Learning causal structures from observational data is a fundamental yet highly complex problem when the number of variables is large. In this paper, we start from linear structural equation models (SEMs) and investigate ways of learning causal structures from the inverse covariance matrix. The proposed method, called $\mathcal{O}$-ICID (for {\it Independence-preserving} Decomposition from Oracle Inverse Covariance matrix), is based on continuous optimization of a type of matrix decomposition that preserves the nonzero patterns of the inverse covariance matrix. We show that $\mathcal{O}$-ICID provides an efficient way for identifying the true directed acyclic graph (DAG) under the knowledge of noise variances. With weaker prior information, the proposed method gives directed graph solutions that are useful for making more refined causal discovery. The proposed method enjoys a low complexity when the true DAG has bounded node degrees, as reflected by its time efficiency in experiments 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，当变量数量庞大时这一问题尤为复杂。本文以线性结构方程模型（SEMs）为起点，探究从逆协方差矩阵中学习因果结构的方法。所提出的方法名为$\mathcal{O}$-ICID（基于{\it 保持独立性}分解的逆协方差矩阵预言机），其核心是一种连续优化方法，旨在实现一种能保留逆协方差矩阵非零模式的矩阵分解。我们证明，在已知噪声方差的情况下，$\mathcal{O}$-ICID能够高效识别真实的有向无环图（DAG）。在先验信息较弱时，该方法可提供有助于进行更精细因果发现的有向图解。当真实DAG的节点度有界时，所提方法具有较低的计算复杂度，这一点在与当前最优算法的实验效率对比中得到了充分体现。