提出新框架，量化分布转移中状态切换带来的泛化风险。
Regime-Arrival Uncertainty in Generalization Bounds under Distribution Shift
- 区分状态错配与状态敏感性，分解泛化误差
- 在马尔可夫切换数据下给出带谱隙修正的有效样本量边界
- 适用于金融时序等罕见状态切换场景，不用于预测未来状态
标准泛化界假设训练与部署分布一致或静态，未考虑状态切换环境（如平静与危机状态比例不同）。本文提出一种泛化框架，量化马尔可夫切换分布偏移下因状态组成不匹配带来的额外风险。通过精确分解，分离出状态错配与状态敏感性；将边界扩展至beta-混合数据，使用考虑谱隙的修正有效样本量；并在合成数据及25年全球股权指数上证明了极小值下界。所提惩罚项为事后实现的泛化差距，而仅基于训练数据的估计器无显著相关性：危机的特征几何可被检测，但时间到达模式无法捕捉。因此该框架并非预测工具，未来状态组成预测仍是罕见状态切换中的开放问题。
原文摘要 · Abstract (English)
The standard generalization bounds assume that the training and deployment distributions are the same, or are static, and don't consider regime switching environments where the ratio of calm vs crisis states is different. This paper proposes a framework that generalizes regime-aware models by quantifying the extra risk due to regime composition mismatch, when distribution shifts are Markov-switching. We obtain an exact decomposition, separating regime mismatch from regime sensitivity; we extend the bound to beta-mixing data using the effective sample size corrected for the spectral gap; and we show a minimax lower bound for synthetic data and on 25 years of global equity indices. The proposed penalty is an ex post realized generalization gap, whereas the training-only estimator does not show significant correlation: the feature geometry of crises can be detected, but not the temporal arrival. Thus, the framework is not a forecast machine. Forecasting the composition of the future regime is an open question in the rare cases of regime change.
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