Model learning for switching linear systems with autonomous mode transitions

We present a novel method for model learning in hybrid discrete-continuous systems. The approach uses approximate expectation-maximization to learn the maximum- likelihood parameters of a switching linear system. The approach extends previous work by 1) considering autonomous mode transitions, where the discrete transitions are conditioned on the continuous state, and 2) learning the effects of control inputs on the system. We evaluate the approach in simulation.

[1]  Philip N. Sabes,et al.  Modeling Sensorimotor Learning with Linear Dynamical Systems , 2006, Neural Computation.

[2]  Malik Ghallab,et al.  Robot introspection through learned hidden Markov models , 2006, Artif. Intell..

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

[4]  Sheila A. McIlraith,et al.  Monitoring a Complez Physical System using a Hybrid Dynamic Bayes Net , 2002, UAI.

[5]  Y. Bar-Shalom,et al.  The interacting multiple model algorithm for systems with Markovian switching coefficientsY. Bar-Shalom , 1988 .

[6]  Geoffrey E. Hinton,et al.  Parameter estimation for linear dynamical systems , 1996 .

[7]  James M. Rehg,et al.  Learning and inference in parametric switching linear dynamic systems , 2005, Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1.

[8]  Masahiro Ono,et al.  Robust, Optimal Predictive Control of Jump Markov Linear Systems Using Particles , 2007, HSCC.

[9]  Brian C. Williams,et al.  Mode Estimation of Probabilistic Hybrid Systems , 2002, HSCC.

[10]  Inseok Hwang,et al.  Inference Methods for Autonomous Stochastic Linear Hybrid Systems , 2004, HSCC.

[11]  Brian C. Williams,et al.  Combining Stochastic and Greedy Search in Hybrid Estimation , 2005, AAAI.

[12]  Geoffrey E. Hinton,et al.  A View of the Em Algorithm that Justifies Incremental, Sparse, and other Variants , 1998, Learning in Graphical Models.

[13]  R. Shumway,et al.  AN APPROACH TO TIME SERIES SMOOTHING AND FORECASTING USING THE EM ALGORITHM , 1982 .

[14]  T. Minka Expectation-Maximization as lower bound maximization , 1998 .

[15]  Nando de Freitas,et al.  Rao-Blackwellised Particle Filtering for Dynamic Bayesian Networks , 2000, UAI.

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

[17]  El Kebir Boukas,et al.  Robust stochastic stabilization of discrete-time linear systems with Markovian jumping parameters , 1999 .

[18]  Melvin Michael Henry,et al.  Model-based Estimation of Probabilistic Hybrid Automata , 2002 .

[19]  Shuonan Dong,et al.  Unsupervised learning and recognition of physical activity plans , 2007 .

[20]  W. L. Koning,et al.  Discrete-time Markovian jump linear systems , 1993 .

[21]  Alessandro N. Vargas,et al.  Constrained model predictive control of jump linear systems with noise and non-observed Markov state , 2006, 2006 American Control Conference.

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