Causal Discovery with Unobserved Confounding and nonGaussian Data
Abstract
We consider the problem of recovering causal structure from multivariate observational data. We assume that the data arise from a linear structural equation model (SEM) in which the idiosyncratic errors are allowed to be dependent in order to capture possible latent confounding. Each SEM can be represented by a graph where vertices represent observed variables, directed edges represent direct causal effects, and bidirected edges represent dependence among error terms. Specifically, we assume that the true model corresponds to a bowfree acyclic path diagram, i.e., a graph that has at most one edge between any pair of nodes and is acyclic in the directed part. We show that when the errors are nonGaussian, the exact causal structure encoded by such a graph, and not merely an equivalence class, can be consistently recovered from observational data. The Bowfree Acylic NonGaussian (BANG) method we propose for this purpose uses estimates of suitable moments, but, in contrast to previous results, does not require specifying the number of latent variables a priori. We illustrate the effectiveness of BANG in simulations and an application to an ecology data set.
 Publication:

arXiv eprints
 Pub Date:
 July 2020
 arXiv:
 arXiv:2007.11131
 Bibcode:
 2020arXiv200711131W
 Keywords:

 Statistics  Methodology