  The recent empirical success of unsupervised cross-domain mapping algorithms,
between two domains that share common characteristics, is not well-supported by
theoretical justifications. This lacuna is especially troubling, given the
clear ambiguity in such mappings.
  We work with adversarial training methods based on IPMs and derive a novel
risk bound, which upper bounds the risk between the learned mapping $h$ and the
target mapping $y$, by a sum of three terms: (i) the risk between $h$ and the
most distant alternative mapping that was learned by the same cross-domain
mapping algorithm, (ii) the minimal discrepancy between the target domain and
the domain obtained by applying a hypothesis $h^*$ on the samples of the source
domain, where $h^*$ is a hypothesis selectable by the same algorithm. The bound
is directly related to Occam's razor and encourages the selection of the
minimal architecture that supports a small mapping discrepancy and (iii) an
approximation error term that decreases as the complexity of the class of
discriminators increases and is empirically shown to be small.
  The bound leads to multiple algorithmic consequences, including a method for
hyperparameters selection and for early stopping in cross-domain mapping GANs.
We also demonstrate a novel capability for unsupervised learning of estimating
confidence in the mapping of every specific sample.
