6 research outputs found
Guiding the One-to-one Mapping in CycleGAN via Optimal Transport
CycleGAN is capable of learning a one-to-one mapping between two data
distributions without paired examples, achieving the task of unsupervised data
translation. However, there is no theoretical guarantee on the property of the
learned one-to-one mapping in CycleGAN. In this paper, we experimentally find
that, under some circumstances, the one-to-one mapping learned by CycleGAN is
just a random one within the large feasible solution space. Based on this
observation, we explore to add extra constraints such that the one-to-one
mapping is controllable and satisfies more properties related to specific
tasks. We propose to solve an optimal transport mapping restrained by a
task-specific cost function that reflects the desired properties, and use the
barycenters of optimal transport mapping to serve as references for CycleGAN.
Our experiments indicate that the proposed algorithm is capable of learning a
one-to-one mapping with the desired properties.Comment: The Thirty-Third AAAI Conference on Artificial Intelligence (AAAI
2019
Semi-supervised Learning of Pushforwards For Domain Translation & Adaptation
Given two probability densities on related data spaces, we seek a map pushing
one density to the other while satisfying application-dependent constraints.
For maps to have utility in a broad application space (including domain
translation, domain adaptation, and generative modeling), the map must be
available to apply on out-of-sample data points and should correspond to a
probabilistic model over the two spaces. Unfortunately, existing approaches,
which are primarily based on optimal transport, do not address these needs. In
this paper, we introduce a novel pushforward map learning algorithm that
utilizes normalizing flows to parameterize the map. We first re-formulate the
classical optimal transport problem to be map-focused and propose a learning
algorithm to select from all possible maps under the constraint that the map
minimizes a probability distance and application-specific regularizers; thus,
our method can be seen as solving a modified optimal transport problem. Once
the map is learned, it can be used to map samples from a source domain to a
target domain. In addition, because the map is parameterized as a composition
of normalizing flows, it models the empirical distributions over the two data
spaces and allows both sampling and likelihood evaluation for both data sets.
We compare our method (parOT) to related optimal transport approaches in the
context of domain adaptation and domain translation on benchmark data sets.
Finally, to illustrate the impact of our work on applied problems, we apply
parOT to a real scientific application: spectral calibration for
high-dimensional measurements from two vastly different environmentsComment: 19 pages, 7 figure