鲁棒线性估计器拟合#
这里使用 3 阶多项式拟合正弦函数,用于接近零的值。
在不同情况下演示了鲁棒拟合
没有测量误差,只有建模误差(用多项式拟合正弦曲线)
X 中的测量误差
y 中的测量误差
未损坏新数据的平均绝对偏差用于判断预测的质量。
我们可以看到
RANSAC 对于 y 方向上的强异常值很有用
TheilSen 适用于 X 和 y 方向上的小异常值,但有一个断点,超过该断点,它的性能比 OLS 差。
HuberRegressor 的分数可能无法直接与 TheilSen 和 RANSAC 进行比较,因为它不会尝试完全过滤异常值,而是会降低其影响。
import numpy as np
from matplotlib import pyplot as plt
from sklearn.linear_model import (
HuberRegressor,
LinearRegression,
RANSACRegressor,
TheilSenRegressor,
)
from sklearn.metrics import mean_squared_error
from sklearn.pipeline import make_pipeline
from sklearn.preprocessing import PolynomialFeatures
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()
脚本总运行时间:(0 分钟 1.960 秒)
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