Success concepts for causal discovery

Abstract Existing causal discovery algorithms are often evaluated using two success criteria, one that is typically unachievable and the other which too weak for practical purposes. The criterion—uniform consistency—requires a algorithm identify correct structure at known sample size. but achievable criterion— pointwise only in limit. We investigate intermediate criteria— decidability progressive solvability —that stricter than mere consistency weaker uniform consistency. To do so, we review several topological theorems characterizing problems decidable and/or progressively solvable. These apply to any problem of statistical model selection, this paper, selection models. show, under common modeling assumptions, there no uniformly consistent procedure identifying direction edge, decision procedures solutions. focus on linear models error terms either non-Gaussian or contain Gaussian components ; latter assumption novel paper. especially criteria remain feasible when confounders present.