Regime-Arrival Uncertainty in Generalization Bounds under Distribution Shift
For machine learning practitioners dealing with distribution shifts in financial or other regime-switching environments, this work provides a theoretical decomposition of generalization risk but is limited by the inability to forecast regime composition.
The paper proposes a framework to quantify extra risk from regime composition mismatch under Markov-switching distribution shifts, deriving an exact decomposition and extending bounds to beta-mixing data. On 25 years of global equity indices, the framework shows that the training-only estimator lacks significant correlation with the realized generalization gap, indicating that regime arrival cannot be forecasted.
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.