When does a predictor know its own loss?

TL;DR

This paper explores the theoretical relationship between loss prediction accuracy and multicalibration, revealing that effective loss prediction is fundamentally linked to fairness notions and can be used to assess model calibration.

Contribution

It establishes a formal connection between loss prediction and multicalibration, showing that improving loss prediction relates directly to multicalibration failures.

Findings

Loss prediction and multicalibration are tightly connected.

Better loss predictors indicate multicalibration errors.

Experiments show correlation between multicalibration error and loss prediction efficacy.

Abstract

Given a predictor and a loss function, how well can we predict the loss that the predictor will incur on an input? This is the problem of loss prediction, a key computational task associated with uncertainty estimation for a predictor. In a classification setting, a predictor will typically predict a distribution over labels and hence have its own estimate of the loss that it will incur, given by the entropy of the predicted distribution. Should we trust this estimate? In other words, when does the predictor know what it knows and what it does not know? In this work we study the theoretical foundations of loss prediction. Our main contribution is to establish tight connections between nontrivial loss prediction and certain forms of multicalibration, a multigroup fairness notion that asks for calibrated predictions across computationally identifiable subgroups. Formally, we show that a loss predictor that is able to improve on the self-estimate of a predictor yields a witness to a failure of multicalibration, and vice versa. This has the implication that nontrivial loss prediction is in effect no easier or harder than auditing for multicalibration. We support our theoretical results with experiments that show a robust positive correlation between the multicalibration error of a predictor and the efficacy of training a loss predictor.