Graph-Smoothed Bayesian Black-Box Shift Estimator and Its Information Geometry
This addresses the brittleness of classical black-box shift estimators for domain adaptation in machine learning, offering a more robust and theoretically grounded method, though it is an incremental improvement over existing approaches.
The paper tackled the problem of label shift adaptation by developing a fully probabilistic estimator, Graph-Smoothed Bayesian BBSE, which recovers target class priors with proven identifiability, N^{-1/2} contraction, and variance bounds that shrink with graph connectivity, achieving robustness to misspecification.
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. We present Graph-Smoothed Bayesian BBSE (GS-B$^3$SE), a fully probabilistic alternative that places Laplacian-Gaussian priors on both target log-priors and confusion-matrix columns, tying them together on a label-similarity graph. The resulting posterior is tractable with HMC or a fast block Newton-CG scheme. We prove identifiability, $N^{-1/2}$ contraction, variance bounds that shrink with the graph's algebraic connectivity, and robustness to Laplacian misspecification. We also reinterpret GS-B$^3$SE through information geometry, showing that it generalizes existing shift estimators.