Radon-Nikod'ym Derivative: Re-imagining Anomaly Detection from a Measure Theoretic Perspective

2025-02-25

AI Summary

论文提出基于测度理论的RN-Loss方法，通过将损失函数与Radon-Nikodým导数相乘，提升异常检测性能，并在多领域数据集上验证其优越性。

Technology Category

• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Machine Learning: Adversarial Learning & Robustness
• Computer Vision: Adversarial Attacks & Robustness

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Which principle underpins the design of an effective anomaly detection loss function? The answer lies in the concept of nthm{} theorem, a fundamental concept in measure theory. The key insight is -- Multiplying the vanilla loss function with the nthm{} derivative improves the performance across the board. We refer to this as RN-Loss. This is established using PAC learnability of anomaly detection. We further show that the nthm{} derivative offers important insights into unsupervised clustering based anomaly detections as well. We evaluate our algorithm on 96 datasets, including univariate and multivariate data from diverse domains, including healthcare, cybersecurity, and finance. We show that RN-Derivative algorithms outperform state-of-the-art methods on 68% of Multivariate datasets (based on F-1 scores) and also achieves peak F1-scores on 72% of time series (Univariate) datasets.

Problem

• Enhancing anomaly detection loss functions
• Applying Radon-Nikodým derivative to improve performance
• Outperforming methods in multivariate and univariate datasets

Innovation

• RN-Loss enhances anomaly detection
• RN-Derivative improves unsupervised clustering
• PAC learnability validates anomaly detection