# A Predictive View on Streaming Hidden Markov Models

arXiv: https://arxiv.org/abs/2604.09208 · HTML: https://mlsanity.com/paper/2604.09208/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 25 references that are in the map.
- First posted on arXiv 10 Apr 2026.

## Builds on (most cited first, 9 of 9)

- [Rao-Blackwellised Particle Filtering for Dynamic Bayesian Networks](https://mlsanity.com/paper/1301.3853/) (2013)
- [Martingale posterior distributions](https://mlsanity.com/paper/2103.15671/) (2021)
- [Variational Gaussian Process State-Space Models](https://mlsanity.com/paper/1406.4905/) (2014)
- [Outlier-robust Kalman Filtering through Generalised Bayes](https://mlsanity.com/paper/2405.05646/) (2024)
- [Robust and Scalable Bayesian Online Changepoint Detection](https://mlsanity.com/paper/2302.04759/) (2023)
- [Robust and Conjugate Gaussian Process Regression](https://mlsanity.com/paper/2311.00463/) (2023)
- [On recursive Bayesian predictive distributions](https://mlsanity.com/paper/1508.07448/) (2015)
- [A unifying framework for generalised Bayesian online learning in non-stationary environments](https://mlsanity.com/paper/2411.10153/) (2024)
- [Martingale Posterior Neural Networks for Fast Sequential Decision Making](https://mlsanity.com/paper/2506.11898/) (2025)

## Built on by (most cited first, 1 of 1)

- [How Wrong Can a Good Predictor Be? Diverging Updates with Vanishing Predictive KL](https://mlsanity.com/paper/2609.11132/) (2026)

## Abstract (arXiv)

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.