RED-HDP-HMM: Observation-Dependent Durations for Bayesian Nonparametric Sequential Models

The Hierarchical Dirichlet Process Hidden Markov Model (HDP-HMM) is a Bayesian nonparametric extension of the classical Hidden Markov Model, well-suited for learning from (spatio-)temporal data. To relax the restrictive geometric assumption on state durations, the HDP Hidden Semi-Markov Model was introduced. However, both models assume stationary state durations, which limits their expressive power. In this work, we extend the HDP-HMM framework by incorporating recurrent explicit duration modeling, resulting in a more general and flexible model: the Recurrent Explicit Duration HDP-HMM (RED-HDP-HMM). We propose a Gibbs sampling method for efficient inference in this model. Empirical results on both synthetic and real-world segmentation tasks demonstrate that RED-HDP-HMM consistently outperforms the disentangled sticky HDP-HMM and the standard sticky HDP-HMM. We provide theoretical results on truncation error, expressiveness relative to HDP-HSMM. Empirically, RED-HDP-HMM yields consistent gains: a 2.6 percentage point accuracy increase on honey bee waggle dance data (89.9\% vs.~87.3\%) and 4–10 percentage point improvements on neural segmentation tasks over sticky and disentangled sticky HDP-HMM baselines.