Causal inference for multivariate stochastic process prediction

Abstract

Numerous real world systems of major interest are modeled as sets of analog continuous stochastic processes with delayed and varying causal relationships. Yet studying their dynamic becomes often difficult, as it involves sensing, understanding and predicting a system of inter-dependent random variables in a given context and over time. In the present work we develop systematic, rigorous and efficient framework to structurally characterize and forecast such systems in a flexible manner. In particular we use a graph method based on a maximum spanning tree approach, to capture the causal dependence structure based on directed information theory. To this end we address the sparsity problem in information causality estimation in general, and we propose a new method that identifies and eliminates redundant calculations. To forecast child nodes based on their inferred causal parents we use a linear model aiming to capture the closest approximation of functional relations. We further account for dependencies using causal conditional information by adding links that improve child nodes estimation. The result is a comprehensive and flexible approach to understanding and predicting large sets of inter-dependent narrowband processes, as we demonstrate on both synthetic and real datasets.