# Leveraging the Christoffel Function for Outlier Detection in Data Streams

arXiv: https://arxiv.org/abs/2508.16617 · HTML: https://mlsanity.com/paper/2508.16617/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 52 references that are in the map.
- First posted on arXiv 13 Aug 2025.

## Builds on (most cited first, 5 of 5)

- [A Unifying Review of Deep and Shallow Anomaly Detection](https://mlsanity.com/paper/2009.11732/) (2020)
- [How to Evaluate the Quality of Unsupervised Anomaly Detection Algorithms?](https://mlsanity.com/paper/1607.01152/) (2016)
- [Optimal Quantile Approximation in Streams](https://mlsanity.com/paper/1603.05346/) (2016)
- [Rate of convergence for geometric inference based on the empirical Christoffel function](https://mlsanity.com/paper/1910.14458/) (2019)
- [Moment-Based Quantile Sketches for Efficient High Cardinality Aggregation Queries](https://mlsanity.com/paper/1803.01969/) (2018)

## Built on by (most cited first, 4 of 4)

- [Scalable anomaly detection via a univariate Christoffel function](https://mlsanity.com/paper/2606.12483/) (2026)
- [CLOE: Christoffel Loss Autoencoder for Anomaly Detection](https://mlsanity.com/paper/2607.20530/) (2026)
- [Cost Trade-offs in Matrix Inversion Updates for Streaming Outlier Detection](https://mlsanity.com/paper/2603.16697/) (2026)
- [Early Failure Prediction from Near-Anomaly Detection: A Proactive Approach](https://mlsanity.com/paper/2607.26704/) (2026)

## Abstract (arXiv)

Outlier detection holds significant importance in the realm of data mining, particularly with the growing pervasiveness of data acquisition methods. The ability to identify outliers in data streams is essential for maintaining data quality and detecting faults. However, dealing with data streams presents challenges due to the non-stationary nature of distributions and the ever-increasing data volume. While numerous methods have been proposed to tackle this challenge, a common drawback is the lack of straightforward parameterization in many of them. This article introduces two novel methods: DyCF and DyCG. DyCF leverages the Christoffel function from the theory of approximation and orthogonal polynomials. Conversely, DyCG capitalizes on the growth properties of the Christoffel function, eliminating the need for tuning parameters. Both approaches are firmly rooted in a well-defined algebraic framework, meeting crucial demands for data stream processing, with a specific focus on addressing low-dimensional aspects and maintaining data history without memory cost. A comprehensive comparison between DyCF, DyCG, and state-of-the-art methods is presented, using both synthetic and real industrial data streams. The results show that DyCF outperforms fine-tuning methods, offering superior performance in terms of execution time and memory usage. DyCG performs less well, but has the considerable advantage of requiring no tuning at all.