Top-label calibration and multiclass-to-binary reductions

Chirag Gupta, Aaditya Ramdas

Keywords: calibration, multiclass, uncertainty quantification, distribution-free, histogram binning

Abstract: We propose a new notion of multiclass calibration called top-label calibration. A classifier is said to be top-label calibrated if the reported probability for the predicted class label---the top-label---is calibrated, conditioned on the top-label. This conditioning is essential for practical utility of the calibration property, since the top-label is always reported and we must condition on what is reported. However, the popular notion of confidence calibration erroneously skips this conditioning. Furthermore, we outline a multiclass-to-binary (M2B) reduction framework that unifies confidence, top-label, and class-wise calibration, among others. As its name suggests, M2B works by reducing multiclass calibration to different binary calibration problems; various types of multiclass calibration can then be achieved using simple binary calibration routines. We instantiate the M2B framework with the well-studied histogram binning (HB) binary calibrator, and prove that the overall procedure is multiclass calibrated without making any assumptions on the underlying data distribution. In an empirical evaluation with four deep net architectures on CIFAR-10 and CIFAR-100, we find that the M2B + HB procedure achieves lower top-label and class-wise calibration error than other approaches such as temperature scaling. Code for this work is available at https://github.com/aigen/df-posthoc-calibration.

One-sentence Summary: We propose top-label calibration, a new and arguably natural notion for multiclass calibration, along with 'wrapper' calibration algorithms that reduce multiclass calibration to binary calibration.