Effective Split-Merge Monte Carlo Methods for Nonparametric Models of Sequential Data

Applications of Bayesian nonparametric methods require learning and inference algorithms which efficiently explore models of unbounded complexity. We develop new Markov chain Monte Carlo methods for the beta process hidden Markov model (BP-HMM), enabling discovery of shared activity patterns in large video and motion capture databases. By introducing split-merge moves based on sequential allocation, we allow large global changes in the shared feature structure. We also develop data-driven reversible jump moves which more reliably discover rare or unique behaviors. Our proposals apply to any choice of conjugate likelihood for observed data, and we show success with multinomial, Gaussian, and autoregressive emission models. Together, these innovations allow tractable analysis of hundreds of time series, where previous inference required clever initialization and at least ten thousand burn-in iterations for just six sequences.