Granger Causality Networks for Categorical Time Series: Convex Mixture Transition Distribution

• Activity Number: 600 - High-Dimensional Time Series and Applications in Social and Biological Sciences
• Type: Invited
• Date/Time: Thursday, August 3, 2017 : 8:30 AM to 10:20 AM
• Sponsor: WNAR
• Author(s): Alex Tank* and Ali Shojaie and Emily Fox
• Companies: University of Washington and University of Washington and University of Washington
• Keywords: time series ; categorical ; mixture transition distribution ; convex ; identifiability ; networks

Abstract

We develop a method for detecting Granger causality relationships in multivariate categorical time series data based on the mixture transition distribution (MTD) model. While the MTD model has been studied for 30 years the best inference procedures are plagued by many local modes, hampering extensions to higher dimensional series. In particular, current MTD formulations are nonconvex with many linear equality and inequality constraints. By utilizing a simple substitution trick we recast inference in the MTD model as a convex problem. The convex framework both allows us to add sparsifying convex penalties to select for Granger causality, scale inference to higher dimensions, and derive and enforce novel identifiability conditions. For optimization we develop a projected gradient algorithm. Through simulations we compare our convex MTD model to a categorical GLM for time series.