Statistics Papers

Document Type

Journal Article

Date of this Version

4-2011

Publication Source

IEEE Transactions on Signal Processing

Volume

59

Issue

4

Start Page

1569

Last Page

1585

DOI

10.1109/TSP.2010.2102756

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 lineardynamical system (SLDS) and the switching vector autoregressive (VAR) process. Our Bayesiannonparametric 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 orswitching 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.

Keywords

Bayes methods, autoregressive processes, inference mechanisms, linear systems, nonparametric statistics, sampling methods, target tracking, time-varying systems, Bayesian nonparametric inference, IBOVESPA stock index, complex dynamical phenomena, conditionally linear dynamical mode, dancing honey bee, hierarchical Dirichlet process, state sequence, switching dynamic linear model, target tracking sampling algorithm, vector autoregressive process, autoregressive processes, Bayesian methods, hidden Markov models, state-space methods, time series analysis, unsupervised learning

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Date Posted: 27 November 2017

This document has been peer reviewed.