Sampling from Arbitrary Functions via PSD Models

In many fields such as biochemistry, statistical mechanics and machine learning, effectively sampling arbitrary numbers of independent and identically distributed (i.i.d.) samples from probability distributions is a key task [5, 7, 6]. Basic sampling methods include rejection sampling and gridding, and rely on simple properties of the density. However, they are suitable only in small dimensions, except for very structured cases. Moreover, they are hard to adapt to probabilities which are known up to their renormalization constant, which is often the case when dealing with exponential models that are common in applications [13]. More involved methods have been developed to address these dimensionality and renormalization issues, in the class of so-called Markov chain Monte Carlo (MCMC) methods. However, they are complex to set up: in particular, independence between samples is not directly guaranteed, convergence can be slow and hard to measure non-asymptotically [6, 13]. In this work, we address the problem in a different way, by incorporating a modeling step.