  We propose a Bayesian nonparametric approach to the problem of jointly
modeling multiple related time series. Our approach is based on the discovery
of a set of latent, shared dynamical behaviors. Using a beta process prior, the
size of the set and the sharing pattern are both inferred from data. We develop
efficient Markov chain Monte Carlo methods based on the Indian buffet process
representation of the predictive distribution of the beta process, without
relying on a truncated model. In particular, our approach uses the sum-product
algorithm to efficiently compute Metropolis-Hastings acceptance probabilities,
and explores new dynamical behaviors via birth and death proposals. We examine
the benefits of our proposed feature-based model on several synthetic datasets,
and also demonstrate promising results on unsupervised segmentation of visual
motion capture data.
