# Anomaly Detection with Density Estimation

arXiv: https://arxiv.org/abs/2001.04990 · HTML: https://mlsanity.com/paper/2001.04990/

## Key facts

- Cited by 72 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Jan 2020.

## Built on by (most cited first, 30 of 72)

- [A Living Review of Machine Learning for Particle Physics](https://mlsanity.com/paper/2102.02770/) (2021)
- [Machine Learning in the Search for New Fundamental Physics](https://mlsanity.com/paper/2112.03769/) (2021)
- [CaloFlow: Fast and Accurate Generation of Calorimeter Showers with Normalizing Flows](https://mlsanity.com/paper/2106.05285/) (2021)
- [Fair Normalizing Flows](https://mlsanity.com/paper/2106.05937/) (2021)
- [Machine Learning for Anomaly Detection in Particle Physics](https://mlsanity.com/paper/2312.14190/) (2023)
- [The Dark Machines Anomaly Score Challenge: Benchmark Data and Model Independent Event Classification for the Large Hadron Collider](https://mlsanity.com/paper/2105.14027/) (2021)
- [Distribution learning via neural differential equations: a nonparametric statistical perspective](https://mlsanity.com/paper/2309.01043/) (2023)
- [Better Latent Spaces for Better Autoencoders](https://mlsanity.com/paper/2104.08291/) (2021)
- [Learning new physics efficiently with nonparametric methods](https://mlsanity.com/paper/2204.02317/) (2022)
- [Bump Hunting in Latent Space](https://mlsanity.com/paper/2103.06595/) (2021)
- [Deep Generative Models for Detector Signature Simulation: A Taxonomic Review](https://mlsanity.com/paper/2312.09597/) (2023)
- [Understanding Event-Generation Networks via Uncertainties](https://mlsanity.com/paper/2104.04543/) (2021)
- [Deep Learning Advancements in Anomaly Detection: A Comprehensive Survey](https://mlsanity.com/paper/2503.13195/) (2025)
- [Challenges for Unsupervised Anomaly Detection in Particle Physics](https://mlsanity.com/paper/2110.06948/) (2021)
- [E Pluribus Unum Ex Machina: Learning from Many Collider Events at Once](https://mlsanity.com/paper/2101.07263/) (2021)
- [Online-compatible Unsupervised Non-resonant Anomaly Detection](https://mlsanity.com/paper/2111.06417/) (2021)
- [Comparing Weak- and Unsupervised Methods for Resonant Anomaly Detection](https://mlsanity.com/paper/2104.02092/) (2021)
- [Convolutional L2LFlows: Generating Accurate Showers in Highly Granular Calorimeters Using Convolutional Normalizing Flows](https://mlsanity.com/paper/2405.20407/) (2024)
- [High-dimensional and Permutation Invariant Anomaly Detection](https://mlsanity.com/paper/2306.03933/) (2023)
- [nu-Flows: Conditional Neutrino Regression](https://mlsanity.com/paper/2207.00664/) (2022)
- [Anomalies, Representations, and Self-Supervision](https://mlsanity.com/paper/2301.04660/) (2023)
- [Learning Likelihood Ratios with Neural Network Classifiers](https://mlsanity.com/paper/2305.10500/) (2023)
- [Latent Space Refinement for Deep Generative Models](https://mlsanity.com/paper/2106.00792/) (2021)
- [Snowmass 2021 Computational Frontier CompF03 Topical Group Report: Machine Learning](https://mlsanity.com/paper/2209.07559/) (2022)
- [CURTAINs Flows For Flows: Constructing Unobserved Regions with Maximum Likelihood Estimation](https://mlsanity.com/paper/2305.04646/) (2023)
- [Improving new physics searches with diffusion models for event observables and jet constituents](https://mlsanity.com/paper/2312.10130/) (2023)
- [Unravelling physics beyond the standard model with classical and quantum anomaly detection](https://mlsanity.com/paper/2301.10787/) (2023)
- [IRC-safe Graph Autoencoder for unsupervised anomaly detection](https://mlsanity.com/paper/2204.12231/) (2022)
- [Neural Embedding: Learning the Embedding of the Manifold of Physics Data](https://mlsanity.com/paper/2208.05484/) (2022)
- [Anomaly Detection with Variance Stabilized Density Estimation](https://mlsanity.com/paper/2306.00582/) (2023)

## Abstract (arXiv)

We leverage recent breakthroughs in neural density estimation to propose a new unsupervised anomaly detection technique (ANODE). By estimating the probability density of the data in a signal region and in sidebands, and interpolating the latter into the signal region, a likelihood ratio of data vs. background can be constructed. This likelihood ratio is broadly sensitive to overdensities in the data that could be due to localized anomalies. In addition, a unique potential benefit of the ANODE method is that the background can be directly estimated using the learned densities. Finally, ANODE is robust against systematic differences between signal region and sidebands, giving it broader applicability than other methods. We demonstrate the power of this new approach using the LHC Olympics 2020 R&D Dataset. We show how ANODE can enhance the significance of a dijet bump hunt by up to a factor of 7 with a 10% accuracy on the background prediction. While the LHC is used as the recurring example, the methods developed here have a much broader applicability to anomaly detection in physics and beyond.