A Wiener Causality Defined by Divergence

Abstract

Discovering causal relationships is a fundamental task in investigating the dynamics of complex systems (Pearl in Stat Surv 3:96–146, 2009). Traditional approaches like Granger causality or transfer entropy fail to capture all the interdependence of the statistic moments, which might lead to wrong causal conclusions. In the previous papers (Chen et al. in 25th international conference, ICONIP 2018, Siem Reap, Cambodia, proceedings, Part II, 2018), the authors proposed a novel definition of Wiener causality for measuring the intervene between time series based on relative entropy, providing an integrated description of statistic causal intervene. In this work, we show that relative entropy is a special case of an existing more general divergence estimation. We argue that any Bregman divergences can be used for detecting the causal relations and in theory remedies the information dropout problem. We discuss the benefits of various choices of divergence functions on causal inferring and the quality of the obtained causal models. As a byproduct, we also obtain the robustness analysis and elucidate that RE causality achieves a faster convergence rate among BD causalities. To substantiate our claims, we provide experimental evidence on how BD causalities improve detection accuracy.