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.

翻译：我们针对流式数据包含异常值且模型设定错误的情况，推导出在线无限隐马尔可夫模型（iHMM）的鲁棒更新规则。利用广义贝叶斯推断的最新进展，我们通过后验影响函数（PIF）定义鲁棒性，并给出在线iHMM具有有界PIF的条件。施加鲁棒性不可避免地会导致状态切换的自适应延迟。我们的方法称为批处理鲁棒iHMM（BR-iHMM），通过两个额外可调参数在自适应性与鲁棒性之间取得平衡。在限价订单簿数据、每小时电力需求数据以及合成高维线性系统上，BR-iHMM将一步预测误差相较于竞争性在线贝叶斯方法降低高达67%。结合有界PIF的理论保证，我们的结果突显了该方法在预测和可解释在线学习中的实用性。