We introduce DeRegiME -- Deep Regime Mixture of Experts -- a direct multi-horizon probabilistic forecaster that separates latent uncertainty regimes from the underlying signal and softly assigns each forecast location to learned recurring regimes using a sparse variational Gaussian process (GP) whose nonstationary regime-mixing kernel and Student-t likelihood combine per-regime sub-kernels and noise processes via a shared gate. This yields a single sparse-GP posterior, not a mixture of GP experts. DeRegiME addresses a key limitation of neural forecasters: point forecasts discard residual uncertainty, and probabilistic heads -- whether single marginals, uninterpreted mixtures, quantile sets, or diffusion samples -- rarely expose the regime structure of the residual. Yet distribution shift in noisy heteroskedastic time series may be abrupt, gradual, or horizon-dependent and often appears in residual uncertainty rather than the conditional mean. DeRegiME yields an interpretable mean-residual-noise decomposition with a direct-sum feature-space representation that anchors regimes as clusters of residual similarity whose transitions surface as implicit changepoints. The effective number of regimes is pruned by the stick-breaking gate. We prove kernel validity and predictive-density propriety, and across ten benchmarks and three encoder grids DeRegiME improves negative log predictive density (NLPD) by 20.3% over the strongest encoder-matched baseline, a DeepAR/GluonTS-style dynamic Student-t head, with parallel gains on CRPS (3.0%) and MSE (4.7%). Improvements are consistent across all datasets, which span abrupt, gradual, and seasonal shifts.
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.
Accurate long-term forecasting in complex systems is frequently compromised by dataset-level distribution shifts, where diverse underlying behavioral modes and evolving system states drive the dynamic multivariate time-series. While existing methods predominantly focus on local temporal shifts, they fail to explicitly model the global structural challenge where datasets are composites of distinct operational regimes. In this paper, we propose NEST, a specialized framework designed to model and recompose these evolving structures through a two-phase dense MoE architecture. NEST first facilitates structural specialization by partitioning the dataset into distinct operational regimes through unsupervised clustering in a principled moment-entropy space. We introduce a regime-oriented router mechanism that generates initial expert weights based on temporal content, subsequently refined through geometric modulation to regime centroids. Crucially, rather than acting as monolithic predictors, individual experts function as specialized kernels that capture regime-specific dynamics by evolving unique variate-attention patterns. Extensive evaluations on diverse benchmarks, including heterogeneous network traffic and physical phenomena, demonstrate that NEST consistently achieves state-of-the-art performance. Our code and datasets are available at https://github.com/Aaralshin/NEST
Non-stationary time series forecasting is challenged by evolving distribution shifts that static models struggle to capture. While Mixture-of-Experts (MoE) architectures offer a promising paradigm for decoupling complex drift patterns, existing approaches are limited by fixed expert pools and memoryless routing, hampering their ability to adapt to abrupt regime shifts. To address this, we propose Dynamic TMoE, a framework that unifies architectural evolution with temporal continuity during learning phase. By detecting distribution shifts via Maximum Mean Discrepancy (MMD), we dynamically instantiate heterogeneous experts and prune redundant ones to optimize capacity. Additionally, a temporal memory router leverages recurrent states and an anomaly repository to ensure stable, context-aware expert selection without requiring test-time updates. Experiments on nine benchmarks demonstrate state-of-the-art performance, reducing MSE by 10.4% and MAE by 7.8%. Code is available at https://github.com/andone-07/Dynamic-TMoE.