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

TL;DR

This paper introduces a novel distribution alignment method using log-likelihood ratio statistics and normalizing flows, providing a robust, quantifiable, and theoretically grounded approach for domain adaptation and image translation.

Contribution

It proposes a new likelihood-based minimization framework for distribution alignment that guarantees convergence and preserves local data structure.

Findings

Achieves domain alignment that maintains local structure.

Provides a lower bound guarantee upon convergence.

Outperforms existing methods in robustness and quantifiability.

Abstract

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