Joint modeling of multiple time series via the beta process with application to motion capture segmentation

Abstract

We propose a Bayesian nonparametric approach to the problem of jointly modeling multiple related time series. Our model discovers a latent set of dynamical behaviors shared among the sequences, and segments each time series into regions defined by a subset of these behaviors. Using a beta process prior, the size of the behavior set and the sharing pattern are both inferred from data. We develop Markov chain Monte Carlo (MCMC) methods based on the Indian buffet process representation of the predictive distribution of the beta process. Our MCMC inference algorithm efficiently adds and removes behaviors via novel split-merge moves as well as data-driven birth and death proposals, avoiding the need to consider a truncated model. We demonstrate promising results on unsupervised segmentation of human motion capture data.

Published in at http://dx.doi.org/10.1214/14-AOAS742 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org). arXiv admin note: text overlap with arXiv:1111.4226

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• Bayesian Nonparametric Inference of Switching Linear Dynamical Systems
• Joint modeling of multiple time series via the beta process with application to motion capture segmentation
• A Split-Merge MCMC Algorithm for the Hierarchical Dirichlet Process
• A sticky HDP-HMM with application to speaker diarization
• Discovering shared and individual latent structure in multiple time series

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