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Graph–Smoothed Bayesian Black-Box Shift Estimator and Its Information Geometry
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Proposes GS-B3SE, a Bayesian black-box label-shift estimator that places graph-Laplacian Gaussian Markov random field priors on target log-priors and confusion-matrix columns, with theory (identifiability, contraction, variance bounds, misspecification robustness, information-geometric view) and experiments on MNIST, CIFAR-10 and CIFAR-100.
Problem
Black-box shift estimation (BBSE) under label shift returns brittle point estimates of target class priors that ignore sampling noise in the confusion matrix and ignore semantic similarity between classes, especially with many classes and rare labels.
Approach
Replace BBSE's point inversion with a joint hierarchical Bayesian model in which target log-priors and every confusion-matrix column carry Laplacian-Gaussian (GMRF) priors on a label-similarity graph built from CLIP text embeddings, giving a full posterior sampled by HMC or block Newton-CG.
Key results
- On CIFAR-100 (K=100), GS-B3SE reduces L1 prior error to 0.22 versus 0.71 for the best baseline (MLLS).
- On MNIST, L1 error falls from 0.010 (MLLS) to 0.002 and post-correction accuracy reaches 0.986.
- On CIFAR-10, post-correction accuracy is 0.844 versus 0.812 for MLLS.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use GS-B³SE instead of MLLS | ResNet-18 label-shift estimation · MNIST | prior L1 error: 0.010 -> 0.002 | Helped |
| Use GS-B³SE instead of MLLS for Saerens correction | ResNet-18 label-shift estimation · MNIST | post-correction accuracy: 0.963 -> 0.986 | Helped |
| Use GS-B³SE instead of MLLS | ResNet-18 label-shift estimation · CIFAR-10 | prior L1 error: 0.052 -> 0.025 | Helped |
| Use GS-B³SE instead of MLLS for Saerens correction | ResNet-18 label-shift estimation · CIFAR-10 | post-correction accuracy: 0.812 -> 0.844 | Helped |
| Use GS-B³SE instead of MLLS | ResNet-18 label-shift estimation · CIFAR-100 | prior L1 error: 0.71 -> 0.22 | Helped |
| Use GS-B³SE instead of MLLS for Saerens correction | ResNet-18 label-shift estimation · CIFAR-100 | post-correction accuracy: 0.734 -> 0.783 | Helped |
Limitations
- Graph is fixed from CLIP or feature embeddings and not learned jointly with the posterior.
- Scaling to larger datasets and extreme label counts is left to future work.
- Several theoretical claims (e.g., Laplacian-misspecification bound, variance bound) rely on heuristic or loosely justified steps in the proofs.
Experimental setup
Datasets: MNIST CIFAR-10 CIFAR-100
Benchmarks: MNIST CIFAR-10 CIFAR-100
Metrics: L1 prior error accuracy after Saerens correction
Baselines: BBSE EM (Saerens) RLLS MLLS
Builds on: black-box shift estimator saerens EM RLLS MLLS
Closest papers by meaning
- Learning from Noisy Labels via Conditional Distributionally Robust Optimization (NeurIPS 2024 · similarity 0.85)
- Classification under Nuisance Parameters and Generalized Label Shift in Likelihood-Free Inference (ICML 2024 · similarity 0.85)
- Uncertainty Estimation on Graphs with Structure Informed Stochastic Partial Differential Equations (NeurIPS 2025 · similarity 0.84)
- From Matrix Inversion to Constraints: Provably Tighter Confidence Regions for Importance Weights in Label Shift (NeurIPS 2026 · similarity 0.84)
- Pairwise Alignment Improves Graph Domain Adaptation (ICML 2024 · similarity 0.84)
- Label Shift Meets Online Learning: Ensuring Consistent Adaptation with Universal Dynamic Regret (CVPR 2025 · similarity 0.84)
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