# Multiple Testing Framework for Out-of-Distribution Detection

arXiv: https://arxiv.org/abs/2206.09522 · HTML: https://mlsanity.com/paper/2206.09522/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 36 references that are in the map.
- First posted on arXiv 20 Jun 2022.

## Builds on (most cited first, 19 of 19)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [Enhancing The Reliability of Out-of-distribution Image Detection in Neural Networks](https://mlsanity.com/paper/1706.02690/) (2017)
- [Energy-based Out-of-distribution Detection](https://mlsanity.com/paper/2010.03759/) (2020)
- [Deep Anomaly Detection with Outlier Exposure](https://mlsanity.com/paper/1812.04606/) (2018)
- [Deep Neural Networks are Easily Fooled: High Confidence Predictions for Unrecognizable Images](https://mlsanity.com/paper/1412.1897/) (2014)
- [On the Importance of Gradients for Detecting Distributional Shifts in the Wild](https://mlsanity.com/paper/2110.00218/) (2021)
- [Exploring the Limits of Out-of-Distribution Detection](https://mlsanity.com/paper/2106.03004/) (2021)
- [Learn then Test: Calibrating Predictive Algorithms to Achieve Risk Control](https://mlsanity.com/paper/2110.01052/) (2021)
- [Testing for Outliers with Conformal p-values](https://mlsanity.com/paper/2104.08279/) (2021)
- [Understanding Failures in Out-of-Distribution Detection with Deep Generative Models](https://mlsanity.com/paper/2107.06908/) (2021)
- [Tracking the risk of a deployed model and detecting harmful distribution shifts](https://mlsanity.com/paper/2110.06177/) (2021)
- [A statistical framework for efficient out of distribution detection in deep neural networks](https://mlsanity.com/paper/2102.12967/) (2021)
- [iDECODe: In-distribution Equivariance for Conformal Out-of-distribution Detection](https://mlsanity.com/paper/2201.02331/) (2022)
- [Model-agnostic out-of-distribution detection using combined statistical tests](https://mlsanity.com/paper/2203.01097/) (2022)

## Built on by (most cited first, 2 of 2)

- [Boosting Out-of-Distribution Detection with Multiple Pre-trained Models](https://mlsanity.com/paper/2212.12720/) (2022)
- [DSDE: Using Proportion Estimation to Improve Model Selection for Out-of-Distribution Detection](https://mlsanity.com/paper/2411.01487/) (2024)

## Abstract (arXiv)

We study the problem of Out-of-Distribution (OOD) detection, that is, detecting whether a learning algorithm's output can be trusted at inference time. While a number of tests for OOD detection have been proposed in prior work, a formal framework for studying this problem is lacking. We propose a definition for the notion of OOD that includes both the input distribution and the learning algorithm, which provides insights for the construction of powerful tests for OOD detection. We propose a multiple hypothesis testing inspired procedure to systematically combine any number of different statistics from the learning algorithm using conformal p-values. We further provide strong guarantees on the probability of incorrectly classifying an in-distribution sample as OOD. In our experiments, we find that threshold-based tests proposed in prior work perform well in specific settings, but not uniformly well across different types of OOD instances. In contrast, our proposed method that combines multiple statistics performs uniformly well across different datasets and neural networks.