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Pré-Publication, Document De Travail Année : 2021

Performance analysis of greedy algorithms for minimising a Maximum Mean Discrepancy

Résumé

We analyse the performance of several iterative algorithms for the quantisation of a probability measure µ, based on the minimisation of a Maximum Mean Discrepancy (MMD). Our analysis includes kernel herding, greedy MMD minimisation and Sequential Bayesian Quadrature (SBQ). We show that the finite-sample-size approximation error, measured by the MMD, decreases as 1/n for SBQ and also for kernel herding and greedy MMD minimisation when using a suitable step-size sequence. The upper bound on the approximation error is slightly better for SBQ, but the other methods are significantly faster, with a computational cost that increases only linearly with the number of points selected. This is illustrated by two numerical examples, with the target measure µ being uniform (a space-filling design application) and with µ a Gaussian mixture.
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Dates et versions

hal-03114891 , version 1 (19-01-2021)
hal-03114891 , version 2 (28-04-2022)

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  • HAL Id : hal-03114891 , version 1

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Luc Pronzato. Performance analysis of greedy algorithms for minimising a Maximum Mean Discrepancy. 2021. ⟨hal-03114891v1⟩
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