Truthfulness of Calibration Measures

Abstract: We initiate the study of the truthfulness of calibration measures in sequential prediction. A calibration measure is said to be truthful if the forecaster (approximately) minimizes the expected penalty by predicting the conditional expectation of the next outcome, given the prior distribution of outcomes. Truthfulness is an important property of calibration measures, ensuring that the forecaster is not incentivized to exploit the system with deliberate poor forecasts. This makes it an essential desideratum for calibration measures, alongside typical requirements, such as soundness and completeness.

We conduct a taxonomy of existing calibration measures and their truthfulness. Perhaps surprisingly, we find that all of them are far from being truthful. That is, under existing calibration measures, there are simple distributions on which a polylogarithmic (or even zero) penalty is achievable, while truthful prediction leads to a polynomial penalty. Our main contribution is the introduction of a new calibration measure termed the Subsampled Smooth Calibration Error (SSCE) under which truthful prediction is optimal up to a constant multiplicative factor.

Bio: Mingda Qiao a FODSI postdoc hosted by Ronitt Rubinfeld at the MIT Theory of Computation (TOC) Group, and an incoming assistant professor at UMass Amherst (starting Fall'25). His research focuses on the theory of prediction, learning, and decision-making in sequential settings, as well as collaborative federated learning. Prior to MIT, Mingda was a FODSI postdoc at UC Berkeley, received his PhD in Computer Science from Stanford University, and received his BEng in Computer Science from Tsinghua University.