30 research outputs found
Energy-guided Entropic Neural Optimal Transport
Energy-Based Models (EBMs) are known in the Machine Learning community for
the decades. Since the seminal works devoted to EBMs dating back to the
noughties there have been appearing a lot of efficient methods which solve the
generative modelling problem by means of energy potentials (unnormalized
likelihood functions). In contrast, the realm of Optimal Transport (OT) and, in
particular, neural OT solvers is much less explored and limited by few recent
works (excluding WGAN based approaches which utilize OT as a loss function and
do not model OT maps themselves). In our work, we bridge the gap between EBMs
and Entropy-regularized OT. We present the novel methodology which allows
utilizing the recent developments and technical improvements of the former in
order to enrich the latter. We validate the applicability of our method on toy
2D scenarios as well as standard unpaired image-to-image translation problems.
For the sake of simplicity, we choose simple short- and long- run EBMs as a
backbone of our Energy-guided Entropic OT method, leaving the application of
more sophisticated EBMs for future research
Partial Neural Optimal Transport
We propose a novel neural method to compute partial optimal transport (OT)
maps, i.e., OT maps between parts of measures of the specified masses. We test
our partial neural optimal transport algorithm on synthetic examples
Entropic Neural Optimal Transport via Diffusion Processes
We propose a novel neural algorithm for the fundamental problem of computing
the entropic optimal transport (EOT) plan between probability distributions
which are accessible by samples. Our algorithm is based on the saddle point
reformulation of the dynamic version of EOT which is known as the Schr\"odinger
Bridge problem. In contrast to the prior methods for large-scale EOT, our
algorithm is end-to-end and consists of a single learning step, has fast
inference procedure, and allows handling small values of the entropy
regularization coefficient which is of particular importance in some applied
problems. Empirically, we show the performance of the method on several
large-scale EOT tasks