Bayesian sparse vector autoregressive switching models with application to human gesture phase segmentation

Abstract

We propose a sparse vector autoregressive (VAR) hidden semi-Markov model (HSMM) for modeling temporal and contemporaneous (e.g., spatial) dependencies in multivariate nonstationary time series. The HSMM’s generic state distribution is embedded in a special transition matrix structure, facilitating efficient likelihood evaluations and arbitrary approximation accuracy. To promote sparsity of the VAR coefficients, we deploy an ${\mathit{l}}_1$-ball projection prior, which combines differentiability with a positive probability of obtaining exact zeros, achieving variable selection within each switching state. This also facilitate posterior estimation via HMC. We further place nonlocal priors on the parameters of the HSMM dwell distribution improving the ability of Bayesian model selection to distinguish whether the data is better supported by the simpler hidden Markov model (HMM) or more flexible HSMM. Our proposed methodology is illustrated via an application to human gesture phase segmentation based on sensor data, where we successfully identify and characterize the periods of rest and active gesturing as well as the dynamical patterns involved in the gesture movements associated with each of these states.