arXiv:2512.24696cs.LG2025-12

分离全局与局部混杂因素,提升因果发现准确性

Causal Discovery with Mixed Latent Confounding via Precision Decomposition

  • 通过分解精度矩阵分离全局与局部混杂影响
  • 在合成数据上比直接方法提升定向边识别率
  • 适合处理存在多种混杂机制的复杂系统

我们研究线性高斯系统中受混合潜变量混杂影响的因果发现问题,其中部分未观测因子广泛影响多个变量,而其他因子仅作用于小范围子集。该设定在实际中常见,但现有方法面临挑战:可微分和基于评分的DAG学习器可能将全局潜变量效应误判为因果边,而潜变量图模型仅能恢复无向结构。本文提出DCL-DECOR,一种模块化、以精度为导向的流程:首先通过分解观测精度矩阵,分离出结构化成分(对应消除全局混杂后的条件分布)与低秩成分;结构化成分仅保留由因果图和局部混杂引起的局部依赖关系;随后应用相关噪声DAG学习器在此去混杂表示上恢复有向边,并建模剩余结构化误差相关性;最后通过简单修正步骤确保无弓形结构。我们提供了可识别性结果,刻画了在混合混杂下可恢复的因果目标,并表明整体问题可分解为具有模块化保证的已知子问题。在变化全局混杂强度与维度的合成实验中,该方法在定向边恢复上持续优于直接对混杂数据应用相关噪声DAG学习。

原文摘要 · Abstract (English)

We study causal discovery from observational data in linear Gaussian systems affected by \emph{mixed latent confounding}, where some unobserved factors act broadly across many variables while others influence only small subsets. This setting is common in practice and poses a challenge for existing methods: differentiable and score-based DAG learners can misinterpret global latent effects as causal edges, while latent-variable graphical models recover only undirected structure. We propose \textsc{DCL-DECOR}, a modular, precision-led pipeline that separates these roles. The method first isolates pervasive latent effects by decomposing the observed precision matrix into a structured component and a low-rank component. The structured component corresponds to the conditional distribution after accounting for pervasive confounders and retains only local dependence induced by the causal graph and localized confounding. A correlated-noise DAG learner is then applied to this deconfounded representation to recover directed edges while modeling remaining structured error correlations, followed by a simple reconciliation step to enforce bow-freeness. We provide identifiability results that characterize the recoverable causal target under mixed confounding and show how the overall problem reduces to well-studied subproblems with modular guarantees. Synthetic experiments that vary the strength and dimensionality of pervasive confounding demonstrate consistent improvements in directed edge recovery over applying correlated-noise DAG learning directly to the confounded data.

因果发现潜变量图模型

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