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This paper introduces a framework for quantifying generalization risk in Markov-switching environments by decomposing regime mismatch from regime sensitivity. While the method effectively detects feature geometry during crises, it explicitly cannot forecast the temporal arrival of regime changes, limiting its utility as a predictive tool. The work provides a rigorous theoretical bound for models operating under distribution shifts, offering a more realistic risk assessment for non-stationary data.
Regime-Arrival Uncertainty in Generalization Bounds under Distribution Shift
arXiv:2606.02657v1 Announce Type: new Abstract: 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.
Abstract: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.
Machine Learning (cs.LG); Computational Finance (q-fin.CP); Statistical Finance (q-fin.ST)
I.2.6; G.3; I.5.1; F.2.2
arXiv:2606.02657 [cs.LG]
(or arXiv:2606.02657v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2606.02657 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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