Doubly Outlier-Robust Online Infinite Hidden Markov Model

TL;DR

This paper introduces BR-iHMM, a robust online infinite hidden Markov model that effectively handles outliers and model misspecification, improving forecasting accuracy across diverse datasets.

Contribution

It develops a new robust update rule for online iHMMs using generalized Bayesian inference, balancing robustness and adaptivity with tunable parameters.

Findings

BR-iHMM reduces forecasting error by up to 67% compared to existing methods.

The approach provides theoretical guarantees of bounded influence function.

It demonstrates effectiveness on financial, energy, and synthetic data.

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.