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

Biggs, Felix; Schrab, antonin; Gretton, Arthur; (2023) MMD-Fuse: Learning and Combining Kernels for Two-Sample Testing Without Data Splitting. In: Proceedings of the 37th Conference on Neural Information Processing Systems (NeurIPS 2023). (pp. pp. 1-38). NeurIPS (In press). Green open access

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Abstract

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 well-calibrated 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 tests on both synthetic low-dimensional and real-world high-dimensional data, and compare its performance in terms of power against current state-of-the-art kernel tests.

Type: Proceedings paper
Title: MMD-Fuse: Learning and Combining Kernels for Two-Sample Testing Without Data Splitting
Event: 37th Conference on Neural Information Processing Systems (NeurIPS 2023)
Location: New Orleans, LA, USA
Dates: 10th-16th December 2023
Open access status: An open access version is available from UCL Discovery
Publisher version: https://openreview.net/forum?id=JOkgEY9os2
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher's terms and conditions.
Keywords: Testing, MMD, Kernel Methods, Two-sample testing
UCL classification: UCL
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Life Sciences
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Life Sciences > Gatsby Computational Neurosci Unit
URI: https://discovery.ucl.ac.uk/id/eprint/10181227
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