Maximally Distant Cross Domain Generators for Estimating Per-Sample Error

While in supervised learning, the validation error is an unbiased estimator of the generalization (test) error and complexity-based generalization bounds are abundant, no such bounds exist for learning a mapping in an unsupervised way. As a result, when training GANs and specifically when using GANs for learning to map between domains in a completely unsupervised way, one is forced to select the hyperparameters and the stopping epoch by subjectively examining multiple options. We propose a novel bound for predicting the success of unsupervised cross domain mapping methods, which is motivated by the recently proposed simplicity hypothesis. The bound can be applied both in expectation, for comparing hyperparameters, or per sample, in order to predict the success of a specific cross-domain translation. The utility of the bound is demonstrated in an extensive set of experiments employing multiple recent algorithms.