Seminar: Proper losses: From class probability estimation to market design

Abstract:  Loss functions measure the discrepancy between the true state and model predictions, forming a cornerstone of machine learning and statistical estimation. Over time, many loss functions have been developed, including squared loss, logistic loss, hinge loss, exponential loss, ramp loss, and focal loss, among others. Given a decision problem, which loss function should we use? In this talk, I focus on proper losses, a minimally rational class of loss functions for class probability estimation. I will begin with a brief introduction to the fundamental properties and structure of proper losses and present two of our recent papers. First, we extend proper losses to a new class called calm composite losses to encompass recently developed loss functions for deep learning, such as focal loss and generalized cross-entropy loss. These losses have shown practical advantages in noise tolerance and calibration, yet their underlying structure remains unclear. Calm composite losses provide insight into how these losses elicit rational probability estimates and the divergences they correspond to. Second, we use proper losses to design a prediction market where multiple agents bid on possible outcomes. We demonstrate how prediction markets can effectively address the ill-posed nature of inverse optimization problems, leading to improved decision-making.

[B-Charoenphakdee 25] Calm Composite Losses: Being Improper Yet Proper Composite

[B-Sakaue 25] Inverse Optimization with Prediction Market: A Characterization of Scoring Rules for Elciting System States

Bio:  Han Bao is an associate professor at the Institute of Statistical Mathematics (ISM) in Japan as well as the research fellow of JST PRESTO. Before joining ISM, he received PhD at the University of Tokyo in 2022, and was doing postdoc at Kyoto University Hakubi Center for Advanced Studies from 2022 to 2025. His research focuses on theoretical understanding of statistical machine learning, particularly across loss functions, representation learning, and implicit bias.