Markov switching processes, such as hidden Markov models (HMMs) and switching linear dynamical systems (SLDSs), are often used to describe rich classes of dynamical phenomena. They describe complex temporal behavior via repeated returns to a set of simpler models: imagine, for example, a person alternating between walking, running and jumping behaviors, or a stock index switching between regimes of high and low volatility.
Traditional modeling approaches for Markov switching processes typically assume a fixed, pre-specified number of dynamical models. Here, in contrast, we discuss Bayesian nonparametric approaches that define priors on an unbounded number of potential Markov models by employing stochastic processes including the beta and Dirichlet process. These methods allow the data to define the complexity of inferred classes of models, while permitting efficient computational algorithms for inference.
Interleaved throughout the talk are results from various applications including analysis of the NIST speaker diarization database and human motion capture videos.