Causal Discovery for Linear Non-Gaussian Models with Disjoint Cycles

Mathias Drton, Marina Garrote-López, Niko Nikov, Elina Robeva, Y. Samuel Wang

Keywords: causal discovery; directed graphical models; linear non-Gaussian models; cyclic graphical models; cyclic causal models

TL;DR: We describe equivalent graphs for linear non-Gaussian models, and we give an algorithm to discover a cycle-disjoint graph from data.

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.

Code Link: https://github.com/ysamwang/disjointCycles

Readers: auai.org/UAI/2025/Conference, auai.org/UAI/2025/Conference/Area_Chairs, auai.org/UAI/2025/Conference/Reviewers, auai.org/UAI/2025/Conference/Submission514/Authors, auai.org/UAI/2025/Conference/Submission514/Reproducibility_Reviewers

Submission Number: 514