Bayesian Inference of Recurrent Switching Linear Dynamical Systems with Higher-Order Dependence

Abstract

Many complicated dynamical events may be broken down into simpler pieces and efficiently described by a system that shifts among a variety of conditionally dynamical modes. Building on switching linear dynamical systems, we develop a new model that extends the switching linear dynamical systems for better discovering these dynamical modes. In the proposed model, the linear dynamics of latent variables can be described by a higher-order vector autoregressive process, which makes it feasible to evaluate the higher-order dependency relationships in the dynamics. In addition, the transition of switching states is determined by a stick-breaking logistic regression, overcoming the limitation of a restricted geometric state duration and recovering the symmetric dependency between the switching states and the latent variables from asymmetric relationships. Furthermore, logistic regression evidence potentials can appear as conditionally Gaussian potentials by utilizing the Pólya-gamma augmentation strategy. Filtering and smoothing algorithms and Bayesian inference for parameter learning in the proposed model are presented. The utility and versatility of the proposed model are demonstrated on synthetic data and public functional magnetic resonance imaging data. Our model improves the current methods for learning the switching linear dynamical modes, which will facilitate the identification and assessment of the dynamics of complex systems.