Causal Discovery for Linear Non-Gaussian Models with Disjoint Cycles

2025-07-14

AI Summary

This paper addresses the structure learning problem for linear non-Gaussian causal models containing disjoint directed cycles. To overcome the challenge that cyclic structures invalidate conditional independence and render traditional methods unidentifiable, we derive identifiability conditions based on polynomial relationships among low-order moments (second- and third-order). These conditions enable cycle localization via moment constraints specific to source cycles, and facilitate inference of inter-cycle block topological order through decorrelation followed by multivariate regression. We propose the first consistent, computationally efficient (polynomial-time) causal discovery algorithm for such cyclic linear non-Gaussian models, thereby extending existing linear non-Gaussian methods—previously restricted to acyclic assumptions—to the cyclic setting. Extensive experiments demonstrate that our algorithm significantly outperforms baseline approaches in both accuracy and runtime efficiency.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Characterizing equivalence in linear non-Gaussian cyclic models
• Identifying source cycles using polynomial moment relations
• Learning cycle-disjoint causal structures efficiently

Innovation

• Characterizes linear non-Gaussian model equivalence
• Uses polynomial relations to locate source cycles
• Decorrelates cycles with multivariate regression