Sampling from Arbitrary Functions via PSD Models
This addresses a key task in applied statistics and machine learning for researchers and practitioners needing efficient sampling methods, but it appears incremental as it builds on existing PSD models.
The paper tackles the problem of generating i.i.d. samples from distributions known only through density evaluations, which scales poorly with dimension or requires complex implementations, by using PSD models to approximate densities concisely and providing a simple sampling algorithm, with preliminary empirical results.
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.