Embedding Empirical Distributions for Computing Optimal Transport Maps
This addresses a gap in neural optimal transport methods, which have focused on single maps, by enabling multi-distribution applications in signal processing.
The paper tackles the problem of computing optimal transport maps for multiple empirical distributions, introducing a transformer-based method to embed distributional data of varying lengths and generate maps via a hypernetwork, achieving validated performance in numerical experiments.
Distributional data have become increasingly prominent in modern signal processing, highlighting the necessity of computing optimal transport (OT) maps across multiple probability distributions. Nevertheless, recent studies on neural OT methods predominantly focused on the efficient computation of a single map between two distributions. To address this challenge, we introduce a novel approach to learning transport maps for new empirical distributions. Specifically, we employ the transformer architecture to produce embeddings from distributional data of varying length; these embeddings are then fed into a hypernetwork to generate neural OT maps. Various numerical experiments were conducted to validate the embeddings and the generated OT maps. The model implementation and the code are provided on https://github.com/jiangmingchen/HOTET.