Effective training-time stacking for ensembling of deep neural networks

Ensembling is a popular and effective method for improving machine learning (ML) models. It proves its value not only in classical ML but also for deep learning. Ensembles enhance the quality and trustworthiness of ML solutions, and allow uncertainty estimation. However, they come at a price: training ensembles of deep learning models eat a huge amount of computational resources. A snapshot ensembling collects models in the ensemble along a single training path. As it runs training only one time, the computational time is similar to the training of one model. However, the quality of models along the training path is different: typically, later models are better if no overfitting occurs. So, the models are of varying utility. Our method improves snapshot ensembling by selecting and weighting ensemble members along the training path. It relies on training-time likelihoods without looking at validation sample errors that standard stacking methods do. Experimental evidence for Fashion MNIST, CIFAR-10, and CIFAR-100 datasets demonstrates the superior quality of the proposed weighted ensembles c.t. vanilla ensembling of deep learning models.