Massachusetts Institute of Technology Stochastic Systems Group Nonparametric Bayesian Learning of Switching Dynamical Processes Emily Fox, Erik Sudderth, Michael Jordan, and Alan Willsky Nonparametric Bayes Workshop 2008 Helsinki, Finland Laboratory for Information and Decision Systems
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Nonparametric Bayesian Learning of Switching Dynamical Processes
Laboratory for Information and Decision Systems. Nonparametric Bayesian Learning of Switching Dynamical Processes. Emily Fox, Erik Sudderth, Michael Jordan, and Alan Willsky Nonparametric Bayes Workshop 2008 Helsinki, Finland. Applications. = set of dynamic parameters. Priors on Modes. - PowerPoint PPT Presentation
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Massachusetts Institute of Technology
Stochastic Systems Group
Nonparametric Bayesian Learning of
Switching Dynamical Processes
Emily Fox, Erik Sudderth, Michael Jordan, and Alan Willsky
Nonparametric Bayes Workshop 2008
Helsinki, Finland
Laboratory for Information and Decision Systems
Page 2Massachusetts Institute of Technology
Applications
Page 3Massachusetts Institute of Technology
Priors on Modes
• Switching linear dynamical processes useful for describing nonlinear phenomena
• Goal: allow uncertainty in number of dynamical modes
Utilize hierarchical Dirichlet process (HDP) prior
Cluster based on dynamics
Switching Dynamical Processes
= set of dynamic parameters
Page 4Massachusetts Institute of Technology
Outline
• Background Switching dynamical processes: SLDS, VAR Prior on dynamic parameters Sticky HDP-HMM
• HDP-AR-HMM and HDP-SLDS
• Sampling Techniques
• Results Synthetic IBOVESPA stock index Dancing honey bee
Page 5Massachusetts Institute of Technology
Linear Dynamical Systems
• State space LTI model:
• Vector autoregressive (VAR) process:
Page 6Massachusetts Institute of Technology
Linear Dynamical Systems
• State space LTI model:
State space models
VAR processes
• Vector autoregressive (VAR) process:
Page 7Massachusetts Institute of Technology
Switching Dynamical Systems
• Switching linear dynamical system (SLDS):
• Switching VAR process:
Page 8Massachusetts Institute of Technology
Prior on Dynamic Parameters
Group all observations assigned to mode k
Define the following mode-specific matrices
Results in K decoupled linear regression problems
Rewrite VAR process in matrix form:
Place matrix-normal inverse Wishart prior on:
Page 9Massachusetts Institute of Technology
Sticky HDP-HMM
• Dirichlet process (DP): Mode space of unbounded size Model complexity adapts to
observations
• Hierarchical: Ties mode transition distributions Shared sparsity