Learning Temporal Causal Graphs for Relational Time-Series Analysis

Abstract

Identifying causality in multivariate time-series data is a topic or significant interest due to its many applications in fields as diverse as neuroscience, economics, climate science, and microbiology to name a few. In many applications, one is presented with multiple multivariate time-series rather than a single one. For instance, climate and meteorological data are collected at a variety of different location on the globe, with different instruments and measurement protocols; gene expression microarray data are collected for different species, under different conditions, and by different labs. Moreover, one can usually identify relationships between these different time-series, such as time-series being collected at neighboring locations in the case of climate data, or microarray experiments being conducted on the same species, or under the same conditions. These relationships define a “relational graph” among the different time-series where related time-series are connected by an edge. Given such relational time-series data, one faces the question of how to infer the causal structure for each time-series in manner that is more flexible than requiring a common causal graph for all time-series, while, at the same time, avoiding the brittleness due to data scarcity if one were to independently learn a different causal structure for each time-series. At a first approximation, the