Batch weight for domain adaptation with mass shift

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.