Doubly Outlier-Robust Online Infinite Hidden Markov Model

2026-04-15

AI Summary

This work addresses the limited robustness of online infinite hidden Markov models (iHMMs) in streaming data settings, where outliers and model misspecification can severely degrade performance. To mitigate these issues, the authors propose an online learning approach grounded in generalized Bayesian inference. The method employs update rules with bounded posterior influence functions, integrated with a batching mechanism to simultaneously suppress outlier interference and maintain rapid responsiveness to state transitions. Notably, this is the first study to provide theoretical guarantees of bounded posterior influence for online iHMMs. A dual-parameter scheme is introduced to flexibly balance robustness and adaptability. Empirical evaluations on limit order book data, electricity demand records, and high-dimensional synthetic sequences demonstrate that the proposed method reduces one-step-ahead prediction error by up to 67% compared to existing online Bayesian approaches.

Technology Category

• Machine Learning: Online Learning & Bandits
• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Economics, Online Markets and Human Computation: Humans versus LLMs for data annotation and labeling
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

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.

Problem

• outlier-robust
• online learning
• infinite hidden Markov model
• model misspecification
• streaming data

Innovation

• robust Bayesian inference
• posterior influence function
• online infinite HMM
• adaptation-robustness tradeoff
• streaming data with outliers