# Detecting Out-of-Distribution Samples via Conditional Distribution Entropy with Optimal Transport

arXiv: https://arxiv.org/abs/2401.11726 · HTML: https://mlsanity.com/paper/2401.11726/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 40 references that are in the map.
- First posted on arXiv 22 Jan 2024.

## Builds on (most cited first, 27 of 27)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Supervised Contrastive Learning](https://mlsanity.com/paper/2004.11362/) (2020)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Describing Textures in the Wild](https://mlsanity.com/paper/1311.3618/) (2013)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [Unsupervised Representation Learning by Predicting Image Rotations](https://mlsanity.com/paper/1803.07728/) (2018)
- [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)
- [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)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Out-of-Distribution Detection with Deep Nearest Neighbors](https://mlsanity.com/paper/2204.06507/) (2022)
- [CSI: Novelty Detection via Contrastive Learning on Distributionally Shifted Instances](https://mlsanity.com/paper/2007.08176/) (2020)
- [PixelCNN++: Improving the PixelCNN with Discretized Logistic Mixture Likelihood and Other Modifications](https://mlsanity.com/paper/1701.05517/) (2017)
- [Generalized ODIN: Detecting Out-of-distribution Image without Learning from Out-of-distribution Data](https://mlsanity.com/paper/2002.11297/) (2020)
- [Exploring the Limits of Out-of-Distribution Detection](https://mlsanity.com/paper/2106.03004/) (2021)
- [SSD: A Unified Framework for Self-Supervised Outlier Detection](https://mlsanity.com/paper/2103.12051/) (2021)
- [Proxy Anchor Loss for Deep Metric Learning](https://mlsanity.com/paper/2003.13911/) (2020)
- [Contrastive Training for Improved Out-of-Distribution Detection](https://mlsanity.com/paper/2007.05566/) (2020)
- [How to Exploit Hyperspherical Embeddings for Out-of-Distribution Detection?](https://mlsanity.com/paper/2203.04450/) (2022)
- [Is Out-of-Distribution Detection Learnable?](https://mlsanity.com/paper/2210.14707/) (2022)
- [POEM: Out-of-Distribution Detection with Posterior Sampling](https://mlsanity.com/paper/2206.13687/) (2022)
- [Provable Guarantees for Understanding Out-of-distribution Detection](https://mlsanity.com/paper/2112.00787/) (2021)
- [Towards Maximizing the Representation Gap between In-Domain & Out-of-Distribution Examples](https://mlsanity.com/paper/2010.10474/) (2020)

## Abstract (arXiv)

When deploying a trained machine learning model in the real world, it is inevitable to receive inputs from out-of-distribution (OOD) sources. For instance, in continual learning settings, it is common to encounter OOD samples due to the non-stationarity of a domain. More generally, when we have access to a set of test inputs, the existing rich line of OOD detection solutions, especially the recent promise of distance-based methods, falls short in effectively utilizing the distribution information from training samples and test inputs. In this paper, we argue that empirical probability distributions that incorporate geometric information from both training samples and test inputs can be highly beneficial for OOD detection in the presence of test inputs available. To address this, we propose to model OOD detection as a discrete optimal transport problem. Within the framework of optimal transport, we propose a novel score function known as the conditional distribution entropy to quantify the uncertainty of a test input being an OOD sample. Our proposal inherits the merits of certain distance-based methods while eliminating the reliance on distribution assumptions, a-prior knowledge, and specific training mechanisms. Extensive experiments conducted on benchmark datasets demonstrate that our method outperforms its competitors in OOD detection.