Learning Large Causal Structures from Inverse Covariance Matrix via Sparse Matrix Decomposition

TL;DR

This paper introduces ICID, a novel method for learning large causal structures from inverse covariance matrices using sparse matrix decomposition, which is efficient, robust, and accurate in identifying DAGs in linear SEMs.

Contribution

The paper proposes ICID, a continuous optimization approach that preserves inverse covariance patterns for causal discovery, with theoretical guarantees and empirical robustness.

Findings

ICID efficiently identifies DAGs assuming known noise variances.

ICID is robust to bounded noise variance misspecification.

ICID outperforms state-of-the-art algorithms on simulated fMRI data.

Abstract

Learning causal structures from observational data is a fundamental problem facing important computational challenges when the number of variables is large. In the context of linear structural equation models (SEMs), this paper focuses on learning causal structures from the inverse covariance matrix. The proposed method, called ICID for Independence-preserving Decomposition from Inverse Covariance matrix, is based on continuous optimization of a matrix decomposition model that preserves the nonzero patterns of the inverse covariance matrix. Through theoretical and empirical evidences, we show that ICID efficiently identifies the sought directed acyclic graph (DAG) assuming the knowledge of noise variances. Moreover, ICID is shown empirically to be robust under bounded misspecification of noise variances in the case where the noise variances are non-equal. The proposed method enjoys a low complexity, as reflected by its time efficiency in the experiments, and also enables a novel regularization scheme that yields highly accurate solutions on the Simulated fMRI data (Smith et al., 2011) in comparison with state-of-the-art algorithms.