Kernel quadrature with DPPs

Ayoub Belhadji (1) , R. Bardenet (1, 2) , Pierre Chainais (1, 3)

1 CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
2 CNRS - Centre National de la Recherche Scientifique
3 Centrale Lille

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.

Domaines: Statistiques [math.ST]; Apprentissage [cs.LG]

Ayoub Belhadji, R. Bardenet, Pierre Chainais. Kernel quadrature with DPPs. NeurIPS 2019 - Thirty-third Conference on Neural Information Processing Systems, Jun 2019, Vancouver, Canada. ⟨hal-02161143⟩