On the Richness of Calibration

TL;DR

This paper analyzes various calibration scores for probabilistic predictions, proposing a comprehensive framework that includes grouping choices and error agglomeration, and introduces novel fairness measures at both population and individual levels.

Contribution

It systematically compares calibration scores, formalizes new grouping and agglomeration methods, and introduces fairness deviation measures with desirable properties.

Findings

Grouping data by input features has advantages over prediction-based grouping.

Axiomatization of fairness deviation measures enables new fairness notions.

Framework unifies and extends existing calibration and fairness scores.

Abstract

Probabilistic predictions can be evaluated through comparisons with observed label frequencies, that is, through the lens of calibration. Recent scholarship on algorithmic fairness has started to look at a growing variety of calibration-based objectives under the name of multi-calibration but has still remained fairly restricted. In this paper, we explore and analyse forms of evaluation through calibration by making explicit the choices involved in designing calibration scores. We organise these into three grouping choices and a choice concerning the agglomeration of group errors. This provides a framework for comparing previously proposed calibration scores and helps to formulate novel ones with desirable mathematical properties. In particular, we explore the possibility of grouping datapoints based on their input features rather than on predictions and formally demonstrate advantages of such approaches. We also characterise the space of suitable agglomeration functions for group errors, generalising previously proposed calibration scores. Complementary to such population-level scores, we explore calibration scores at the individual level and analyse their relationship to choices of grouping. We draw on these insights to introduce and axiomatise fairness deviation measures for population-level scores. We demonstrate that with appropriate choices of grouping, these novel global fairness scores can provide notions of (sub-)group or individual fairness.