A Variational inference method for Switching Linear Dynamic Systems

This paper aims to present a structured variational inference algorithm for switching linear dynamical systems (SLDSs) which was initially introduced by Pavlovic and Rehg [14]. Starting with the need for the variational approach, we proceed to the derivation of the generic (model-independent) variational update formulas which are obtained under the mean field assumption. This leads us to the derivation of an approximate variational inference algorithm for an SLDS. The details of deriving the SLDS-specific variational update equations are presented.

[1]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[2]  L. Rabiner,et al.  An introduction to hidden Markov models , 1986, IEEE ASSP Magazine.

[3]  R. Shumway,et al.  Dynamic linear models with switching , 1991 .

[4]  Mari Ostendorf,et al.  A Dynamical System Approach to Continuous Speech Recognition , 1991, HLT.

[5]  Yaakov Bar-Shalom,et al.  Estimation and Tracking: Principles, Techniques, and Software , 1993 .

[6]  J. R. Rohlicek,et al.  ML estimation of a stochastic linear system with the EM algorithm and its application to speech recognition , 1993, IEEE Trans. Speech Audio Process..

[7]  Chang‐Jin Kim,et al.  Dynamic linear models with Markov-switching , 1994 .

[8]  Mari Ostendorf,et al.  From HMM's to segment models: a unified view of stochastic modeling for speech recognition , 1996, IEEE Trans. Speech Audio Process..

[9]  Christoph Bregler,et al.  Learning and recognizing human dynamics in video sequences , 1997, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[10]  Vladimir Pavlovic,et al.  A dynamic Bayesian network approach to figure tracking using learned dynamic models , 1999, Proceedings of the Seventh IEEE International Conference on Computer Vision.

[11]  Zoubin Ghahramani,et al.  A Unifying Review of Linear Gaussian Models , 1999, Neural Computation.

[12]  Gautam Biswas,et al.  Bayesian Fault Detection and Diagnosis in Dynamic Systems , 2000, AAAI/IAAI.

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

[14]  Vladimir Pavlovic,et al.  Impact of dynamic model learning on classification of human motion , 2000, Proceedings IEEE Conference on Computer Vision and Pattern Recognition. CVPR 2000 (Cat. No.PR00662).

[15]  Michael Isard,et al.  Learning and Classification of Complex Dynamics , 2000, IEEE Trans. Pattern Anal. Mach. Intell..

[16]  Christophe Andrieu,et al.  Iterative algorithms for state estimation of jump Markov linear systems , 2001, IEEE Trans. Signal Process..

[17]  Arnaud Doucet,et al.  Particle filters for state estimation of jump Markov linear systems , 2001, IEEE Trans. Signal Process..

[18]  Terrence J. Sejnowski,et al.  Variational Learning for Switching State-Space Models , 2001 .

[19]  Uri Lerner,et al.  Inference in Hybrid Networks: Theoretical Limits and Practical Algorithms , 2001, UAI.

[20]  Harry Shum,et al.  Motion texture: a two-level statistical model for character motion synthesis , 2002, ACM Trans. Graph..

[21]  Tom Heskes,et al.  Hierarchical Visualization of Time-Series Data Using Switching Linear Dynamical Systems , 2003, IEEE Trans. Pattern Anal. Mach. Intell..

[22]  Mark J. F. Gales,et al.  Rao-Blackwellised Gibbs sampling for switching linear dynamical systems , 2004, 2004 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[23]  James M. Rehg,et al.  Data-Driven MCMC for Learning and Inference in Switching Linear Dynamic Systems , 2005, AAAI.