# Density of States Estimation for Out-of-Distribution Detection

arXiv: https://arxiv.org/abs/2006.09273 · HTML: https://mlsanity.com/paper/2006.09273/

## Key facts

- Cited by 74 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jun 2020.

## Built on by (most cited first, 30 of 74)

- [CutPaste: Self-Supervised Learning for Anomaly Detection and Localization](https://mlsanity.com/paper/2104.04015/) (2021)
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- [Denoising diffusion models for out-of-distribution detection](https://mlsanity.com/paper/2211.07740/) (2022)
- [Understanding Failures in Out-of-Distribution Detection with Deep Generative Models](https://mlsanity.com/paper/2107.06908/) (2021)
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- [Does Your Dermatology Classifier Know What It Doesn't Know? Detecting the Long-Tail of Unseen Conditions](https://mlsanity.com/paper/2104.03829/) (2021)
- [Unsupervised Out-of-Distribution Detection with Diffusion Inpainting](https://mlsanity.com/paper/2302.10326/) (2023)
- [Neural Mean Discrepancy for Efficient Out-of-Distribution Detection](https://mlsanity.com/paper/2104.11408/) (2021)
- [A Geometric Explanation of the Likelihood OOD Detection Paradox](https://mlsanity.com/paper/2403.18910/) (2024)
- [Out-of-Distribution Detection with a Single Unconditional Diffusion Model](https://mlsanity.com/paper/2405.11881/) (2024)
- [Reliable and Trustworthy Machine Learning for Health Using Dataset Shift Detection](https://mlsanity.com/paper/2110.14019/) (2021)
- [Sensitivity-Aware Amortized Bayesian Inference](https://mlsanity.com/paper/2310.11122/) (2023)
- [A Learning Based Hypothesis Test for Harmful Covariate Shift](https://mlsanity.com/paper/2212.02742/) (2022)
- [On Out-of-distribution Detection with Energy-based Models](https://mlsanity.com/paper/2107.08785/) (2021)
- [Bayesian OOD detection with aleatoric uncertainty and outlier exposure](https://mlsanity.com/paper/2102.12959/) (2021)
- [Task-agnostic Continual Learning with Hybrid Probabilistic Models](https://mlsanity.com/paper/2106.12772/) (2021)
- [Entropic Issues in Likelihood-Based OOD Detection](https://mlsanity.com/paper/2109.10794/) (2021)
- [Adversarial vulnerability of powerful near out-of-distribution detection](https://mlsanity.com/paper/2201.07012/) (2022)
- [Model-agnostic out-of-distribution detection using combined statistical tests](https://mlsanity.com/paper/2203.01097/) (2022)
- [Out-of-Distribution Detection Methods Answer the Wrong Questions](https://mlsanity.com/paper/2507.01831/) (2025)
- [Natural Posterior Network: Deep Bayesian Uncertainty for Exponential Family Distributions](https://mlsanity.com/paper/2105.04471/) (2021)
- [Out-of-Distribution Detection with Reconstruction Error and Typicality-based Penalty](https://mlsanity.com/paper/2212.12641/) (2022)
- [Likelihood-based Out-of-Distribution Detection with Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2310.17432/) (2023)
- [Forte : Finding Outliers with Representation Typicality Estimation](https://mlsanity.com/paper/2410.01322/) (2024)
- [Boosting Out-of-Distribution Detection with Multiple Pre-trained Models](https://mlsanity.com/paper/2212.12720/) (2022)
- [Detecting Anomalous Event Sequences with Temporal Point Processes](https://mlsanity.com/paper/2106.04465/) (2021)
- [Detect, Distill and Update: Learned DB Systems Facing Out of Distribution Data](https://mlsanity.com/paper/2210.05508/) (2022)
- [CLIP-driven Outliers Synthesis for few-shot OOD detection](https://mlsanity.com/paper/2404.00323/) (2024)
- [K4: Online Log Anomaly Detection Via Unsupervised Typicality Learning](https://mlsanity.com/paper/2507.20051/) (2025)

## Abstract (arXiv)

Perhaps surprisingly, recent studies have shown probabilistic model likelihoods have poor specificity for out-of-distribution (OOD) detection and often assign higher likelihoods to OOD data than in-distribution data. To ameliorate this issue we propose DoSE, the density of states estimator. Drawing on the statistical physics notion of ``density of states,'' the DoSE decision rule avoids direct comparison of model probabilities, and instead utilizes the ``probability of the model probability,'' or indeed the frequency of any reasonable statistic. The frequency is calculated using nonparametric density estimators (e.g., KDE and one-class SVM) which measure the typicality of various model statistics given the training data and from which we can flag test points with low typicality as anomalous. Unlike many other methods, DoSE requires neither labeled data nor OOD examples. DoSE is modular and can be trivially applied to any existing, trained model. We demonstrate DoSE's state-of-the-art performance against other unsupervised OOD detectors on previously established ``hard'' benchmarks.