This page is about our paper

Scalable Optimal Transport in High Dimensions for Graph Distances, Embedding Alignment, and More
by Johannes Gasteiger, Marten Lienen and Stephan Günnemann
Published at the International Conference on Machine Learning (ICML) 2021

Note that the author's name has changed from Johannes Klicpera to Johannes Gasteiger.

Abstract

The current best practice for computing optimal transport (OT) is via entropy regularization and Sinkhorn iterations. This algorithm runs in quadratic time as it requires the full pairwise cost matrix, which is prohibitively expensive for large sets of objects. In this work we propose two effective log-linear time approximations of the cost matrix: First, a sparse approximation based on locality sensitive hashing (LSH) and, second, a Nyström approximation with LSH-based sparse corrections, which we call locally corrected Nyström (LCN). These approximations enable general log-linear time algorithms for entropy-regularized OT that perform well even for the complex, high-dimensional spaces common in deep learning. We analyse these approximations theoretically and evaluate them experimentally both directly and end-to-end as a component for real-world applications. Using our approximations for unsupervised word embedding alignment enables us to speed up a state-of-the-art method by a factor of 3 while also improving the accuracy by 3.1 percentage points without any additional model changes. For graph distance regression we propose the graph transport network (GTN), which combines graph neural networks (GNNs) with enhanced Sinkhorn. GTN outcompetes previous models by 48% and still scales log-linearly in the number of nodes.

Cite

Please cite our paper if you use the model, experimental results, or our code in your own work:

@inproceedings{gasteiger_lcn_2021,
title = {Scalable Optimal Transport in High Dimensions for Graph Distances, Embedding Alignment, and More},
author = {Gasteiger, Johannes and Lienen, Marten and G{\"u}nnemann, Stephan},
booktitle={International Conference on Machine Learning (ICML)},
year = {2021}
}

Links

[Paper | Poster | LCN GitHub | GTN GitHub]