Certified Learning under Distribution Shift: Sound Verification and Identifiable Structure
This addresses the challenge of ensuring reliable model predictions in real-world applications where data distributions may shift, though it appears incremental by building on existing verification and shift analysis frameworks.
The paper tackles the problem of certifying the performance of machine learning models under distribution shift by providing explicit upper bounds on excess risk, with verification sound for nontrivial sizes and interpretability enforced through identifiability conditions.
Proposition. Let $f$ be a predictor trained on a distribution $P$ and evaluated on a shifted distribution $Q$. Under verifiable regularity and complexity constraints, the excess risk under shift admits an explicit upper bound determined by a computable shift metric and model parameters. We develop a unified framework in which (i) risk under distribution shift is certified by explicit inequalities, (ii) verification of learned models is sound for nontrivial sizes, and (iii) interpretability is enforced through identifiability conditions rather than post hoc explanations. All claims are stated with explicit assumptions. Failure modes are isolated. Non-certifiable regimes are characterized.