RegimeUnfold: Continual Regime-Space Learning for Deep Hidden Markov Process Forecasting

Deep hidden Markov process forecasting aims to predict future observations while explicitly identifying the latent regimes governing their dynamics. Existing approaches typically combine deep learning with Hidden Markov Models (HMMs) or their variants, seeking to retain the strong nonlinear predictive capability of deep models while preserving explicit latent regime representations. However, these methods generally operate over a fixed regime set, making their performance sensitive to a prespecified regime-space size and limiting adaptation after deployment. To address this limitation, we propose RegimeUnfold, a continual regime-space learning framework with offline regime discovery and online regime evolution for deep hidden Markov process forecasting. During the offline stage, RegimeUnfold jointly infers discrete regime assignments and learns predictive dynamics while progressively constructing and refining the regime space without predefining its size. During the online stage, it performs hard regime decoding and uses predictive-insufficiency and structural-novelty evidence to retain applicable regimes, update drifting regimes, or expand the regime space under stability constraints. Experiments on five synthetic and four real-world datasets demonstrate accurate forecasting, reliable regime inference, and effective adaptation to evolving predictive dynamics.