发表机构
Artificial Intelligence Laboratory, Fujitsu Limited（富士通有限公司人工智能实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对小样本下线性非高斯无环模型因果发现困难，提出AdaPS-LiNGAM方法，通过自适应选择稀疏前驱子集重构残差，实现准确且稳健的因果结构恢复。
AI 中文摘要
当可用样本量相对于变量数量较小时，因果发现变得尤为困难。这一挑战同样出现在线性非高斯无环模型（LiNGAM）中，该模型是从观测数据进行因果发现的可识别框架。DirectLiNGAM通过依次识别外生变量并消除其对剩余变量的线性效应来估计因果顺序，该顺序将变量排列为使原因先于其效应。我们确立了该过程的一个结构性限制：当变量数量超过样本量时，在完整因果顺序确定之前，重复残差化必然退化。我们的分析进一步揭示，每个残差可以仅使用因果顺序中较早放置的、由图确定的变量子集（称为活动边界）来重构。这一结果促使了AdaPS-LiNGAM（自适应前驱选择LiNGAM）的提出，该方法使用从这些较早变量中自适应选择的稀疏子集，直接从原始观测中重构每个残差。相同的子集选择原则也应用于最终剪枝步骤以进行边估计。在合成数据上的实验表明，AdaPS-LiNGAM在样本受限设置下提供了准确的因果结构恢复，并且随着样本量的减少，其退化更为平缓。
英文摘要
Causal discovery becomes particularly challenging when the available sample size is small relative to the number of variables. This challenge also arises in the linear non-Gaussian acyclic model (LiNGAM), an identifiable framework for causal discovery from observational data. DirectLiNGAM estimates a causal order, which arranges variables so that causes precede their effects, by sequentially identifying an exogenous variable and removing its linear effect from the remaining variables. We establish a structural limitation of this procedure: when the number of variables exceeds the sample size, repeated residualization necessarily becomes degenerate before the full causal order can be determined. Our analysis further reveals that each residual can be reconstructed using only a graph-determined subset of variables already placed earlier in the causal order, termed the active boundary. This result motivates AdaPS-LiNGAM (Adaptive Predecessor Selection LiNGAM), which reconstructs each residual directly from the original observations using an adaptively chosen sparse subset of those earlier variables. The same subset-selection principle is also applied to the final pruning step for edge estimation. Experiments on synthetic data demonstrate that AdaPS-LiNGAM provides accurate causal-structure recovery in sample-limited settings and degrades more gradually as the sample size decreases.
