# Confidence estimation in Deep Neural networks via density modelling

arXiv: https://arxiv.org/abs/1707.07013 · HTML: https://mlsanity.com/paper/1707.07013/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jul 2017.

## Built on by (most cited first, 7 of 7)

- [MOS: Towards Scaling Out-of-distribution Detection for Large Semantic Space](https://mlsanity.com/paper/2105.01879/) (2021)
- [Enhanced Isotropy Maximization Loss: Seamless and High-Performance Out-of-Distribution Detection Simply Replacing the SoftMax Loss](https://mlsanity.com/paper/2105.14399/) (2021)
- [Confidence estimation of classification based on the distribution of the neural network output layer](https://mlsanity.com/paper/2210.07745/) (2022)
- [Exploring the Trade-off between Plausibility, Change Intensity and Adversarial Power in Counterfactual Explanations using Multi-objective Optimization](https://mlsanity.com/paper/2205.10232/) (2022)
- [Augmentation by Counterfactual Explanation -- Fixing an Overconfident Classifier](https://mlsanity.com/paper/2210.12196/) (2022)
- [Advancing Out-of-Distribution Detection through Data Purification and Dynamic Activation Function Design](https://mlsanity.com/paper/2403.03412/) (2024)
- [Towards Robust Deep Learning using Entropic Losses](https://mlsanity.com/paper/2208.03566/) (2022)

## Abstract (arXiv)

State-of-the-art Deep Neural Networks can be easily fooled into providing incorrect high-confidence predictions for images with small amounts of adversarial noise. Does this expose a flaw with deep neural networks, or do we simply need a better way to estimate confidence? In this paper we consider the problem of accurately estimating predictive confidence. We formulate this problem as that of density modelling, and show how traditional methods such as softmax produce poor estimates. To address this issue, we propose a novel confidence measure based on density modelling approaches. We test these measures on images distorted by blur, JPEG compression, random noise and adversarial noise. Experiments show that our confidence measure consistently shows reduced confidence scores in the presence of such distortions - a property which softmax often lacks.