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.

通过多校准，建立一个新的无模型偏见优化框架，确保预测器在一组重叠群体中实现校准，从而与协变量偏移下的统计推断的稳健性相关联，并扩展多校准以包括考虑协变量和标签的分组函数，从而实现包括概念变化在内的预测任务的稳健性。