Bayesian Nonparametric Inference of Switching Linear Dynamical Systems

TL;DR

This paper introduces a Bayesian nonparametric method for inferring switching linear dynamical systems, capable of automatically determining the number of modes and their dependencies, demonstrated on diverse real-world data.

Contribution

It develops a hierarchical Dirichlet process-based approach with automatic relevance determination for flexible, data-driven modeling of switching dynamical systems.

Findings

Successfully infers unknown number of modes

Learns sparse dynamic dependencies

Demonstrates effectiveness on real-world data

Abstract

Many complex dynamical phenomena can be effectively modeled by a system that switches among a set of conditionally linear dynamical modes. We consider two such models: the switching linear dynamical system (SLDS) and the switching vector autoregressive (VAR) process. Our Bayesian nonparametric approach utilizes a hierarchical Dirichlet process prior to learn an unknown number of persistent, smooth dynamical modes. We additionally employ automatic relevance determination to infer a sparse set of dynamic dependencies allowing us to learn SLDS with varying state dimension or switching VAR processes with varying autoregressive order. We develop a sampling algorithm that combines a truncated approximation to the Dirichlet process with efficient joint sampling of the mode and state sequences. The utility and flexibility of our model are demonstrated on synthetic data, sequences of dancing honey bees, the IBOVESPA stock index, and a maneuvering target tracking application.