EnsLoss: Stochastic Calibrated Loss Ensembles for Preventing Overfitting in Classification

摘要

Empirical risk minimization (ERM) with a computationally feasible surrogate loss is a widely accepted approach for classification. Notably, the convexity and calibration (CC) properties of a loss function ensure consistency of ERM in maximizing accuracy, thereby offering a wide range of options for surrogate losses. In this article, we propose a novel ensemble method, namely *EnsLoss*, which extends the ensemble learning concept to combine loss functions within the ERM framework. A key feature of our method is the consideration on preserving the "legitimacy" of the combined losses, i.e., ensuring the CC properties. Specifically, we first transform the CC conditions of losses into loss-derivatives, thereby bypassing the need for explicit loss functions and directly generating calibrated loss-derivatives. Therefore, inspired by Dropout, *EnsLoss* enables loss ensembles through one training process with doubly stochastic gradient descent (i.e., random batch samples and random calibrated loss-derivatives). We theoretically establish the statistical consistency of our approach and provide insights into its benefits. The numerical effectiveness of *EnsLoss* compared to fixed loss methods is demonstrated through experiments on a broad range of 45 pairs of CIFAR10 datasets, the PCam image dataset, and 14 OpenML tabular datasets and with various deep learning architectures. Python repository and source code are available on our Github (https://github.com/statmlben/ensLoss).