# Detecting Localized Density Anomalies in Multivariate Data via Coin-Flip Statistics

arXiv: https://arxiv.org/abs/2503.23927 · HTML: https://mlsanity.com/paper/2503.23927/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 62 references that are in the map.
- First posted on arXiv 31 Mar 2025.

## Builds on (most cited first, 15 of 15)

- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [A Unifying Review of Deep and Shallow Anomaly Detection](https://mlsanity.com/paper/2009.11732/) (2020)
- [On Wasserstein Two Sample Testing and Related Families of Nonparametric Tests](https://mlsanity.com/paper/1509.02237/) (2015)
- [On Contrastive Learning for Likelihood-free Inference](https://mlsanity.com/paper/2002.03712/) (2020)
- [Approximating Likelihood Ratios with Calibrated Discriminative Classifiers](https://mlsanity.com/paper/1506.02169/) (2015)
- [Likelihood-free inference by ratio estimation](https://mlsanity.com/paper/1611.10242/) (2016)
- [Anomaly Detection with Density Estimation](https://mlsanity.com/paper/2001.04990/) (2020)
- [Classification without labels: Learning from mixed samples in high energy physics](https://mlsanity.com/paper/1708.02949/) (2017)
- [DADApy: Distance-based Analysis of DAta-manifolds in Python](https://mlsanity.com/paper/2205.03373/) (2022)
- [Bump Hunting in Latent Space](https://mlsanity.com/paper/2103.06595/) (2021)
- [Automatic topography of high-dimensional data sets by non-parametric Density Peak clustering](https://mlsanity.com/paper/1802.10549/) (2018)
- [Comparing Weak- and Unsupervised Methods for Resonant Anomaly Detection](https://mlsanity.com/paper/2104.02092/) (2021)
- [Anomalies, Representations, and Self-Supervision](https://mlsanity.com/paper/2301.04660/) (2023)
- [PQMass: Probabilistic Assessment of the Quality of Generative Models using Probability Mass Estimation](https://mlsanity.com/paper/2402.04355/) (2024)
- [A Differentiable Rank-Based Objective For Better Feature Learning](https://mlsanity.com/paper/2502.09445/) (2025)

## Built on by (most cited first, 1 of 1)

- [Unsupervised Domain Shift Detection with Interpretable Subspace Attribution](https://mlsanity.com/paper/2605.15920/) (2026)

## Abstract (arXiv)

Detecting localized differences between two samples is a central task in scientific data analysis, required for the identification of signal events, regime changes, or model mismatch. We introduce EagleEye, a method that pinpoints local over- and under-densities in multivariate feature spaces. EagleEye assigns each point an anomaly score by encoding its ordered k-nearest-neighbour list as a binary membership sequence and testing whether the cumulative number of successes in this sequence is consistent with a binomial (coin-flipping) null model. In the presence of a genuine local anomaly, neighbours will preferentially belong to one of the two datasts, yielding an excess of ``successes'' relative to the binomial null model. These local, pointwise detections are consolidated into interpretable anomaly sets through a deterministic refinement procedure that can also estimate the irreducible background and local density anomaly purity. We demonstrate EagleEye's efficacy in three scenarios. We first consider an artificial data example with known localized over- and under-densities. Second, we demonstrate how EagleEye may be used for new physics searches at particle collider experiments in the presence of systematic background modelling differences. Finally, we conduct a climate analysis study that reveals localized changes in spatiotemporal temperature-pattern recurrence.