Generative Conditional Distributions by Neural (Entropic) Optimal Transport

TL;DR

This paper presents a neural entropic optimal transport method for learning conditional distributions, especially with limited data, by training two neural networks with Lipschitz regularization to improve generative modeling.

Contribution

Introduces a novel neural entropic optimal transport approach for conditional distribution learning using minimax training and Lipschitz regularization.

Findings

Effective on real-world datasets

Outperforms state-of-the-art methods

Robust with limited samples

Abstract

Learning conditional distributions is challenging because the desired outcome is not a single distribution but multiple distributions that correspond to multiple instances of the covariates. We introduce a novel neural entropic optimal transport method designed to effectively learn generative models of conditional distributions, particularly in scenarios characterized by limited sample sizes. Our method relies on the minimax training of two neural networks: a generative network parametrizing the inverse cumulative distribution functions of the conditional distributions and another network parametrizing the conditional Kantorovich potential. To prevent overfitting, we regularize the objective function by penalizing the Lipschitz constant of the network output. Our experiments on real-world datasets show the effectiveness of our algorithm compared to state-of-the-art conditional distribution learning techniques. Our implementation can be found at https://github.com/nguyenngocbaocmt02/GENTLE.