# An Upper Bound for the Distribution Overlap Index and Its Applications

arXiv: https://arxiv.org/abs/2212.08701 · HTML: https://mlsanity.com/paper/2212.08701/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 57 references that are in the map.
- First posted on arXiv 16 Dec 2022.

## Builds on (most cited first, 22 of 22)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [Describing Textures in the Wild](https://mlsanity.com/paper/1311.3618/) (2013)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015)
- [Energy-based Out-of-distribution Detection](https://mlsanity.com/paper/2010.03759/) (2020)
- [Generalized Out-of-Distribution Detection: A Survey](https://mlsanity.com/paper/2110.11334/) (2021)
- [Network In Network](https://mlsanity.com/paper/1312.4400/) (2013)
- [Fine-Pruning: Defending Against Backdooring Attacks on Deep Neural Networks](https://mlsanity.com/paper/1805.12185/) (2018)
- [Unsupervised Anomaly Detection with Generative Adversarial Networks to Guide Marker Discovery](https://mlsanity.com/paper/1703.05921/) (2017)
- [STRIP: A Defence Against Trojan Attacks on Deep Neural Networks](https://mlsanity.com/paper/1902.06531/) (2019)
- [Invisible Backdoor Attack with Sample-Specific Triggers](https://mlsanity.com/paper/2012.03816/) (2020)
- [Reflection Backdoor: A Natural Backdoor Attack on Deep Neural Networks](https://mlsanity.com/paper/2007.02343/) (2020)
- [OCGAN: One-class Novelty Detection Using GANs with Constrained Latent Representations](https://mlsanity.com/paper/1903.08550/) (2019)
- [TurkerGaze: Crowdsourcing Saliency with Webcam based Eye Tracking](https://mlsanity.com/paper/1504.06755/) (2015)
- [Rethinking the Backdoor Attacks' Triggers: A Frequency Perspective](https://mlsanity.com/paper/2104.03413/) (2021)
- [Provable Guarantees for Understanding Out-of-distribution Detection](https://mlsanity.com/paper/2112.00787/) (2021)
- [One-Class Classification: Taxonomy of Study and Review of Techniques](https://mlsanity.com/paper/1312.0049/) (2013)
- [NNoculation: Catching BadNets in the Wild](https://mlsanity.com/paper/2002.08313/) (2020)
- [Detecting Backdoors in Neural Networks Using Novel Feature-Based Anomaly Detection](https://mlsanity.com/paper/2011.02526/) (2020)
- [Privacy-Preserving Collaborative Learning through Feature Extraction](https://mlsanity.com/paper/2212.06322/) (2022)

## Abstract (arXiv)

This paper proposes an easy-to-compute upper bound for the overlap index between two probability distributions without requiring any knowledge of the distribution models. The computation of our bound is time-efficient and memory-efficient and only requires finite samples. The proposed bound shows its value in one-class classification and domain shift analysis. Specifically, in one-class classification, we build a novel one-class classifier by converting the bound into a confidence score function. Unlike most one-class classifiers, the training process is not needed for our classifier. Additionally, the experimental results show that our classifier can be accurate with only a small number of in-class samples and outperform many state-of-the-art methods on various datasets in different one-class classification scenarios. In domain shift analysis, we propose a theorem based on our bound. The theorem is useful in detecting the existence of domain shift and inferring data information. The detection and inference processes are both computation-efficient and memory-efficient. Our work shows significant promise toward broadening the applications of overlap-based metrics.