Multi-Head Multi-Loss Model Calibration

Abstract

Delivering meaningful uncertainty estimates is essential for a successful deployment of machine learning models in the clinical practice. A central aspect of uncertainty quantification is the ability of a model to return predictions that are well-aligned with the actual probability of the model being correct, also known as model calibration. Although many methods have been proposed to improve calibration, no technique can match the simple, but expensive approach of training an ensemble of deep neural networks. In this paper we introduce a form of simplified ensembling that bypasses the costly training and inference of deep ensembles, yet it keeps its calibration capabilities. The idea is to replace the common linear classifier at the end of a network by a set of heads that are supervised with different loss functions to enforce diversity on their predictions. Specifically, each head is trained to minimize a weighted Cross-Entropy loss, but the weights are different among the different branches. We show that the resulting averaged predictions can achieve excellent calibration without sacrificing accuracy in two challenging datasets for histopathological and endoscopic image classification. Our experiments indicate that Multi-Head Multi-Loss classifiers are inherently well-calibrated, outperforming other recent calibration techniques and even challenging Deep Ensembles' performance. Code to reproduce our experiments can be found at \url{https://github.com/agaldran/mhml_calibration} .