# Uncertainty Measurement of Deep Learning System based on the Convex Hull of Training Sets

arXiv: https://arxiv.org/abs/2405.16082 · HTML: https://mlsanity.com/paper/2405.16082/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 45 references that are in the map.
- First posted on arXiv 25 May 2024.

## Builds on (most cited first, 23 of 23)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Towards Evaluating the Robustness of Neural Networks](https://mlsanity.com/paper/1608.04644/) (2016)
- [Adversarial examples in the physical world](https://mlsanity.com/paper/1607.02533/) (2016)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [MedMNIST v2 -- A large-scale lightweight benchmark for 2D and 3D biomedical image classification](https://mlsanity.com/paper/2110.14795/) (2021)
- [High-Performance Large-Scale Image Recognition Without Normalization](https://mlsanity.com/paper/2102.06171/) (2021)
- [DeepXplore: Automated Whitebox Testing of Deep Learning Systems](https://mlsanity.com/paper/1705.06640/) (2017)
- [DeepTest: Automated Testing of Deep-Neural-Network-driven Autonomous Cars](https://mlsanity.com/paper/1708.08559/) (2017)
- [DeepGauge: Multi-Granularity Testing Criteria for Deep Learning Systems](https://mlsanity.com/paper/1803.07519/) (2018)
- [Guiding Deep Learning System Testing using Surprise Adequacy](https://mlsanity.com/paper/1808.08444/) (2018)
- [Invertible Concept-based Explanations for CNN Models with Non-negative Concept Activation Vectors](https://mlsanity.com/paper/2006.15417/) (2020)
- [A General Framework for Uncertainty Estimation in Deep Learning](https://mlsanity.com/paper/1907.06890/) (2019)
- [Confidence-Aware Learning for Deep Neural Networks](https://mlsanity.com/paper/2007.01458/) (2020)
- [Recent advances and clinical applications of deep learning in medical image analysis](https://mlsanity.com/paper/2105.13381/) (2021)
- [Grounding Visual Explanations](https://mlsanity.com/paper/1807.09685/) (2018)
- [PRIMA: General and Precise Neural Network Certification via Scalable Convex Hull Approximations](https://mlsanity.com/paper/2103.03638/) (2021)
- [Confidence Estimation via Auxiliary Models](https://mlsanity.com/paper/2012.06508/) (2020)
- [Boosting Operational DNN Testing Efficiency through Conditioning](https://mlsanity.com/paper/1906.02533/) (2019)
- [Input Prioritization for Testing Neural Networks](https://mlsanity.com/paper/1901.03768/) (2019)
- [Sparse Approximation via Generating Point Sets](https://mlsanity.com/paper/1507.02574/) (2015)

## Built on by (most cited first, 1 of 1)

- [HybridFlow: Quantification of Aleatoric and Epistemic Uncertainty with a Single Hybrid Model](https://mlsanity.com/paper/2510.05054/) (2025)

## Abstract (arXiv)

Deep Learning (DL) has made remarkable achievements in computer vision and adopted in safety critical domains such as medical imaging or autonomous drive. Thus, it is necessary to understand the uncertainty of the model to effectively reduce accidents and losses due to misjudgment of the Deep Neural Networks (DNN). This can start by efficiently selecting data that could potentially malfunction to the model. Traditionally, data collection and labeling have been done manually, but recently test data selection methods have emerged that focus on capturing samples that are not relevant to what the model had been learned. They're selected based on the activation pattern of neurons in DNN, entropy minimization based on softmax output of the DL. However, these methods cannot quantitatively analyze the extent to which unseen samples are extrapolated from the training data. Therefore, we propose To-hull Uncertainty and Closure Ratio, which measures an uncertainty of trained model based on the convex hull of training data. It can observe the positional relation between the convex hull of the learned data and an unseen sample and infer how extrapolate the sample is from the convex hull. To evaluate the proposed method, we conduct empirical studies on popular datasets and DNN models, compared to state-of-the art test selection metrics. As a result of the experiment, the proposed To-hull Uncertainty is effective in finding samples with unusual patterns (e.g. adversarial attack) compared to the existing test selection metric.