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 twostep approach by first modeling the probability distribution and then sampling from that model. We use the recently introduced class of positive semidefinite (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.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.10527
 Bibcode:
 2021arXiv211010527M
 Keywords:

 Computer Science  Artificial Intelligence;
 Computer Science  Machine Learning;
 Mathematics  Statistics Theory