeros((3,1))

cost_init = costFunction(X,y,theta)
print(cost_init)

# 梯度下降
def gradientDescent(X, y, theta, alpha, iters,isprint=False):
    costs = []
    m = len(X)  # 获取样本数量

    for i in range(iters):
        predictions = X @ theta
        errors = predictions - y
        gradient = X.T @ errors / m
        theta -= alpha * gradient
        cost = costFunction(X, y, theta)
        costs.append(cost)

        if i % 100 == 0:
            if isprint:
                print(f"Cost after iteration {i}: {cost}")

    return theta, costs

# 不同alpha下的效果
candidate_alpha = [0.0003,0.003,0.03,0.0001,0.001,0.01]
iters = 2000

fig,ax = plt.subplots()

for alpha in candidate_alpha:
    _,costs = gradientDescent(X,y,theta,alpha,iters)
    ax.plot(np.arange(iters),costs,label = "alpha:{}".format(alpha))

ax.set(xlabel = "iters",ylabel = "cost",title = "cost vs iters")

plt.legend()

plt.show()

运行结果: