Joint Modeling of Multiple Related Time Series via the Beta Process

TL;DR

This paper introduces a Bayesian nonparametric method using the beta process to jointly model multiple related time series, discovering shared dynamical behaviors and inferring their structure directly from data.

Contribution

It presents a novel beta process prior framework for modeling shared behaviors in multiple time series, with efficient MCMC algorithms that do not require truncation.

Findings

Effective in synthetic datasets for discovering shared dynamics

Demonstrates promising results in unsupervised segmentation of motion capture data

Provides a scalable, nonparametric approach for related time series modeling

Abstract

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.