Graph–Smoothed Bayesian Black-Box Shift Estimator and Its Information Geometry

Label shift adaptation aims to recover target class priors when the labelled source distribution $P$ and the unlabelled target distribution $Q$ share $P(X \mid Y) = Q(X \mid Y)$ but $P(Y) \neq Q(Y)$. Classical black box shift estimators invert an empirical confusion matrix of a frozen classifier, producing a brittle point estimate that ignores sampling noise and similarity among classes.