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Maximum Mean Discrepancy Gradient Flow

Arbel, M; Korba, A; Salim, A; Gretton, A; (2019) Maximum Mean Discrepancy Gradient Flow. In: Wallach, H and Larochelle, H and Beygelzimer, A and d'Alché-Buc, F and Fox, E and Garnett, R, (eds.) Advances in Neural Information Processing Systems 32 (NIPS 2019). NIPS Proceedingsβ: Vancouver, Canada. Green open access

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Abstract

We construct a Wasserstein gradient flow of the maximum mean discrepancy (MMD) and study its convergence properties. The MMD is an integral probability metric defined for a reproducing kernel Hilbert space (RKHS), and serves as a metric on probability measures for a sufficiently rich RKHS. We obtain conditions for convergence of the gradient flow towards a global optimum, that can be related to particle transport when optimizing neural networks. We also propose a way to regularize this MMD flow, based on an injection of noise in the gradient. This algorithmic fix comes with theoretical and empirical evidence. The practical implementation of the flow is straightforward, since both the MMD and its gradient have simple closed-form expressions, which can be easily estimated with samples.

Type: Proceedings paper
Title: Maximum Mean Discrepancy Gradient Flow
Event: NeurIPS
Location: Vancouver
Open access status: An open access version is available from UCL Discovery
Publisher version: https://papers.nips.cc/paper/8876-maximum-mean-dis...
Language: English
Additional information: This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions.
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
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
URI: https://discovery.ucl.ac.uk/id/eprint/10090053
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