https://grdm.io/tags/hidden-markov-models/Recent content in Hidden-Markov-Models on Gerardo Duran-MartinHugoen-usFri, 10 Apr 2026 00:00:00 +0000https://grdm.io/articles/streaming-hmm2026/Fri, 10 Apr 2026 00:00:00 +0000https://grdm.io/articles/streaming-hmm2026/<h2 id="abstract">Abstract</h2> <p>We develop a predictive-first optimisation framework for streaming hidden Markov models. Unlike classical approaches that prioritise full posterior recovery under a fully specified generative model, we assume access to regime-specific predictive models whose parameters are learned online while maintaining a fixed transition prior over regimes. Our objective is to sequentially identify latent regimes while maintaining accurate step-ahead predictive distributions. Because the number of possible regime paths grows exponentially, exact filtering is infeasible. We therefore formulate streaming inference as a constrained projection problem in predictive-distribution space: under a fixed hypothesis budget, we approximate the full posterior predictive by the forward-KL optimal mixture supported on S paths. The solution is the renormalised top-S posterior-weighted mixture, providing a principled derivation of beam search for HMMs. The resulting algorithm is fully recursive and deterministic, performing beam-style truncation with closed-form predictive updates and requiring neither EM nor sampling. Empirical comparisons against Online EM and Sequential Monte Carlo under matched computational budgets demonstrate competitive prequential performance.</p>