线性回归曲线和过拟合判断

import matplotlib.pyplot as plt
import mglearn
from scipy import sparse
import numpy as np
import matplotlib as mt
import pandas as pd
from IPython.display import display
from sklearn.linear_model import LinearRegression
from sklearn.model_selection import train_test_split

#wave数据集
#wave数据集只有一个特征
#公式为y=w[0]x[0]+b
#w为斜率，b为轴偏移或截距，分别在sklearn中使用 coef_[0],  intercept_表示
mglearn.plots.plot_linear_regression_wave()
plt.show()

#boston数据集
#boston数据集有506个样本，105个特征
X, y = mglearn.datasets.load_extended_boston()
X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=0)
lr = LinearRegression().fit(X_train, y_train)
print("Training set score: {:.2f}".format(lr.score(X_train, y_train)))
print("Test set score: {:.2f}".format(lr.score(X_test, y_test)))

结果：

w[0]: 0.393906 b: -0.031804

plot_linear_regression_wave源码

import numpy as np
import matplotlib.pyplot as plt

from sklearn.linear_model import LinearRegression
from sklearn.model_selection import train_test_split
from .datasets import make_wave
from .plot_helpers import cm2


def plot_linear_regression_wave():
    X, y = make_wave(n_samples=60)
    X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=42)

    line = np.linspace(-3, 3, 100).reshape(-1, 1)

    lr = LinearRegression().fit(X_train, y_train)
    print("w[0]: %f  b: %f" % (lr.coef_[0], lr.intercept_))

    plt.figure(figsize=(8, 8))
    plt.plot(line, lr.predict(line))
    plt.plot(X, y, 'o', c=cm2(0))
    ax = plt.gca()
    ax.spines['left'].set_position('center')
    ax.spines['right'].set_color('none')
    ax.spines['bottom'].set_position('center')
    ax.spines['top'].set_color('none')
    ax.set_ylim(-3, 3)
    #ax.set_xlabel("Feature")
    #ax.set_ylabel("Target")
    ax.legend(["model", "training data"], loc="best")
    ax.grid(True)
    ax.set_aspect('equal')

结果2：

Training set score: 0.95
Test set score: 0.61

可以看出出现了过拟合，这是因为波士顿房价的各个特征的差距非常大，不适合使用最小二乘法，需要使用“正则化”来做显式约束，使用岭回归避免过拟合。

Ridge岭回归用到L2正则化。

Lasso回归用到L1正则，还可以使用ElasticNet弹性网络回归。