Certified Learning under Distribution Shift: Sound Verification and Identifiable Structure

TL;DR

This paper introduces a framework for certifying learning models under distribution shift, providing explicit risk bounds, sound verification, and interpretability through identifiability, with clear assumptions and failure mode analysis.

Contribution

It presents a unified approach combining risk certification, sound verification, and interpretability via identifiability, with explicit assumptions and failure mode analysis.

Findings

Explicit upper bounds on risk under distribution shift.

Framework for sound verification of models.

Characterization of non-certifiable regimes.

Abstract

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.