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
Traditional modeling approaches for Markov switching processes
typically assume a fixed, pre-specified number of dynamical models.
Here, in contrast, I develop Bayesian nonparametric approaches that
define priors on an unbounded number of potential Markov models. Using
stochastic processes including the beta and Dirichlet process, I
develop methods that allow the data to define the complexity of
inferred classes of models, while permitting efficient computational
algorithms for inference. The new methodology also has generalizations
for modeling and discovery of dynamic structure shared by multiple
related time series.
Interleaved throughout the talk are results from studies of the NIST
speaker diarization database, stochastic volatility of a stock index,
the dances of honeybees, and human motion capture videos.