An analysis of Ermakov-Zolotukhin quadrature using kernels

Ayoub Belhadji (1, 2)

1 DANTE - Dynamic Networks : Temporal and Structural Capture Approach
2 LIP - Laboratoire de l'Informatique du Parallélisme

We study a quadrature, proposed by Ermakov and Zolotukhin in the sixties, through the lens of kernel methods. The nodes of this quadrature rule follow the distribution of a determinantal point process, while the weights are defined through a linear system, similarly to the optimal kernel quadrature. In this work, we show how these two classes of quadrature are related, and we prove a tractable formula of the expected value of the squared worst-case integration error on the unit ball of an RKHS of the former quadrature. In particular, this formula involves the eigenvalues of the corresponding kernel and leads to improving on the existing theoretical guarantees of the optimal kernel quadrature with determinantal point processes.

Domaines: Calcul [stat.CO]; Analyse numérique [math.NA]

Ayoub Belhadji. An analysis of Ermakov-Zolotukhin quadrature using kernels. NeurIPS 2021 - 35th Conference on Neural Information Processing Systems, Dec 2021, Virtual-only Conference, Australia. pp.1-17. ⟨hal-03405615⟩