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Uncertainty quantification is a central challenge in reliable and trustworthymachine learning. Naive measures such as last-layer scores are well-known toyield overconfident estimates in the context of overparametrized neuralnetworks. Several methods, ranging from temperature scaling to differentBayesian treatments of neural networks, have been proposed to mitigateoverconfidence, most often supported by the numerical observation that theyyield better calibrated uncertainty measures. In this work, we provide a sharpcomparison between popular uncertainty measures for binary classification in amathematically tractable model for overparametrized neural networks: the randomfeatures model. We discuss a trade-off between classification accuracy andcalibration, unveiling a double descent like behavior in the calibration curveof optimally regularized estimators as a function of overparametrization. Thisis in contrast with the empirical Bayes method, which we show to be wellcalibrated in our setting despite the higher generalization error andoverparametrization.

On double-descent in uncertainty quantification in overparametrized models