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<p>Discovering causal relationships by recovering directed acyclic graphs (DAGs) from observed data is a challenging combinatorial problem. The presence of latent variables further complicates this task. In this paper, we propose a fast and accurate DAG recovery algorithm based on the Cholesky factorization of the data covariance matrix. Our method, Causal Discovery via Cholesky Factorization (CDCF), has a time complexity of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal {O}(p^3)\)</EquationSource> </InlineEquation> and is guaranteed to recover the true graph exactly under standard assumptions. On both synthetic and real-world datasets, CDCF significantly outperforms existing methods in speed and achieves state-of-the-art accuracy. Furthermore, under an equal error variances assumption, we extend CDCF to handle latent variables by incorporating a sparsity-encouraging optimization procedure, resulting in the CDCF<sup>+</sup> algorithm. Extensive numerical simulations demonstrate that CDCF<sup>+</sup> successfully recovers the ground-truth graph in most cases and surpasses the performance of current baselines.</p>

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Recovering linear causal models with latent variables via Cholesky factorization of covariance matrix

  • 期刊论文

  • 发表日期：

    2026年4月24日

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  • Yunfeng Cai,
  • Xu Li,
  • Mingming Sun,
  • Ping Li

摘要

Discovering causal relationships by recovering directed acyclic graphs (DAGs) from observed data is a challenging combinatorial problem. The presence of latent variables further complicates this task. In this paper, we propose a fast and accurate DAG recovery algorithm based on the Cholesky factorization of the data covariance matrix. Our method, Causal Discovery via Cholesky Factorization (CDCF), has a time complexity of \(\mathcal {O}(p^3)\) and is guaranteed to recover the true graph exactly under standard assumptions. On both synthetic and real-world datasets, CDCF significantly outperforms existing methods in speed and achieves state-of-the-art accuracy. Furthermore, under an equal error variances assumption, we extend CDCF to handle latent variables by incorporating a sparsity-encouraging optimization procedure, resulting in the CDCF+ algorithm. Extensive numerical simulations demonstrate that CDCF+ successfully recovers the ground-truth graph in most cases and surpasses the performance of current baselines.