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交叉验证（Cross-Validation）

PublishedJuly 24, 2026Document7 pages

Contents

留出法回顾 (The Hold-out Approach)
概率工具箱：三件集中不等式 (Probability Toolkit)
Markov 不等式 (Markov's Inequality)
Chebyshev 不等式 (Chebyshev's Inequality)
Chernoff 界 (Chernoff Bound)
用 Chernoff 界估计真误差 (Estimating True Error via Chernoff)
留出集为何「昂贵」(Why the Hold-out is Expensive)
k 折交叉验证 (k-Fold Cross-Validation)
用交叉验证选超参：决策树深度 10 vs 15
实践要点：k 取值、并行、运行时与可分析性

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