  Unsupervised domain transfer is the task of transferring or translating
samples from a source distribution to a different target distribution. Current
solutions unsupervised domain transfer often operate on data on which the modes
of the distribution are well-matched, for instance have the same frequencies of
classes between source and target distributions. However, these models do not
perform well when the modes are not well-matched, as would be the case when
samples are drawn independently from two different, but related, domains. This
mode imbalance is problematic as generative adversarial networks (GANs), a
successful approach in this setting, are sensitive to mode frequency, which
results in a mismatch of semantics between source samples and generated samples
of the target distribution. We propose a principled method of re-weighting
training samples to correct for such mass shift between the transferred
distributions, which we call batch-weight. We also provide rigorous
probabilistic setting for domain transfer and new simplified objective for
training transfer networks, an alternative to complex, multi-component loss
functions used in the current state-of-the art image-to-image translation
models. The new objective stems from the discrimination of joint distributions
and enforces cycle-consistency in an abstract, high-level, rather than
pixel-wise, sense. Lastly, we experimentally show the effectiveness of the
proposed methods in several image-to-image translation tasks.
