Sampling from Arbitrary Functions via PSD Models

• URL: http://arxiv.org/abs/2110.10527v1
• Date: Wed, 20 Oct 2021 12:25:22 GMT
• Title: Sampling from Arbitrary Functions via PSD Models
• Authors: Ulysse Marteau-Ferey (SIERRA, PSL), Alessandro Rudi (PSL, SIERRA), Francis Bach (PSL, SIERRA)
• Abstract summary: We take a two-step approach by first modeling the probability distribution and then sampling from that model. 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.
• Score: 55.41644538483948
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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