2024/02/15 by Muthu Chidambaram, Holden Lee, Chidambaram, Muthu +5 · 1 citation
Computer Science · #60E05 (Secondary) #68T37 (Primary) 62-08 #Explainable Artificial Intelligence (XAI) #FOS: Computer and information sciences #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Generative Adversarial Networks and Image Synthesis #Machine Learning (cs.LG) #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2402.10046
openalex publication_date 2024/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Informally, a model is calibrated if its predictions are correct with a probability that matches the confidence of the prediction. By far the most common method in the literature for measuring calibration is the expected calibration error (ECE). Recent work, however, has pointed out drawbacks of ECE, such as the fact that it is discontinuous in the space of predictors. In this work, we ask: how fundamental are these issues, and what are their impacts on existing results? Towards this end, we completely characterize the discontinuities of ECE with respect to general probability measures on Polish spaces. We then use the nature of these discontinuities to motivate a novel continuous, easily estimated miscalibration metric, which we term Logit-Smoothed ECE (LS-ECE). By comparing the ECE and LS-ECE of pre-trained image classification models, we show in initial experiments that binned ECE closely tracks LS-ECE, indicating that the theoretical pathologies of ECE may be avoidable in practice.