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.

翻译：从观测数据中学习因果结构是一个基础性问题，但在变量数量较大时面临着重要计算挑战。在线性结构方程模型（SEMs）背景下，本文聚焦于从逆协方差矩阵中学习因果结构。所提出的方法称为ICID（基于逆协方差矩阵的独立保持分解法），该方法基于一种矩阵分解模型的连续优化，该模型保留了逆协方差矩阵的非零模式。通过理论和实证证据，我们证明ICID在已知噪声方差假设下能够高效识别目标有向无环图（DAG）。此外，当噪声方差不等时，ICID在噪声方差有界误设情况下表现出稳健性。所提方法具有低复杂度，这反映在实验中的时间效率上，并且还引入了一种新颖的正则化方案，在与最先进算法的比较中，该方案在模拟fMRI数据（Smith et al., 2011）上产生了高精度的解。