Differentiable Causal Discovery for Singular Linear Models under Confounding

תקציר מקורי באנגליתarXiv:2601.01368v2 Announce Type: replace Abstract: Score-based causal discovery in the presence of unobserved confounders requires both a consistent scoring criterion and an efficient search over graph structures. Linear causal models with correlated errors are naturally represented by acyclic directed mixed graphs (ADMGs), whose induced model families include singular statistical models for which the standard Bayesian Information Criterion is inconsistent. We develop a score-based framework for causal discovery over linear Gaussian ADMGs grounded in singular learning theory. We first verify that the conditions for consistency of the Widely Applicable Bayesian Information Criterion (WBIC) are satisfied by the linear causal model class. We then propose a scalable approximation of the WBIC