Integrable Nonparametric Flows

• URL: http://arxiv.org/abs/2012.02035v1
• Date: Thu, 3 Dec 2020 16:19:52 GMT
• Title: Integrable Nonparametric Flows
• Authors: David Pfau, Danilo Rezende
• Abstract summary: We introduce a method for reconstructing an infinitesimal normalizing flow given only an infinitesimal change to a probability distribution. This reverses the conventional task of normalizing flows. We discuss potential applications to problems in quantum Monte Carlo and machine learning.
• Score: 5.9774834479750805
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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