嵌套式与非嵌套式交叉验证#

本示例比较了在鸢尾花数据集分类器上非嵌套式和嵌套式交叉验证策略。嵌套式交叉验证 (CV) 通常用于训练需要优化超参数的模型。嵌套式 CV 估计了基础模型及其（超）参数搜索的泛化误差。选择使非嵌套式 CV 最大化的参数会使模型偏向数据集，从而产生过于乐观的分数。

没有嵌套式 CV 的模型选择使用相同的数据来调整模型参数和评估模型性能。因此，信息可能会“泄露”到模型中并导致数据过拟合。这种影响的大小主要取决于数据集的大小和模型的稳定性。有关这些问题的分析，请参阅 Cawley 和 Talbot [1]。

为避免此问题，嵌套式 CV 有效地使用一系列训练/验证/测试集划分。在内循环中（此处由 GridSearchCV 执行），通过对每个训练集拟合模型来近似最大化分数，然后在验证集上选择（超）参数时直接最大化。在外循环中（此处在 cross_val_score 中），泛化误差通过对多个数据集划分的测试集分数进行平均来估计。

下面的示例使用带非线性核的支持向量分类器，通过网格搜索构建一个具有优化超参数的模型。我们通过比较非嵌套式和嵌套式 CV 策略的分数差异来评估它们的性能。

另请参阅

参考文献

Non-Nested and Nested Cross Validation on Iris Dataset

Average difference of 0.007581 with std. dev. of 0.007833.

# Authors: The scikit-learn developers
# SPDX-License-Identifier: BSD-3-Clause

import numpy as np
from matplotlib import pyplot as plt

from sklearn.datasets import load_iris
from sklearn.model_selection import GridSearchCV, KFold, cross_val_score
from sklearn.svm import SVC

# Number of random trials
NUM_TRIALS = 30

# Load the dataset
iris = load_iris()
X_iris = iris.data
y_iris = iris.target

# Set up possible values of parameters to optimize over
p_grid = {"C": [1, 10, 100], "gamma": [0.01, 0.1]}

# We will use a Support Vector Classifier with "rbf" kernel
svm = SVC(kernel="rbf")

# Arrays to store scores
non_nested_scores = np.zeros(NUM_TRIALS)
nested_scores = np.zeros(NUM_TRIALS)

# Loop for each trial
for i in range(NUM_TRIALS):
    # Choose cross-validation techniques for the inner and outer loops,
    # independently of the dataset.
    # E.g "GroupKFold", "LeaveOneOut", "LeaveOneGroupOut", etc.
    inner_cv = KFold(n_splits=4, shuffle=True, random_state=i)
    outer_cv = KFold(n_splits=4, shuffle=True, random_state=i)

    # Non_nested parameter search and scoring
    clf = GridSearchCV(estimator=svm, param_grid=p_grid, cv=outer_cv)
    clf.fit(X_iris, y_iris)
    non_nested_scores[i] = clf.best_score_

    # Nested CV with parameter optimization
    clf = GridSearchCV(estimator=svm, param_grid=p_grid, cv=inner_cv)
    nested_score = cross_val_score(clf, X=X_iris, y=y_iris, cv=outer_cv)
    nested_scores[i] = nested_score.mean()

score_difference = non_nested_scores - nested_scores

print(
    "Average difference of {:6f} with std. dev. of {:6f}.".format(
        score_difference.mean(), score_difference.std()
    )
)

# Plot scores on each trial for nested and non-nested CV
plt.figure()
plt.subplot(211)
(non_nested_scores_line,) = plt.plot(non_nested_scores, color="r")
(nested_line,) = plt.plot(nested_scores, color="b")
plt.ylabel("score", fontsize="14")
plt.legend(
    [non_nested_scores_line, nested_line],
    ["Non-Nested CV", "Nested CV"],
    bbox_to_anchor=(0, 0.4, 0.5, 0),
)
plt.title(
    "Non-Nested and Nested Cross Validation on Iris Dataset",
    x=0.5,
    y=1.1,
    fontsize="15",
)

# Plot bar chart of the difference.
plt.subplot(212)
difference_plot = plt.bar(range(NUM_TRIALS), score_difference)
plt.xlabel("Individual Trial #")
plt.legend(
    [difference_plot],
    ["Non-Nested CV - Nested CV Score"],
    bbox_to_anchor=(0, 1, 0.8, 0),
)
plt.ylabel("score difference", fontsize="14")

plt.show()

脚本总运行时间： (0 分钟 6.277 秒)

嵌套式与非嵌套式交叉验证#

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