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Bibliographic Details
Main Authors: Bourigault, Pauline, Mandic, Danilo P.
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2501.15265
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author Bourigault, Pauline
Mandic, Danilo P.
author_facet Bourigault, Pauline
Mandic, Danilo P.
contents We present a novel approach to anomaly detection by integrating Generalized Hyperbolic (GH) processes into kernel-based methods. The GH distribution, known for its flexibility in modeling skewness, heavy tails, and kurtosis, helps to capture complex patterns in data that deviate from Gaussian assumptions. We propose a GH-based kernel function and utilize it within Kernel Density Estimation (KDE) and One-Class Support Vector Machines (OCSVM) to develop anomaly detection frameworks. Theoretical results confirmed the positive semi-definiteness and consistency of the GH-based kernel, ensuring its suitability for machine learning applications. Empirical evaluation on synthetic and real-world datasets showed that our method improves detection performance in scenarios involving heavy-tailed and asymmetric or imbalanced distributions. https://github.com/paulinebourigault/GHKernelAnomalyDetect
format Preprint
id arxiv_https___arxiv_org_abs_2501_15265
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Kernel-Based Anomaly Detection Using Generalized Hyperbolic Processes
Bourigault, Pauline
Mandic, Danilo P.
Machine Learning
We present a novel approach to anomaly detection by integrating Generalized Hyperbolic (GH) processes into kernel-based methods. The GH distribution, known for its flexibility in modeling skewness, heavy tails, and kurtosis, helps to capture complex patterns in data that deviate from Gaussian assumptions. We propose a GH-based kernel function and utilize it within Kernel Density Estimation (KDE) and One-Class Support Vector Machines (OCSVM) to develop anomaly detection frameworks. Theoretical results confirmed the positive semi-definiteness and consistency of the GH-based kernel, ensuring its suitability for machine learning applications. Empirical evaluation on synthetic and real-world datasets showed that our method improves detection performance in scenarios involving heavy-tailed and asymmetric or imbalanced distributions. https://github.com/paulinebourigault/GHKernelAnomalyDetect
title Kernel-Based Anomaly Detection Using Generalized Hyperbolic Processes
topic Machine Learning
url https://arxiv.org/abs/2501.15265