Reliable uncertainty with cheaper neural network ensembles: a case study in industrial parts classification

In operations research (OR), predictive models often encounter out-of-distribution (OOD) scenarios where the data distribution differs from the training data distribution. In recent years, neural networks (NNs) are gaining traction in OR for their exceptional performance in fields such as image classification. However, NNs tend to make confident yet incorrect predictions when confronted with OOD data. Uncertainty estimation offers a solution to overconfident models, communicating when the output should (not) be trusted. Hence, reliable uncertainty quantification in NNs is crucial in the OR domain. Deep ensembles, composed of multiple independent NNs, have emerged as a promising approach, offering not only strong predictive accuracy but also reliable uncertainty estimation. However, their deployment is challenging due to substantial computational demands. Recent fundamental research has proposed more efficient NN ensembles, namely the snapshot, batch, and multi-input multi-output ensemble. This study is the first to provide a comprehensive comparison of a single NN, a deep ensemble, and the three efficient NN ensembles. In addition, we propose a Diversity Quality metric to quantify the ensembles' performance on the in-distribution and OOD sets in one single metric. The OR case study discusses industrial parts classification to identify and manage spare parts, important for timely maintenance of industrial plants. The results highlight the batch ensemble as a cost-effective and competitive alternative to the deep ensemble. It outperforms the deep ensemble in both uncertainty and accuracy while exhibiting a training time speedup of 7x, a test time speedup of 8x, and 9x memory savings.