A Predictive View on Streaming Hidden Markov Models
2026-04-10 • Machine Learning
Machine Learning
AI summaryⓘ
The authors propose a new method to track hidden changes (regimes) in data that arrives over time using hidden Markov models. Instead of trying to fully understand all possible scenarios, they focus on predicting the next steps accurately by keeping only the most promising sequences. To do this efficiently, they use a technique similar to beam search that limits complexity and updates predictions in a straightforward way without heavy computations. Their approach works recursively and performs well compared to existing online methods under similar computing limits.
hidden Markov modelsregime switchingonline learningbeam searchpredictive distributionsfilteringforward-KL divergencesequential inferencemixture modelsrecursive algorithms
Authors
Gerardo Duran-Martin
Abstract
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.