Bayesian Nonparametric Methods for Learning Markov Switching Processes

Markov switching processes, such as the hidden Markov model (HMM) and switching linear dynamical system (SLDS), are often used to describe rich dynamical phenomena. They describe complex behavior via repeated returns to a set of simpler models: imagine a person alternating between walking, running, and jumping behaviors, or a stock index switching between regimes of high and low volatility. Classical approaches to identification and estimation of these models assume a fixed, prespecified number of dynamical models. We instead examine Bayesian nonparametric approaches that define a prior on Markov switching processes with an unbounded number of potential model parameters (i.e., Markov modes). By leveraging stochastic processes such as the beta and Dirichlet process (DP), these methods allow the data to drive the complexity of the learned model, while still permitting efficient inference algorithms. They also lead to generalizations that discover and model dynamical behaviors shared among multiple related time series. © 2010 IEEE.