Kernel quadrature with DPPs

Abstract : We study quadrature rules for functions living in an RKHS, using nodes sampled from a projection determinantal point process (DPP). DPPs are parametrized by a kernel, and we use a truncated and saturated version of the RKHS kernel. This natural link between the two kernels, along with DPP machinery, leads to relatively tight bounds on the quadrature error, that depend on the spectrum of the RKHS kernel. Finally, we experimentally compare DPPs to existing kernel-based quadratures such as herding, Bayesian quadrature, or continuous leverage score sampling. Numerical results confirm the interest of DPPs, and even suggest faster rates than our bounds in particular cases.
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https://hal.archives-ouvertes.fr/hal-02161143
Contributor : Rémi Bardenet <>
Submitted on : Thursday, June 20, 2019 - 2:44:07 PM
Last modification on : Friday, June 21, 2019 - 1:46:54 AM

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  • HAL Id : hal-02161143, version 1
  • ARXIV : 1906.07832

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Ayoub Belhadji, R. Bardenet, Pierre Chainais. Kernel quadrature with DPPs. 2019. ⟨hal-02161143⟩

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