PEC: Improving Posterior Edge Confidence for Constraint-Based Causal Discovery

Causal discovery has attracted growing attention across scientific fields, as most causal downstream analyses rely on the recovered causal graph. In practice, however, finite samples, incomplete data, and violated assumptions frequently yield erroneous edges, and this problem is aggravated in constraint-based algorithms, where errors in conditional independence (CI) tests can propagate through the subsequent decisions. In response, several methods also provide edge-wise scores that indicate how reliable each edge is, which helps verify the recovered causal graph. Yet these scores typically quantify the strength of causal influence or provide conservative bounds for statistical error control over the set of discovered edges, rather than the posterior probability of edge existence. We introduce Posterior Edge Confidence (PEC), a framework that estimates posterior edge probabilities for constraint-based causal discovery. PEC models the distributions of the test statistic under both hypotheses and combines them by probability rules derived from the logical structure of the skeleton search, rather than taking a single representative statistic. In experiments on synthetic datasets, we show PEC ranks edges more accurately than an existing representative-statistic baseline and improves the baseline as well.