# Real-Time Nonparametric Anomaly Detection in High-Dimensional Settings

arXiv: https://arxiv.org/abs/1809.05250 · HTML: https://mlsanity.com/paper/1809.05250/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Sep 2018.

## Built on by (most cited first, 10 of 10)

- [A Log-Linear Non-Parametric Online Changepoint Detection Algorithm based on Functional Pruning](https://mlsanity.com/paper/2302.02718/) (2023)
- [Few-Shot Anomaly Detection via Category-Agnostic Registration Learning](https://mlsanity.com/paper/2406.08810/) (2024)
- [Sequential Multivariate Change Detection with Calibrated and Memoryless False Detection Rates](https://mlsanity.com/paper/2108.00883/) (2021)
- [Review of the state of the art in autonomous artificial intelligence](https://mlsanity.com/paper/2210.10659/) (2022)
- [OptIForest: Optimal Isolation Forest for Anomaly Detection](https://mlsanity.com/paper/2306.12703/) (2023)
- [Optimal Online Change Detection via Random Fourier Features](https://mlsanity.com/paper/2505.17789/) (2025)
- [Super forecasting the technological singularity risks from artificial intelligence](https://mlsanity.com/paper/2301.10028/) (2022)
- [Noise-contrastive Online Change Point Detection](https://mlsanity.com/paper/2206.10143/) (2022)
- [Score-based change point detection via tracking the best of infinitely many experts](https://mlsanity.com/paper/2408.14073/) (2024)
- [RDD: Pareto Analysis of the Rate-Distortion-Distinguishability Trade-off](https://mlsanity.com/paper/2509.24805/) (2025)

## Abstract (arXiv)

Timely detection of abrupt anomalies is crucial for real-time monitoring and security of modern systems producing high-dimensional data. With this goal, we propose effective and scalable algorithms. Proposed algorithms are nonparametric as both the nominal and anomalous multivariate data distributions are assumed unknown. We extract useful univariate summary statistics and perform anomaly detection in a single-dimensional space. We model anomalies as persistent outliers and propose to detect them via a cumulative sum-like algorithm. In case the observed data have a low intrinsic dimensionality, we learn a submanifold in which the nominal data are embedded and evaluate whether the sequentially acquired data persistently deviate from the nominal submanifold. Further, in the general case, we learn an acceptance region for nominal data via Geometric Entropy Minimization and evaluate whether the sequentially observed data persistently fall outside the acceptance region. We provide an asymptotic lower bound and an asymptotic approximation for the average false alarm period of the proposed algorithm. Moreover, we provide a sufficient condition to asymptotically guarantee that the decision statistic of the proposed algorithm does not diverge in the absence of anomalies. Experiments illustrate the effectiveness of the proposed schemes in quick and accurate anomaly detection in high-dimensional settings.