A Dictionary of Closed-Form Kernel Mean Embeddings

Fuente: arXiv
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Hauptverfasser: Briol, François-Xavier, Gessner, Alexandra, Karvonen, Toni, Mahsereci, Maren
Format: Preprint
Veröffentlicht: 2025
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author Briol, François-Xavier
Gessner, Alexandra
Karvonen, Toni
Mahsereci, Maren
author_facet Briol, François-Xavier
Gessner, Alexandra
Karvonen, Toni
Mahsereci, Maren
contents Kernel mean embeddings -- integrals of a kernel with respect to a probability distribution -- are essential in Bayesian quadrature, but also widely used in other computational tools for numerical integration or for statistical inference based on the maximum mean discrepancy. These methods often require, or are enhanced by, the availability of a closed-form expression for the kernel mean embedding. However, deriving such expressions can be challenging, limiting the applicability of kernel-based techniques when practitioners do not have access to a closed-form embedding. This paper addresses this limitation by providing a comprehensive dictionary of known kernel mean embeddings, along with practical tools for deriving new embeddings from known ones. We also provide a Python library that includes minimal implementations of the embeddings.
format Preprint
id arxiv_https___arxiv_org_abs_2504_18830
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A Dictionary of Closed-Form Kernel Mean Embeddings
Briol, François-Xavier
Gessner, Alexandra
Karvonen, Toni
Mahsereci, Maren
Machine Learning
Numerical Analysis
Computation
Kernel mean embeddings -- integrals of a kernel with respect to a probability distribution -- are essential in Bayesian quadrature, but also widely used in other computational tools for numerical integration or for statistical inference based on the maximum mean discrepancy. These methods often require, or are enhanced by, the availability of a closed-form expression for the kernel mean embedding. However, deriving such expressions can be challenging, limiting the applicability of kernel-based techniques when practitioners do not have access to a closed-form embedding. This paper addresses this limitation by providing a comprehensive dictionary of known kernel mean embeddings, along with practical tools for deriving new embeddings from known ones. We also provide a Python library that includes minimal implementations of the embeddings.
title A Dictionary of Closed-Form Kernel Mean Embeddings
topic Machine Learning
Numerical Analysis
Computation
url https://arxiv.org/abs/2504.18830