Summary of Variance Norms For Kernelized Anomaly Detection, by Thomas Cass et al.
Variance Norms for Kernelized Anomaly Detection
by Thomas Cass, Lukas Gonon, Nikita Zozoulenko
First submitted to arxiv on: 16 Jul 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Probability (math.PR)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary The paper proposes a unified theory for anomaly detection on Banach spaces using ideas from Cameron-Martin theory. This framework generalizes classical settings such as Euclidean, functional, and kernelized approaches to Mahalanobis-type anomaly detection. The authors show that the proposed variance norm can be consistently estimated using empirical measures, allowing for data-driven notions of anomaly distance. The framework also recovers the kernelized Mahalanobis distance by working on reproducing kernel Hilbert spaces. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper creates a new way to find unusual patterns in data using math from Cameron-Martin theory. This method can be used with different types of data, such as numbers or functions, and can handle complex relationships between variables. The authors prove that their approach is consistent and works well for many types of data. |
Keywords
* Artificial intelligence * Anomaly detection
