Bridging Multicalibration and Out-of-distribution Generalization Beyond Covariate Shift

TL;DR

This paper introduces a new framework linking multicalibration with out-of-distribution generalization, providing theoretical insights and a practical algorithm that improves robustness under distribution shifts.

Contribution

It extends multicalibration to include joint covariate-label groupings, establishing a theoretical connection with invariance and robustness beyond covariate shift, and proposes a practical algorithm for OOD generalization.

Findings

The extended multicalibration framework captures robustness beyond covariate shift.

The MC-Pseudolabel algorithm achieves superior OOD performance on real datasets.

A unifying theory connects multicalibration, invariance, and robustness in distribution shift scenarios.

Abstract

We establish a new model-agnostic optimization framework for out-of-distribution generalization via multicalibration, a criterion that ensures a predictor is calibrated across a family of overlapping groups. Multicalibration is shown to be associated with robustness of statistical inference under covariate shift. We further establish a link between multicalibration and robustness for prediction tasks both under and beyond covariate shift. We accomplish this by extending multicalibration to incorporate grouping functions that consider covariates and labels jointly. This leads to an equivalence of the extended multicalibration and invariance, an objective for robust learning in existence of concept shift. We show a linear structure of the grouping function class spanned by density ratios, resulting in a unifying framework for robust learning by designing specific grouping functions. We propose MC-Pseudolabel, a post-processing algorithm to achieve both extended multicalibration and out-of-distribution generalization. The algorithm, with lightweight hyperparameters and optimization through a series of supervised regression steps, achieves superior performance on real-world datasets with distribution shift.