Note

Go to the end to download the full example code. or to run this example in your browser via Binder

梯度提升袋外估计#

袋外（OOB）估计可以作为一种有用的启发式方法来估计“最佳”提升迭代次数。 OOB估计与交叉验证估计几乎相同，但可以即时计算，无需重复模型拟合。 OOB估计仅适用于随机梯度提升（即 subsample < 1.0 ），这些估计是基于未包含在自助样本中的示例（即所谓的袋外示例）的损失改进得出的。 OOB估计是对真实测试损失的悲观估计，但对于少量树来说仍然是一个相当好的近似。图中显示了负OOB改进的累积和作为提升迭代函数的变化情况。正如你所见，它在前一百次迭代中跟踪测试损失，但随后以悲观的方式偏离。图中还显示了3折交叉验证的性能，通常它能更好地估计测试损失，但计算要求更高。

Accuracy: 0.6860

# 作者：scikit-learn 开发者
# SPDX-License-Identifier: BSD-3-Clause

import matplotlib.pyplot as plt
import numpy as np
from scipy.special import expit

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

# 生成数据（改编自G. Ridgeway的gbm示例）
n_samples = 1000
random_state = np.random.RandomState(13)
x1 = random_state.uniform(size=n_samples)
x2 = random_state.uniform(size=n_samples)
x3 = random_state.randint(0, 4, size=n_samples)

p = expit(np.sin(3 * x1) - 4 * x2 + x3)
y = random_state.binomial(1, p, size=n_samples)

X = np.c_[x1, x2, x3]

X = X.astype(np.float32)
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.5, random_state=9)

# 使用袋外估计拟合分类器
params = {
    "n_estimators": 1200,
    "max_depth": 3,
    "subsample": 0.5,
    "learning_rate": 0.01,
    "min_samples_leaf": 1,
    "random_state": 3,
}
clf = ensemble.GradientBoostingClassifier(**params)

clf.fit(X_train, y_train)
acc = clf.score(X_test, y_test)
print("Accuracy: {:.4f}".format(acc))

n_estimators = params["n_estimators"]
x = np.arange(n_estimators) + 1


def heldout_score(clf, X_test, y_test):
    """计算 ``X_test`` 和 ``y_test`` 的偏差分数。"""
    score = np.zeros((n_estimators,), dtype=np.float64)
    for i, y_proba in enumerate(clf.staged_predict_proba(X_test)):
        score[i] = 2 * log_loss(y_test, y_proba[:, 1])
    return score


def cv_estimate(n_splits=None):
    cv = KFold(n_splits=n_splits)
    cv_clf = ensemble.GradientBoostingClassifier(**params)
    val_scores = np.zeros((n_estimators,), dtype=np.float64)
    for train, test in cv.split(X_train, y_train):
        cv_clf.fit(X_train[train], y_train[train])
        val_scores += heldout_score(cv_clf, X_train[test], y_train[test])
    val_scores /= n_splits
    return val_scores


# 使用交叉验证估计最佳 n_estimator
cv_score = cv_estimate(3)

# 计算测试数据的最佳 n_estimator
test_score = heldout_score(clf, X_test, y_test)

# 负的oob改进累积和
cumsum = -np.cumsum(clf.oob_improvement_)

# 根据OOB的最小损失
oob_best_iter = x[np.argmin(cumsum)]

# 根据测试的最小损失（归一化使得第一个损失为0）
test_score -= test_score[0]
test_best_iter = x[np.argmin(test_score)]

# 根据交叉验证的最小损失（归一化使得第一个损失为0）
cv_score -= cv_score[0]
cv_best_iter = x[np.argmin(cv_score)]

# 三条曲线的颜色酿造
oob_color = list(map(lambda x: x / 256.0, (190, 174, 212)))
test_color = list(map(lambda x: x / 256.0, (127, 201, 127)))
cv_color = list(map(lambda x: x / 256.0, (253, 192, 134)))

# 三条曲线的线型
oob_line = "dashed"
test_line = "solid"
cv_line = "dashdot"

# 绘制最佳迭代的曲线和垂直线
plt.figure(figsize=(8, 4.8))
plt.plot(x, cumsum, label="OOB loss", color=oob_color, linestyle=oob_line)
plt.plot(x, test_score, label="Test loss", color=test_color, linestyle=test_line)
plt.plot(x, cv_score, label="CV loss", color=cv_color, linestyle=cv_line)
plt.axvline(x=oob_best_iter, color=oob_color, linestyle=oob_line)
plt.axvline(x=test_best_iter, color=test_color, linestyle=test_line)
plt.axvline(x=cv_best_iter, color=cv_color, linestyle=cv_line)

# 在xticks上添加三条垂直线
xticks = plt.xticks()
xticks_pos = np.array(
    xticks[0].tolist() + [oob_best_iter, cv_best_iter, test_best_iter]
)
xticks_label = np.array(list(map(lambda t: int(t), xticks[0])) + ["OOB", "CV", "Test"])
ind = np.argsort(xticks_pos)
xticks_pos = xticks_pos[ind]
xticks_label = xticks_label[ind]
plt.xticks(xticks_pos, xticks_label, rotation=90)

plt.legend(loc="upper center")
plt.ylabel("normalized loss")
plt.xlabel("number of iterations")

plt.show()