How Flawed Is ECE? An Analysis via Logit Smoothing
This work addresses calibration measurement for machine learning models, but it is incremental as it builds on known drawbacks of ECE and proposes a refinement rather than a breakthrough.
The paper analyzed the theoretical flaws of Expected Calibration Error (ECE) as a calibration metric, particularly its discontinuities, and introduced a continuous alternative called Logit-Smoothed ECE (LS-ECE). Initial experiments on pre-trained image classification models showed that binned ECE closely tracks LS-ECE, suggesting that ECE's theoretical issues may not be problematic in practice.
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.