Causal Discovery via Simultaneous DAG Recovery Using the Angles Space of Directional Dependence Measures

Abstract

Most causal discovery algorithms utilizing a Directed Acyclic Graph (DAG) framework execute sequentially (e.g. constraint-based models) or iteratively (e.g. score-based or functional causal models). In contrast, we develop a new method, Angles-based Directional Dependence (ADD), that executes over the entire DAG space simultaneously, based on only two matrix estimations. We apply dual orderings on any (positive definite) directional dependence measure for all pairwise relationships, identify statistically significant directional dependence in the (positive definite) angles space, and then enforce acyclicality to make proper causal interpretations. Potential benefits of the approach include increased coherence, due to simultaneous edge-calling within a positive definite space, increased power, due to the ability to use any directional dependence measure and thus, opportunistically adapt to different or varying data conditions, and increased speed and scalability, due to the need for only two matrix estimations, and two (fast) simulations to define empirical confidence bounds under independence (regardless of the size of the DAG space). We conduct a preliminary empirical study evaluating direct adjacency under nonlinear, asymmetric, heavy-tailed data conditions. The promising results indicate applications to feature selection in quantitative finance, and justify and encourage a more extensive follow-up study to benchmark against competing algorithms to more fully test the above-mentioned potential benefits of ADD.