Learning Bi-clustered Vector Autoregressive Models

Abstract

Vector Auto-regressive (VAR) models are useful for analyzing temporal dependencies among multivariate time series, known as Granger causality. There exist methods for learning sparse VAR models, leading directly to causal networks among the variables of interest. Another useful type of analysis comes from clustering methods, which summarize multiple time series by putting them into groups. We develop a methodology that integrates both types of analyses, motivated by the intuition that Granger causal relations in real-world time series may exhibit some clustering structure, in which case the estimation of both should be carried out together. Our methodology combines sparse learning and a nonparametric bi-clustered prior over the VAR model, conducting full Bayesian inference via blocked Gibbs sampling. Experiments on simulated and real data demonstrate improvements in both model estimation and clustering quality over standard alternatives, and in particular biologically more meaningful clusters in a T-cell activation gene expression time series dataset than those by other methods.