MMD-Balls as Credal Sets: A PAC-Bayesian Framework for Epistemic Uncertainty in Test-Time Adaptation
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Computer Science > Machine Learning
Title:MMD-Balls as Credal Sets: A PAC-Bayesian Framework for Epistemic Uncertainty in Test-Time Adaptation
Abstract:Test-time adaptation (TTA) methods improve model performance under distribution shift but lack formal guarantees connecting shift magnitude to prediction reliability. We develop a PAC-Bayesian framework yielding generalization bounds explicitly parameterized by the maximum mean discrepancy (MMD) between source and target distributions. Our principal contribution is interpreting MMD-balls around the source distribution as credal sets in Walley's imprecise probability theory, yielding natural epistemic uncertainty quantification. We establish: (i) a PAC-Bayesian bound with an MMD-dependent shift penalty under an RKHS-Lipschitz loss assumption; (ii) a finite-sample version via MMD concentration; (iii) a uniform worst-case risk bound over all distributions in the credal set, with a lower-upper risk decomposition; and (iv) geodesic preservation bounds explaining why kernel-guided adaptation protects local feature geometry. The credal set interpretation separates epistemic from aleatoric uncertainty and provides a principled decision criterion for when adaptation is warranted.
| Comments: | 15 pages, 0 figures. Accepted at the 2nd Workshop on Epistemic Intelligence in Machine Learning (EIML@ICML 2026) |
| Subjects: | Machine Learning (cs.LG); Machine Learning (stat.ML) |
| MSC classes: | 68T05, 62C20, 68Q32 |
| ACM classes: | I.2.6; G.3 |
| Cite as: | arXiv:2605.21783 [cs.LG] |
| (or arXiv:2605.21783v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.21783
arXiv-issued DOI via DataCite (pending registration)
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