Positively Weighted Kernel Quadrature via Subsampling

Abstract

We study kernel quadrature rules with convex weights. Our approach combines the spectral properties of the kernel with recombination results about point measures. This results in effective algorithms that construct convex quadrature rules using only access to i.i.d. samples from the underlying measure and evaluation of the kernel and that result in a small worst-case error. In addition to our theoretical results and the benefits resulting from convex weights, our experiments indicate that this construction can compete with the optimal bounds in well-known examples.

29 pages, NeurIPS 2022 camera-ready version

References in corpus (3)

• On the Equivalence between Herding and Conditional Gradient Algorithms
• Sparse projections onto the simplex
• Estimating the probability that a given vector is in the convex hull of a random sample

Cited by in corpus (3)

• Bayesian Model Selection of Lithium-Ion Battery Models via Bayesian Quadrature
• Hypercontractivity Meets Random Convex Hulls: Analysis of Randomized Multivariate Cubatures
• Markov Chain Approximations to Stochastic Differential Equations by Recombination on Lattice Trees