# Understanding Measures of Uncertainty for Adversarial Example Detection

arXiv: https://arxiv.org/abs/1803.08533 · HTML: https://mlsanity.com/paper/1803.08533/

## Key facts

- Cited by 177 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Mar 2018.

## Built on by (most cited first, 30 of 177)

- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [A Comprehensive Survey on Test-Time Adaptation under Distribution Shifts](https://mlsanity.com/paper/2303.15361/) (2023)
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- [Quantifying Aleatoric and Epistemic Uncertainty in Machine Learning: Are Conditional Entropy and Mutual Information Appropriate Measures?](https://mlsanity.com/paper/2209.03302/) (2022)
- [Benchmarking Uncertainty Quantification Methods for Large Language Models with LM-Polygraph](https://mlsanity.com/paper/2406.15627/) (2024)
- [Shifts: A Dataset of Real Distributional Shift Across Multiple Large-Scale Tasks](https://mlsanity.com/paper/2107.07455/) (2021)
- [A Survey of Safety and Trustworthiness of Large Language Models through the Lens of Verification and Validation](https://mlsanity.com/paper/2305.11391/) (2023)
- [Prior and Posterior Networks: A Survey on Evidential Deep Learning Methods For Uncertainty Estimation](https://mlsanity.com/paper/2110.03051/) (2021)
- [Deep Ensembles Work, But Are They Necessary?](https://mlsanity.com/paper/2202.06985/) (2022)
- [Adversarial Example Detection for DNN Models: A Review and Experimental Comparison](https://mlsanity.com/paper/2105.00203/) (2021)
- [A Call to Reflect on Evaluation Practices for Failure Detection in Image Classification](https://mlsanity.com/paper/2211.15259/) (2022)
- [Improving black-box optimization in VAE latent space using decoder uncertainty](https://mlsanity.com/paper/2107.00096/) (2021)
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- [Posterior Meta-Replay for Continual Learning](https://mlsanity.com/paper/2103.01133/) (2021)
- [Credal Bayesian Deep Learning](https://mlsanity.com/paper/2302.09656/) (2023)
- [Rethinking Aleatoric and Epistemic Uncertainty](https://mlsanity.com/paper/2412.20892/) (2024)
- [Generating Interpretable Counterfactual Explanations By Implicit Minimisation of Epistemic and Aleatoric Uncertainties](https://mlsanity.com/paper/2103.08951/) (2021)
- [LiBRe: A Practical Bayesian Approach to Adversarial Detection](https://mlsanity.com/paper/2103.14835/) (2021)
- [Is the Volume of a Credal Set a Good Measure for Epistemic Uncertainty?](https://mlsanity.com/paper/2306.09586/) (2023)
- [Multi-Objective Hyperparameter Optimization in Machine Learning -- An Overview](https://mlsanity.com/paper/2206.07438/) (2022)
- [Explaining Predictive Uncertainty with Information Theoretic Shapley Values](https://mlsanity.com/paper/2306.05724/) (2023)
- [Uncertainty-Aware Machine Translation Evaluation](https://mlsanity.com/paper/2109.06352/) (2021)
- [Second-Order Uncertainty Quantification: A Distance-Based Approach](https://mlsanity.com/paper/2312.00995/) (2023)
- [ImageNet-Hard: The Hardest Images Remaining from a Study of the Power of Zoom and Spatial Biases in Image Classification](https://mlsanity.com/paper/2304.05538/) (2023)
- [Learning to Reject with a Fixed Predictor: Application to Decontextualization](https://mlsanity.com/paper/2301.09044/) (2023)
- [Detecting Adversarial Examples from Sensitivity Inconsistency of Spatial-Transform Domain](https://mlsanity.com/paper/2103.04302/) (2021)
- [QU-BraTS: MICCAI BraTS 2020 Challenge on Quantifying Uncertainty in Brain Tumor Segmentation - Analysis of Ranking Scores and Benchmarking Results](https://mlsanity.com/paper/2112.10074/) (2021)
- [Quantification of Uncertainty with Adversarial Models](https://mlsanity.com/paper/2307.03217/) (2023)
- [Introducing an Improved Information-Theoretic Measure of Predictive Uncertainty](https://mlsanity.com/paper/2311.08309/) (2023)

## Abstract (arXiv)

Measuring uncertainty is a promising technique for detecting adversarial examples, crafted inputs on which the model predicts an incorrect class with high confidence. But many measures of uncertainty exist, including predictive en- tropy and mutual information, each capturing different types of uncertainty. We study these measures, and shed light on why mutual information seems to be effective at the task of adversarial example detection. We highlight failure modes for MC dropout, a widely used approach for estimating uncertainty in deep models. This leads to an improved understanding of the drawbacks of current methods, and a proposal to improve the quality of uncertainty estimates using probabilistic model ensembles. We give illustrative experiments using MNIST to demonstrate the intuition underlying the different measures of uncertainty, as well as experiments on a real world Kaggle dogs vs cats classification dataset.