Sampling from Arbitrary Functions via PSD Models

Ulysse Marteau-Ferey (1, 2) , Francis Bach (2, 1) , Alessandro Rudi (2, 1)

1 SIERRA - Statistical Machine Learning and Parsimony
2 PSL - Université Paris Sciences et Lettres

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.

Mots clés: sampling; kernel methods; machine learning

Domaines: Apprentissage [cs.LG]; Intelligence artificielle [cs.AI]; Statistiques [math.ST]

Ulysse Marteau-Ferey, Francis Bach, Alessandro Rudi. Sampling from Arbitrary Functions via PSD Models. 2021. ⟨hal-03386544v2⟩