Causal Discovery for Linear Non-Gaussian Models with Disjoint Cycles

TL;DR

This paper introduces a novel method for learning causal structures with disjoint cycles in linear non-Gaussian models, using polynomial relations among moments and cycle decorrelation techniques, enabling efficient causal discovery.

Contribution

It characterizes when two graphs define the same model and proposes a consistent, efficient algorithm for learning disjoint-cycle causal structures.

Findings

Identifies conditions for graph equivalence in non-Gaussian models.

Uses polynomial relations among moments to locate source cycles.

Develops a cycle decorrelation strategy for causal inference.

Abstract

The paradigm of linear structural equation modeling readily allows one to incorporate causal feedback loops in the model specification. These appear as directed cycles in the common graphical representation of the models. However, the presence of cycles entails difficulties such as the fact that models need no longer be characterized by conditional independence relations. As a result, learning cyclic causal structures remains a challenging problem. In this paper, we offer new insights on this problem in the context of linear non-Gaussian models. First, we precisely characterize when two directed graphs determine the same linear non-Gaussian model. Next, we take up a setting of cycle-disjoint graphs, for which we are able to show that simple quadratic and cubic polynomial relations among low-order moments of a non-Gaussian distribution allow one to locate source cycles. Complementing this with a strategy of decorrelating cycles and multivariate regression allows one to infer a block-topological order among the directed cycles, which leads to a {consistent and computationally efficient algorithm} for learning causal structures with disjoint cycles.