MDL Meets Latent Confounders: LNML-based Causal Discovery

2026-07-05

AI Summary

This work addresses the challenge of causal discovery in the presence of nonlinear mechanisms and latent confounding by proposing a novel approach grounded in the Minimum Description Length (MDL) principle. The method explicitly models latent confounding and accommodates nonlinear causal relationships by minimizing the Luckiness Normalized Maximum Likelihood (LNML) code length. It introduces the innovative notion of Δ-pseudocollinearity to identify dependency structures induced by latent variables and integrates this with a greedy search algorithm, termed PCG-CD, to construct a causal discovery framework that dispenses with assumptions of linearity or causal sufficiency. Empirical evaluations demonstrate that the proposed method accurately infers directed causal relationships and effectively detects latent confounding across both synthetic and real-world datasets.

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.

Problem

• causal discovery
• latent confounders
• nonlinear mechanisms
• causal sufficiency

Innovation

• MDL
• latent confounders
• LNML
• nonlinear causal discovery
• pseudo-collinearity