A Predictive View on Streaming Hidden Markov Models

TL;DR

This paper introduces a predictive-first streaming inference framework for hidden Markov models that uses a beam search-like approximation to efficiently identify latent regimes with accurate predictions.

Contribution

It proposes a novel recursive, deterministic algorithm that approximates the full posterior predictive in streaming HMMs without EM or sampling, using a constrained projection approach.

Findings

Competitive performance against Online EM and Sequential Monte Carlo.

Efficient recursive algorithm with closed-form predictive updates.

Principled derivation of beam search for HMMs.

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.