Sampling from Arbitrary Functions via PSD Models

Ulysse Marteau-Ferey · Francis Bach · Alessandro Rudi

[ Abstract ]
Wed 30 Mar 3:30 a.m. PDT — 5 a.m. PDT
Oral presentation: Oral 8: Learning theory / Sampling methods
Wed 30 Mar midnight PDT — 1 a.m. PDT


In many areas of applied statistics and machine learning, generating an arbitrary number of inde- pendent 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 implemen- tations. 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 ecient 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 eectively sample from these models. We also present preliminary empirical results to illustrate our assertions.

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