Nonparametric Bayesian Identification of Jump Systems with Sparse Dependencies

Abstract Many nonlinear dynamical phenomena can be effectively modeled by a system that switches among a set of conditionally linear dynamical modes. We consider two such Markov jump linear systems: the switching linear dynamical system (SLDS) and the switching vector autoregressive (S-VAR) process. In this paper, we present a nonparametric Bayesian approach to identifying an unknown number of persistent, smooth dynamical modes by utilizing a hierarchical Dirichlet process prior.We additionally employ automatic relevance determination to infer a sparse set of dynamic dependencies. The utility and flexibility of our models are demonstrated on synthetic data and a set of honey bee dances.

[1]  René Vidal,et al.  Realization theory of stochastic jump-Markov linear systems , 2007, 2007 46th IEEE Conference on Decision and Control.

[2]  Vladimir Pavlovic,et al.  Learning Switching Linear Models of Human Motion , 2000, NIPS.

[3]  Kevin P. Murphy,et al.  Modeling changing dependency structure in multivariate time series , 2007, ICML '07.

[4]  Carlos M. Carvalho,et al.  Simulation-based sequential analysis of Markov switching stochastic volatility models , 2007, Comput. Stat. Data Anal..

[5]  Michael I. Jordan,et al.  Hierarchical Dirichlet Processes , 2006 .

[6]  M. West,et al.  Bayesian forecasting and dynamic models , 1989 .

[7]  V. Jilkov,et al.  Survey of maneuvering target tracking. Part V. Multiple-model methods , 2005, IEEE Transactions on Aerospace and Electronic Systems.

[8]  Matthew J. Beal Variational algorithms for approximate Bayesian inference , 2003 .

[9]  James M. Rehg,et al.  Learning and Inferring Motion Patterns using Parametric Segmental Switching Linear Dynamic Systems , 2008, International Journal of Computer Vision.

[10]  Zacharias Psaradakis,et al.  Joint Determination of the State Dimension and Autoregressive Order for Models with Markov Regime Switching , 2006 .

[11]  René Vidal,et al.  Identification of Hybrid Systems: A Tutorial , 2007, Eur. J. Control.

[12]  H. Ishwaran,et al.  Exact and approximate sum representations for the Dirichlet process , 2002 .

[13]  Carl E. Rasmussen,et al.  Factorial Hidden Markov Models , 1997 .

[14]  Michael I. Jordan,et al.  An HDP-HMM for systems with state persistence , 2008, ICML '08.

[15]  S. Sastry,et al.  An algebraic geometric approach to the identification of a class of linear hybrid systems , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).