梯度提升正则化#

不同正则化策略对梯度提升的影响说明。该示例取自 Hastie 等人 2009 年的论文 [1]。

使用的损失函数是二项偏差。通过收缩进行正则化（learning_rate < 1.0）可以显著提高性能。结合收缩，随机梯度提升（subsample < 1.0）可以通过 bagging 减少方差来生成更准确的模型。没有收缩的子采样通常表现不佳。另一种减少方差的策略是通过对特征进行子采样，类似于随机森林中的随机分割（通过 max_features 参数）。

# Author: Peter Prettenhofer <[email protected]>
#
# License: BSD 3 clause

import matplotlib.pyplot as plt
import numpy as np

from sklearn import datasets, ensemble
from sklearn.metrics import log_loss
from sklearn.model_selection import train_test_split

X, y = datasets.make_hastie_10_2(n_samples=4000, random_state=1)

# map labels from {-1, 1} to {0, 1}
labels, y = np.unique(y, return_inverse=True)

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.8, random_state=0)

original_params = {
    "n_estimators": 400,
    "max_leaf_nodes": 4,
    "max_depth": None,
    "random_state": 2,
    "min_samples_split": 5,
}

plt.figure()

for label, color, setting in [
    ("No shrinkage", "orange", {"learning_rate": 1.0, "subsample": 1.0}),
    ("learning_rate=0.2", "turquoise", {"learning_rate": 0.2, "subsample": 1.0}),
    ("subsample=0.5", "blue", {"learning_rate": 1.0, "subsample": 0.5}),
    (
        "learning_rate=0.2, subsample=0.5",
        "gray",
        {"learning_rate": 0.2, "subsample": 0.5},
    ),
    (
        "learning_rate=0.2, max_features=2",
        "magenta",
        {"learning_rate": 0.2, "max_features": 2},
    ),
]:
    params = dict(original_params)
    params.update(setting)

    clf = ensemble.GradientBoostingClassifier(**params)
    clf.fit(X_train, y_train)

    # compute test set deviance
    test_deviance = np.zeros((params["n_estimators"],), dtype=np.float64)

    for i, y_proba in enumerate(clf.staged_predict_proba(X_test)):
        test_deviance[i] = 2 * log_loss(y_test, y_proba[:, 1])

    plt.plot(
        (np.arange(test_deviance.shape[0]) + 1)[::5],
        test_deviance[::5],
        "-",
        color=color,
        label=label,
    )

plt.legend(loc="upper right")
plt.xlabel("Boosting Iterations")
plt.ylabel("Test Set Deviance")

plt.show()

脚本总运行时间：（0 分 9.261 秒）