The Recurrent Sticky Hierarchical Dirichlet Process Hidden Markov Model

TL;DR

RS-HDP-HMM is developed, a more general model that outperforms disentangled sticky HDP-HMM, sticky HDP-HMM, and HDP-HMM in both synthetic and real data segmentation and develops a novel Gibbs sampling strategy for efficient inference in this model.

Abstract

The Hierarchical Dirichlet Process Hidden Markov Model (HDP-HMM) is a natural Bayesian nonparametric extension of the classical Hidden Markov Model for learning from (spatio-)temporal data. A sticky HDP-HMM has been proposed to strengthen the self-persistence probability in the HDP-HMM. Then, disentangled sticky HDP-HMM has been proposed to disentangle the strength of the self-persistence prior and transition prior. However, the sticky HDP-HMM assumes that the self-persistence probability is stationary, limiting its expressiveness. Here, we build on previous work on sticky HDP-HMM and disentangled sticky HDP-HMM, developing a more general model: the recurrent sticky HDP-HMM (RS-HDP-HMM). We develop a novel Gibbs sampling strategy for efficient inference in this model. We show that RS-HDP-HMM outperforms disentangled sticky HDP-HMM, sticky HDP-HMM, and HDP-HMM in both synthetic and real data segmentation.

Figures (12)

• Figure 1: Graphical models for sticky HDP-HMM (a) and disentangled sticky HDP-HMM (b) and recurrent sticky HDP-HMM (c)
• Figure 2: Trajectory of NASCAR $^{\circledR}$ used to test the models.
• Figure 3: Log-likelihood during models' fitting on NASCAR $^{\circledR}$ dataset. Our model obtains the highest likelihood scores. It presents a diverse range of likelihood scores within a single run. Additionally, we observe that the other models often converge to local optima. Furthermore, the RS-HDP-HMM model exhibits a considerably shorter burn-in time.
• Figure 4: Distribution of NASCAR$^{\circledR}$ log-likelihoods taken after 200 burn-in iterations. Our model attains the highest likelihood scores and generates the most coherent results. However, it is worth noting that it also demonstrates the greatest variability in likelihood within a single execution.
• Figure 5: Sample results of NASCAR $^{\circledR}$ segmentation. The color represents an assigned segment. Methods other than RS-HDP-HMM often fail to differentiate two "straight" states.