机器学习--岭回归（RidgeRegression）

机器学习–岭回归模型（RidgeRegression） 基本概念

RidgeRegression 通过对系数的大小施加惩罚来解决普通最小二乘法的一些问题。岭系数最小化的是带罚项的残差平方和，优化目标为：
m i n w ∥ w T x − y ∥ 2 2 + α ∥ w ∥ 2 2 \mathop{min}\limits_{w}\Vert w^Tx-y\Vert_2^2+\alpha\Vert w\Vert_2^2 wmin​∥wTx−y∥22​+α∥w∥22​
其中， α ≥ 0 \alpha \geq 0 α≥0 是控制系数收缩量的复杂性参数： α \alpha α 的值越大，收缩量越大，模型对共线性的鲁棒性也更强。

案例

# coding=utf-8
from sklearn import  datasets
from sklearn.linear_model import Ridge
from sklearn.metrics import mean_squared_error, r2_score
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler
import matplotlib.pyplot as plt
import numpy as np

if __name__ == '__main__':

    """
        线性回归最小化目标是：
            min_w ||Xw - y||_2^2 + alpha * ||w||_2^2
    """

    all_data = datasets.load_diabetes()

    x_train, x_test, y_train, y_test =train_test_split(all_data.data, all_data.target, test_size=0.3)

    model = Ridge()

    x_train = x_train[:, 3].reshape(-1, 1)
    x_test = x_test[:, 3].reshape(-1, 1)


    model.fit(x_train, y_train)

    prediction = model.predict(x_test)

    print(f"w = {model.coef_}")
    print(f"w_0 = {model.intercept_}")

    print(f"default score = {model.score(x_test, y_test)}")

    print(f"mean squared error = {mean_squared_error(y_test, prediction)}")

    print(f"r2 score = {r2_score(y_test, prediction)}")

    # Plot outputs
    print(f"x_test.shape = {x_test.shape}, y_test.shape = {y_test.shape}")
    plt.scatter(x_test, y_test, marker='v')
    plt.plot(x_test, prediction, color="blue", linewidth=3)

    plt.xticks(())
    plt.yticks(())

    plt.show()