进行鲁棒的线性模型估计

╰+攻爆jí腚メ 2022-10-25 05:50 277阅读 0赞

### 目录 ###

*  1 参考
 *  2 代码

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80NTI4ODU1Nw_size_16_color_FFFFFF_t_70]输出：

Estimated coefficients (true, linear regression, RANSAC):
    82.1903908407869 [54.17236387] [82.08533159]

*  纯线性回归系数`54.17236387`
 *  去除干扰后的线性拟合系数`82.08533159`

去除后更接近真实的系数`82.1903908407869`

# 1 参考 #

https://mp.weixin.qq.com/s/QjBSf\_6Dus4ltnrQKYxRZA

# 2 代码 #

import numpy as np
    from matplotlib import pyplot as plt
    
    from sklearn import linear_model, datasets
    
    
    n_samples = 1000
    n_outliers = 50
    
    
    X, y, coef = datasets.make_regression(n_samples=n_samples, n_features=1,
                                          n_informative=1, noise=10,
                                          coef=True, random_state=0)
    
    # 添加异常数据
    np.random.seed(0)
    X[:n_outliers] = 3 + 0.5 * np.random.normal(size=(n_outliers, 1))
    y[:n_outliers] = -3 + 10 * np.random.normal(size=n_outliers)
    
    # 使用所有数据拟合直线
    lr = linear_model.LinearRegression()
    lr.fit(X, y)
    
    # 使用RANSAC算法拟合线性模型
    ransac = linear_model.RANSACRegressor()
    ransac.fit(X, y)
    inlier_mask = ransac.inlier_mask_
    outlier_mask = np.logical_not(inlier_mask)
    
    # 预测估计模型的数据(Predict data of estimated models)
    line_X = np.arange(X.min(), X.max())[:, np.newaxis]
    line_y = lr.predict(line_X)
    line_y_ransac = ransac.predict(line_X)
    
    # 比较估计系数
    print("Estimated coefficients (true, linear regression, RANSAC):")
    print(coef, lr.coef_, ransac.estimator_.coef_)
    
    lw = 2
    plt.scatter(X[inlier_mask], y[inlier_mask], color='yellowgreen', marker='.',
                label='Inliers')
    plt.scatter(X[outlier_mask], y[outlier_mask], color='gold', marker='.',
                label='Outliers')
    plt.plot(line_X, line_y, color='navy', linewidth=lw, label='Linear regressor')
    plt.plot(line_X, line_y_ransac, color='cornflowerblue', linewidth=lw,
             label='RANSAC regressor')
    plt.legend(loc='lower right')
    plt.xlabel("Input")
    plt.ylabel("Response")
    plt.show()

[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80NTI4ODU1Nw_size_16_color_FFFFFF_t_70]: /images/20221024/c85552a6850343bfba8ff4245f0d80b4.png