Knockoff-C2ST: False Discovery Controlled Attribution of Distribution Shift

Classifier two-sample tests (C2STs) are a standard reduction for deciding whether a distribution shift has occurred, but the reduction by itself is not a valid explanation of what shifted when coordinates are statistically dependent. In high-correlation regimes, standard feature-attribution scores computed from a C2ST inherit correlation bias: variables that merely predict a shifted covariate can receive larger importance than the shifted covariate itself, producing uncontrolled and often severe false discoveries. We introduce Knockoff-C2ST, a feature-attributed two-sample testing procedure that augments C2STs with Model-X knockoff variables and selects shifted coordinates by a sign-symmetric contrast statistic. Under exact Model-X exchangeability and a null defined by invariance of the conditional source and target laws, the selected set obeys finite-sample false discovery rate control at a user-specified level. The method preserves the modeling flexibility of C2STs while converting feature attribution into a multiple-testing procedure with formal error control. Experiments show strong FDR calibration under dependence, severe false-discovery inflation for naive attributions, and a present power bottleneck: tree-gain and loss-difference statistics are conservative, while stability aggregation gives nonzero but still limited recovery.