Integrable Nonparametric Flows
Abstract
We introduce a method for reconstructing an infinitesimal normalizing flow given only an infinitesimal change to a (possibly unnormalized) probability distribution. This reverses the conventional task of normalizing flows -- rather than being given samples from a unknown target distribution and learning a flow that approximates the distribution, we are given a perturbation to an initial distribution and aim to reconstruct a flow that would generate samples from the known perturbed distribution. While this is an underdetermined problem, we find that choosing the flow to be an integrable vector field yields a solution closely related to electrostatics, and a solution can be computed by the method of Green's functions. Unlike conventional normalizing flows, this flow can be represented in an entirely nonparametric manner. We validate this derivation on low-dimensional problems, and discuss potential applications to problems in quantum Monte Carlo and machine learning.
Keywords
Cite
@article{arxiv.2012.02035,
title = {Integrable Nonparametric Flows},
author = {David Pfau and Danilo Rezende},
journal= {arXiv preprint arXiv:2012.02035},
year = {2020}
}
Comments
Accepted to 3rd NeurIPS Workshop on Machine Learning and Physical Sciences