从 RANSAC 回归中提取系数

Posted 2023-03-12

【中文标题】从 RANSAC 回归中提取系数

【英文标题】：Extracting coefficients from RANSAC regression

【发布时间】：2022-01-18 13:08:01

【问题描述】：

我的代码 sn-p 取自 here。我没有做的是从预测数据中提取参数。即对于三次函数，我想知道 ax^3 + bx^2 + cx + d 方程中的 a、b、c 和 d。这如何在管道中完成，尤其是对于 RANSAC 估计器？

from matplotlib import pyplot as plt
import numpy as np

from sklearn.linear_model import (
    LinearRegression,
    TheilSenRegressor,
    RANSACRegressor,
    HuberRegressor,
)
from sklearn.metrics import mean_squared_error
from sklearn.preprocessing import PolynomialFeatures
from sklearn.pipeline import make_pipeline

np.random.seed(42)

X = np.random.normal(size=400)
y = np.sin(X)
# Make sure that it X is 2D
X = X[:, np.newaxis]

X_test = np.random.normal(size=200)
y_test = np.sin(X_test)
X_test = X_test[:, np.newaxis]

y_errors = y.copy()
y_errors[::3] = 3

X_errors = X.copy()
X_errors[::3] = 3

y_errors_large = y.copy()
y_errors_large[::3] = 10

X_errors_large = X.copy()
X_errors_large[::3] = 10

estimators = [
    ("OLS", LinearRegression()),
    ("Theil-Sen", TheilSenRegressor(random_state=42)),
    ("RANSAC", RANSACRegressor(random_state=42)),
    ("HuberRegressor", HuberRegressor()),
]
colors = 
    "OLS": "turquoise",
    "Theil-Sen": "gold",
    "RANSAC": "lightgreen",
    "HuberRegressor": "black",

linestyle = "OLS": "-", "Theil-Sen": "-.", "RANSAC": "--", "HuberRegressor": "--"
lw = 3

x_plot = np.linspace(X.min(), X.max())
for title, this_X, this_y in [
    ("Modeling Errors Only", X, y),
    ("Corrupt X, Small Deviants", X_errors, y),
    ("Corrupt y, Small Deviants", X, y_errors),
    ("Corrupt X, Large Deviants", X_errors_large, y),
    ("Corrupt y, Large Deviants", X, y_errors_large),
]:
    plt.figure(figsize=(5, 4))
    plt.plot(this_X[:, 0], this_y, "b+")

    for name, estimator in estimators:
        model = make_pipeline(PolynomialFeatures(3), estimator)
        model.fit(this_X, this_y)
        mse = mean_squared_error(model.predict(X_test), y_test)
        y_plot = model.predict(x_plot[:, np.newaxis])
        plt.plot(
            x_plot,
            y_plot,
            color=colors[name],
            linestyle=linestyle[name],
            linewidth=lw,
            label="%s: error = %.3f" % (name, mse),
        )

    legend_title = "Error of Mean\nAbsolute Deviation\nto Non-corrupt Data"
    legend = plt.legend(
        loc="upper right", frameon=False, title=legend_title, prop=dict(size="x-small")
    )
    plt.xlim(-4, 10.2)
    plt.ylim(-2, 10.2)
    plt.title(title)
plt.show()

【参考方案1】：

在我看来，在安装管道之后，您可能需要在第二个 for 循环中插入类似于以下 sn-p 的内容：

if name == 'RANSAC':
    print(model.named_steps['ransacregressor'].estimator_.coef_)
    print(model.named_steps['ransacregressor'].estimator_.intercept_)

确实，根据documentation：

估计器_：对象

最佳拟合模型（base_estimator 对象的副本）。

因此，您需要在您需要的管道步骤中输入（named_steps['step_name'] 是一种方法），然后访问estimator_ 的学习系数。