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Machine learning algorithms have been effectively applied into various realworld tasks. However, it is difficult to provide high-quality machine learningsolutions to accommodate an unknown distribution of input datasets; thisdifficulty is called the uncertainty prediction problems. In this paper, amargin-based Pareto deep ensemble pruning (MBPEP) model is proposed. Itachieves the high-quality uncertainty estimation with a small value of theprediction interval width (MPIW) and a high confidence of prediction intervalcoverage probability (PICP) by using deep ensemble networks. In addition tothese networks, unique loss functions are proposed, and these functions makethe sub-learners available for standard gradient descent learning. Furthermore,the margin criterion fine-tuning-based Pareto pruning method is introduced tooptimize the ensembles. Several experiments including predicting uncertaintiesof classification and regression are conducted to analyze the performance ofMBPEP. The experimental results show that MBPEP achieves a small interval widthand a low learning error with an optimal number of ensembles. For thereal-world problems, MBPEP performs well on input datasets with unknowndistributions datasets incomings and improves learning performance on a multitask problem when compared to that of each single model.

The MBPEP: a deep ensemble pruning algorithm providing high quality uncertainty prediction