Integrable Nonparametric Flows

Understand

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.