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

arXiv: https://arxiv.org/abs/1902.09238 · HTML: https://mlsanity.com/paper/1902.09238/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Feb 2019.

## Built on by (most cited first, 10 of 10)

- [PID-GAN: A GAN Framework based on a Physics-informed Discriminator for Uncertainty Quantification with Physics](https://mlsanity.com/paper/2106.02993/) (2021)
- [Looks Too Good To Be True: An Information-Theoretic Analysis of Hallucinations in Generative Restoration Models](https://mlsanity.com/paper/2405.16475/) (2024)
- [What's Behind the Mask: Estimating Uncertainty in Image-to-Image Problems](https://mlsanity.com/paper/2211.15211/) (2022)
- [Benchmarking Scalable Epistemic Uncertainty Quantification in Organ Segmentation](https://mlsanity.com/paper/2308.07506/) (2023)
- [Exploring Uncertainty in Deep Learning for Construction of Prediction Intervals](https://mlsanity.com/paper/2104.12953/) (2021)
- [Uncertainty-Aware Null Space Networks for Data-Consistent Image Reconstruction](https://mlsanity.com/paper/2304.06955/) (2023)
- [Predictive uncertainty estimation in deep learning for lung carcinoma classification in digital pathology under real dataset shifts](https://mlsanity.com/paper/2408.08432/) (2024)
- [Evaluating deep learning models for fault diagnosis of a rotating machinery with epistemic and aleatoric uncertainty](https://mlsanity.com/paper/2412.18980/) (2024)
- [How To Effectively Train An Ensemble Of Faster R-CNN Object Detectors To Quantify Uncertainty](https://mlsanity.com/paper/2310.04829/) (2023)
- [SEF: A Method for Computing Prediction Intervals by Shifting the Error Function in Neural Networks](https://mlsanity.com/paper/2409.05206/) (2024)

## Abstract (arXiv)

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