Sampling from Arbitrary Functions via PSD Models
Abstract
In many areas of applied statistics and machine learning, generating an arbitrary number of independent and identically distributed (i.i.d.) samples from a given distribution is a key task. When the distribution is known only through evaluations of the density, current methods either scale badly with the dimension or require very involved implementations. Instead, we take a two-step approach by first modeling the probability distribution and then sampling from that model. We use the recently introduced class of positive semi-definite (PSD) models, which have been shown to be efficient for approximating probability densities. We show that these models can approximate a large class of densities concisely using few evaluations, and present a simple algorithm to effectively sample from these models. We also present preliminary empirical results to illustrate our assertions.
Cite
@article{arxiv.2110.10527,
title = {Sampling from Arbitrary Functions via PSD Models},
author = {Ulysse Marteau-Ferey and Francis Bach and Alessandro Rudi},
journal= {arXiv preprint arXiv:2110.10527},
year = {2021}
}