MMD-FUSE: Learning and Combining Kernels for Two-Sample Testing Without Data Splitting

Biggs, Felix; Schrab, Antonin; Gretton, Arthur

Type de document :

Pré-publication ou Document de travail

Titre :

MMD-FUSE: Learning and Combining Kernels for Two-Sample Testing Without Data Splitting

Auteur(s) :

Biggs, Felix []
University College of London [London] [UCL]
Schrab, Antonin []
Gatsby Computational Neuroscience Unit
Department of Computer science [University College of London] [UCL-CS]
The Inria London Programme [Inria-London]
MOdel for Data Analysis and Learning [MODAL]
University College of London [London] [UCL]
Gretton, Arthur [Auteur]
Gatsby Computational Neuroscience Unit

Date de publication :

2023-06-15

Discipline(s) HAL :

Statistiques [stat]/Machine Learning [stat.ML]

Résumé en anglais : [en]

We propose novel statistics which maximise the power of a two-sample test based on the Maximum Mean Discrepancy (MMD), by adapting over the set of kernels used in defining it. For finite sets, this reduces to combining ...
Lire la suite >We propose novel statistics which maximise the power of a two-sample test based on the Maximum Mean Discrepancy (MMD), by adapting over the set of kernels used in defining it. For finite sets, this reduces to combining (normalised) MMD values under each of these kernels via a weighted soft maximum. Exponential concentration bounds are proved for our proposed statistics under the null and alternative. We further show how these kernels can be chosen in a data-dependent but permutation-independent way, in a wellcalibrated test, avoiding data splitting. This technique applies more broadly to general permutation-based MMD testing, and includes the use of deep kernels with features learnt using unsupervised models such as auto-encoders. We highlight the applicability of our MMD-FUSE test on both synthetic lowdimensional and real-world high-dimensional data, and compare its performance in terms of power against current state-of-the-art kernel tests.Lire moins >

Langue :

Anglais

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

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