Doubly Outlier-Robust Online Infinite Hidden Markov Model

arXiv cs.LG / 4/17/2026

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Key Points

The paper introduces a robust online update rule for the infinite Hidden Markov Model (iHMM) to handle streaming data that includes outliers and where the model may be misspecified.
It uses posterior influence functions (PIF) from generalized Bayesian inference to define robustness, and proves conditions that ensure the online iHMM has bounded PIF.
Making the update robust necessarily causes an adaptation lag when regimes switch, which the authors explicitly account for in the method design.
The proposed approach, Batched Robust iHMM (BR-iHMM), adds two tunable parameters to balance adaptivity versus robustness.
Experiments on limit order book data, hourly electricity demand, and synthetic high-dimensional systems show up to a 67% reduction in one-step-ahead forecasting error compared with other online Bayesian methods, while also emphasizing interpretability and practical online learning.

Abstract

We derive a robust update rule for the online infinite hidden Markov model (iHMM) for when the streaming data contains outliers and the model is misspecified. Leveraging recent advances in generalised Bayesian inference, we define robustness via the posterior influence function (PIF), and provide conditions under which the online iHMM has bounded PIF. Imposing robustness inevitably induces an adaptation lag for regime switching. Our method, which is called Batched Robust iHMM (BR-iHMM), balances adaptivity and robustness with two additional tunable parameters. Across limit order book data, hourly electricity demand, and a synthetic high-dimensional linear system, BR-iHMM reduces one-step-ahead forecasting error by up to 67% relative to competing online Bayesian methods. Together with theoretical guarantees of bounded PIF, our results highlight the practicality of our approach for both forecasting and interpretable online learning.