Log-Likelihood Ratio Minimizing Flows: Towards Robust and Quantifiable\n Neural Distribution Alignment

Distribution alignment has many applications in deep learning, including\ndomain adaptation and unsupervised image-to-image translation. Most prior work\non unsupervised distribution alignment relies either on minimizing simple\nnon-parametric statistical distances such as maximum mean discrepancy or on\nadversarial alignment. However, the former fails to capture the structure of\ncomplex real-world distributions, while the latter is difficult to train and\ndoes not provide any universal convergence guarantees or automatic quantitative\nvalidation procedures. In this paper, we propose a new distribution alignment\nmethod based on a log-likelihood ratio statistic and normalizing flows. We show\nthat, under certain assumptions, this combination yields a deep neural\nlikelihood-based minimization objective that attains a known lower bound upon\nconvergence. We experimentally verify that minimizing the resulting objective\nresults in domain alignment that preserves the local structure of input\ndomains.\n