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This paper proposes a minimum description length (MDL) method for causal discovery that handles nonlinear mechanisms and hidden confounders, which many existing methods cannot. Its main theoretical claim is an upper bound on the code-length gap that grows at most linearly with sample size, which supports the proposed pseudo-collinearity criterion for flagging suspected confounders. The experiments are limited and the authors acknowledge weak latent-confounder discrimination, so readers should treat this as a methodological step rather than a validated tool.
LNML-based Causal Discovery with Latent Confounders: Theory and Experiments
arXiv:2607.04133v2 Announce Type: replace 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 accommodates latent confounders and flexible nonlinear mechanisms using the luckiness normalized maximum likelihood (LNML) code-length. To complement code-length-based model selection, we introduce $\Delta$-pseudo-collinearity as a criterion for identifying potential latent-confounding candidates. We theoretically show that, in the presence of a latent confounder, the directional code-length gap $\Delta$ admits an upper bound that grows at most linearly with the sample size and decreases as the latent causal mechanisms become more similar, providing support for the proposed criterion. Based on this formulation, we develop a greedy algorithm, termed Pseudo-Collinearity Guided Causal Discovery (PCG-CD). Experiments on synthetic and real-world datasets demonstrate the ability of PCG-CD to recover directed causal relationships and identify potential latent-confounding candidates, while revealing limitations in latent-confounder discrimination.
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 accommodates latent confounders and flexible nonlinear mechanisms using the luckiness normalized maximum likelihood (LNML) code-length. To complement code-length-based model selection, we introduce $\Delta$-pseudo-collinearity as a criterion for identifying potential latent-confounding candidates. We theoretically show that, in the presence of a latent confounder, the directional code-length gap $\Delta$ admits an upper bound that grows at most linearly with the sample size and decreases as the latent causal mechanisms become more similar, providing support for the proposed criterion. Based on this formulation, we develop a greedy algorithm, termed Pseudo-Collinearity Guided Causal Discovery (PCG-CD). Experiments on synthetic and real-world datasets demonstrate the ability of PCG-CD to recover directed causal relationships and identify potential latent-confounding candidates, while revealing limitations in latent-confounder discrimination.
Extended version of the ECML PKDD 2026 paper titled "MDL Meets Latent Confounders: LNML-Based Causal Discovery," with additional theoretical results and experiments. The experimental implementation has been corrected, and the results have been updated accordingly
Machine Learning (cs.LG)
arXiv:2607.04133 [cs.LG]
(or arXiv:2607.04133v2 [cs.LG] for this version)
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