Learning Time-Varying Graphs from Data with Few Causes

Abstract

We propose a novel method for learning time-varying graphs from time-series data by leveraging techniques from directed acyclic graph (DAG) learning. The unknown graphs are parameterized with a time-varying structural vector autoregression model (SVAR), which we view as a linear structural equation model (SEM) by unrolling the graph adjacency matrices over time into a DAG. We then learn the DAG to obtain the unknown graphs under the novel assumption that the data is generated by few causes that percolate in time as dictated by the SEM. Our method shows superior performance over state-of-the-art methods on synthetic data with few causes and yields meaningful graphs when applied to real-world temperature data from the USA and Switzerland.