aiqbench analysis
This paper generalizes variance-based causal structure learning from Gaussian to non-Gaussian noise by swapping conditional variance for a noise-likelihood-based conditional risk. The authors report that the matched-loss versions recover structure more accurately than least-squares variants and LiNGAM, and that the top-down and bottom-up methods separate under non-Gaussian noise, with the bottom-up method failing in some cases such as exponential or Cauchy noise. For ML practitioners, the practical takeaway is that the choice of recovery direction and the assumed noise model can change whether a causal discovery method is correct, not just how well it performs.
Learning Non-Gaussian SEMs with Conditional Risk, and Why the Direction of Recursion Matters
arXiv:2610.14246v1 Announce Type: new Abstract: Variance-based methods recover a Gaussian linear structural equation model (SEM) with equal or suitably constrained error variances, either by recursively identifying the source nodes with smallest conditional variance (top-down method) or sink nodes with highest conditional variance (bottom-up method). We show that the use of conditional variance is incidental: replacing it with the conditional risk, i.e., the minimal expected loss of linear prediction under the negative log-likelihood of the noise distribution, extends both methods to non-Gaussian noise. Existing methods are the least-squares special case. This yields two main results. First, exploiting the noise distribution improves structure recovery: the matched-loss procedures recover the SEM more accurately than their least-squares counterparts and the LiNGAM methods, which are designed for non-Gaussianity. Second, the two methods, interchangeable in the Gaussian setting, separate under non-Gaussian noise: the top-down method is correct for every noise density with finite differential entropy, whereas the bottom-up method requires a regularity condition and can fail without it, for instance under mean-zero exponential or Cauchy noise. Simulations confirm both results.
Abstract:Variance-based methods recover a Gaussian linear structural equation model (SEM) with equal or suitably constrained error variances, either by recursively identifying the source nodes with smallest conditional variance (top-down method) or sink nodes with highest conditional variance (bottom-up method). We show that the use of conditional variance is incidental: replacing it with the conditional risk, i.e., the minimal expected loss of linear prediction under the negative log-likelihood of the noise distribution, extends both methods to non-Gaussian noise. Existing methods are the least-squares special case. This yields two main results. First, exploiting the noise distribution improves structure recovery: the matched-loss procedures recover the SEM more accurately than their least-squares counterparts and the LiNGAM methods, which are designed for non-Gaussianity. Second, the two methods, interchangeable in the Gaussian setting, separate under non-Gaussian noise: the top-down method is correct for every noise density with finite differential entropy, whereas the bottom-up method requires a regularity condition and can fail without it, for instance under mean-zero exponential or Cauchy noise. Simulations confirm both results.
Machine Learning (cs.LG); Machine Learning (stat.ML)
arXiv:2610.14246 [cs.LG]
(or arXiv:2610.14246v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.14246 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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