Paper
A Kernel Two-Sample Test Invariant under Group Action with Applications to Functional Data
Authors
Madison Giacofci, Anouar Meynaoui, Alex Podgorny
Abstract
We introduce a kernel-based two-sample test for comparing probability distributions up to group actions. Our construction yields invariant kernels for locally compact $σ$-compact groups and extends classical Haar-based approaches beyond the compact setting. The resulting invariant Maximum Mean Discrepancy (MMD) test is developed in a general framework where the sample space is assumed to be Polish. Under natural conditions, the invariant kernel induces a characteristic kernel on the quotient space, ensuring consistency of the associated MMD test. The method is well suited to functional data, where invariances such as temporal shifts arise naturally, and its effectiveness is illustrated through simulation studies.
Metadata
Related papers
Fractal universe and quantum gravity made simple
Fabio Briscese, Gianluca Calcagni • 2026-03-25
POLY-SIM: Polyglot Speaker Identification with Missing Modality Grand Challenge 2026 Evaluation Plan
Marta Moscati, Muhammad Saad Saeed, Marina Zanoni, Mubashir Noman, Rohan Kuma... • 2026-03-25
LensWalk: Agentic Video Understanding by Planning How You See in Videos
Keliang Li, Yansong Li, Hongze Shen, Mengdi Liu, Hong Chang, Shiguang Shan • 2026-03-25
Orientation Reconstruction of Proteins using Coulomb Explosions
Tomas André, Alfredo Bellisario, Nicusor Timneanu, Carl Caleman • 2026-03-25
The role of spatial context and multitask learning in the detection of organic and conventional farming systems based on Sentinel-2 time series
Jan Hemmerling, Marcel Schwieder, Philippe Rufin, Leon-Friedrich Thomas, Mire... • 2026-03-25
Raw Data (Debug)
{
"raw_xml": "<entry>\n <id>http://arxiv.org/abs/2603.16294v1</id>\n <title>A Kernel Two-Sample Test Invariant under Group Action with Applications to Functional Data</title>\n <updated>2026-03-17T09:31:38Z</updated>\n <link href='https://arxiv.org/abs/2603.16294v1' rel='alternate' type='text/html'/>\n <link href='https://arxiv.org/pdf/2603.16294v1' rel='related' title='pdf' type='application/pdf'/>\n <summary>We introduce a kernel-based two-sample test for comparing probability distributions up to group actions. Our construction yields invariant kernels for locally compact $σ$-compact groups and extends classical Haar-based approaches beyond the compact setting. The resulting invariant Maximum Mean Discrepancy (MMD) test is developed in a general framework where the sample space is assumed to be Polish. Under natural conditions, the invariant kernel induces a characteristic kernel on the quotient space, ensuring consistency of the associated MMD test. The method is well suited to functional data, where invariances such as temporal shifts arise naturally, and its effectiveness is illustrated through simulation studies.</summary>\n <category scheme='http://arxiv.org/schemas/atom' term='math.ST'/>\n <published>2026-03-17T09:31:38Z</published>\n <arxiv:primary_category term='math.ST'/>\n <author>\n <name>Madison Giacofci</name>\n <arxiv:affiliation>UR2, IRMAR</arxiv:affiliation>\n </author>\n <author>\n <name>Anouar Meynaoui</name>\n <arxiv:affiliation>UR2, IRMAR</arxiv:affiliation>\n </author>\n <author>\n <name>Alex Podgorny</name>\n <arxiv:affiliation>ENSAI, CREST</arxiv:affiliation>\n </author>\n </entry>"
}