Sampling from Arbitrary Functions via PSD Models

TL;DR

This paper introduces a method for efficient sampling from complex distributions by modeling them with PSD models, enabling concise approximation and straightforward sampling, with promising initial empirical results.

Contribution

The paper proposes using PSD models to approximate arbitrary densities efficiently and introduces a simple sampling algorithm, advancing density sampling techniques.

Findings

PSD models can approximate a wide class of densities with few evaluations

The proposed sampling algorithm is simple and effective

Preliminary empirical results support the method's potential

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.