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

arXiv: https://arxiv.org/abs/2505.16251 · HTML: https://mlsanity.com/paper/2505.16251/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 51 references that are in the map.
- First posted on arXiv 22 May 2025.

## Builds on (most cited first, 18 of 18)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [WILDS: A Benchmark of in-the-Wild Distribution Shifts](https://mlsanity.com/paper/2012.07421/) (2020)
- [Detecting and Correcting for Label Shift with Black Box Predictors](https://mlsanity.com/paper/1802.03916/) (2018)
- [A Comprehensive Survey on Test-Time Adaptation under Distribution Shifts](https://mlsanity.com/paper/2303.15361/) (2023)
- [Failing Loudly: An Empirical Study of Methods for Detecting Dataset Shift](https://mlsanity.com/paper/1810.11953/) (2018)
- [A Conceptual Introduction to Hamiltonian Monte Carlo](https://mlsanity.com/paper/1701.02434/) (2017)
- [Regularized Learning for Domain Adaptation under Label Shifts](https://mlsanity.com/paper/1903.09734/) (2019)
- [A Unified View of Label Shift Estimation](https://mlsanity.com/paper/2003.07554/) (2020)
- [Mandoline: Model Evaluation under Distribution Shift](https://mlsanity.com/paper/2107.00643/) (2021)
- [Hamiltonian Monte Carlo for Hierarchical Models](https://mlsanity.com/paper/1312.0906/) (2013)
- [RLSbench: Domain Adaptation Under Relaxed Label Shift](https://mlsanity.com/paper/2302.03020/) (2023)
- [Label Shift Adapter for Test-Time Adaptation under Covariate and Label Shifts](https://mlsanity.com/paper/2308.08810/) (2023)
- [A Short Survey on Importance Weighting for Machine Learning](https://mlsanity.com/paper/2403.10175/) (2024)
- [Density Ratio Estimation via Sampling along Generalized Geodesics on Statistical Manifolds](https://mlsanity.com/paper/2406.18806/) (2024)
- [α-Geodesical Skew Divergence](https://mlsanity.com/paper/2103.17060/) (2021)
- [Information Geometrically Generalized Covariate Shift Adaptation](https://mlsanity.com/paper/2304.09387/) (2023)
- [Geometry of EM and related iterative algorithms](https://mlsanity.com/paper/2209.01301/) (2022)

## Built on by (most cited first, 1 of 1)

- [Information Geometry of Absorbing Markov-Chain and Discriminative Random Walks](https://mlsanity.com/paper/2602.08185/) (2026)

## Abstract (arXiv)

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-B3SE), 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-B3SE through information geometry, showing that it generalizes existing shift estimators.