MDL Meets Latent Confounders: LNML-based Causal Discovery

• URL: http://arxiv.org/abs/2607.04133v1
• Date: Sun, 05 Jul 2026 06:19:48 GMT
• Title: MDL Meets Latent Confounders: LNML-based Causal Discovery
• Abstract summary: We propose an MDL-based causal discovery framework that explicitly accounts for latent confounders.<n>We introduce the notion of $$-pseudo-collinearity to identify dependencies induced by latent confounders.<n>Experiments on synthetic and real-world datasets demonstrate that the proposed method accurately recovers directed causal relationships and effectively detects latent confounders.
• Score: 5.510367725306641
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Causal discovery with nonlinear mechanisms and latent confounders remains challenging. Existing methods often rely on either linear assumptions or causal sufficiency, limiting their applicability. We propose an MDL-based causal discovery framework that explicitly accounts for latent confounders while allowing flexible nonlinear mechanisms by minimizing the luckiness normalized maximum likelihood (LNML) code-length. The causal relationship between each variable pair is determined by selecting the shortest code-length of the causal model, and we introduce the notion of $Δ$-pseudo-collinearity to identify dependencies induced by latent confounders. Based on these ideas, we develop a greedy algorithm, termed Pseudo-Collinearity Guided Causal Discovery (PCG-CD). Experiments on synthetic and real-world datasets demonstrate that the proposed method accurately recovers directed causal relationships and effectively detects latent confounders.

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