aiqbench analysis
This paper addresses a critical bottleneck in causal inference by introducing AdaPS-LiNGAM, a method designed to recover causal structures when sample sizes are smaller than the number of variables. The authors overcome the degeneracy of standard residualization techniques by leveraging an "active boundary" concept that selects sparse subsets of earlier variables for reconstruction. This advancement is significant for machine learning applications requiring robust causal discovery in data-scarce environments without relying on large datasets.
AdaPS-LiNGAM: Adaptive Predecessor Selection for Linear Non-Gaussian Acyclic Models under Small-Sample Settings
arXiv:2610.09782v1 Announce Type: new Abstract: 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.
Abstract: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.
Machine Learning (cs.LG); Machine Learning (stat.ML)
arXiv:2610.09782 [cs.LG]
(or arXiv:2610.09782v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.09782 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 287 words
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