When Does a Predictor Know Its Own Loss?
AuthorsAravind Gollakota, Parikshit Gopalan, Aayush Karan, Charlotte Peale, Udi Wieder
AuthorsAravind Gollakota, Parikshit Gopalan, Aayush Karan, Charlotte Peale, Udi Wieder
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 (Hebert-Johnson et al, 2018), 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.
November 30, 2023research area Fairness, research area Methods and Algorithmsconference NeurIPS
A recent line of work shows that notions of multigroup fairness imply surprisingly strong notions of omniprediction: loss minimization guarantees that apply not just for a specific loss function, but for any loss belonging to a large family of losses. While prior work has derived various notions of omniprediction from multigroup fairness guarantees of varying strength, it was unknown whether the connection goes in both directions. In this work,...
March 10, 2023research area Fairness, research area Methods and Algorithms
We present a new perspective on loss minimization and the recent notion of Omniprediction through the lens of Outcome Indistingusihability. For a collection of losses and hypothesis class, omniprediction requires that a predictor provide a loss-minimization guarantee simultaneously for every loss in the collection compared to the best (loss-specific) hypothesis in the class. We present a generic template to learn predictors satisfying a guarantee...