MMD-Balls as Credal Sets: A PAC-Bayesian Framework for Epistemic Uncertainty in Test-Time Adaptation
Authors: Ahanaf Hasan Ariq
Summary
arXiv:2605. 21783v1 Announce Type: cross Abstract: Test-time adaptation (TTA) methods improve model performance under distribution shift but lack formal guarantees connecting shift magnitude to prediction reliability.
Relevance
Read next because MMD-Balls as Credal Sets: A PAC-Bayesian Framework for Epistemic Uncertainty in Test-Time Adaptation overlaps with clean result "Language-mismatch LoRA SFT on Qwen2.5-7B leaks the trained completion language into bystander directives the model was never trained on, absent under same-language SFT (LOW confidence)", clean result "Training one persona to emit a [ZLT] marker without bystanders adopting it has a one-cell-wide LR x epochs window on Qwen2.5-7B-Instruct (LOW confidence)", clean result "The marker is a representational handle, not a behavioural one — sharing it between a villain persona and the assistant transfers no misalignment (HIGH confidence)". Matching terms: under, source, rate, position, test, model. Source: arxiv stat.ML (Machine Learning).
Abstract
arXiv:2605.21783v1 Announce Type: cross 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.