Scalable Optimal Transport in High Dimensions for Graph Distances, Embedding Alignment, and More

Johannes Klicpera, Marten Lienen, Stephan Günnemann

Publikation: Beitrag in Buch/Bericht/KonferenzbandKonferenzbeitragBegutachtung

7 Zitate (Scopus)

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.

OriginalspracheEnglisch
TitelProceedings of the 38th International Conference on Machine Learning, ICML 2021
Herausgeber (Verlag)ML Research Press
Seiten5616-5627
Seitenumfang12
ISBN (elektronisch)9781713845065
PublikationsstatusVeröffentlicht - 2021
Veranstaltung38th International Conference on Machine Learning, ICML 2021 - Virtual, Online
Dauer: 18 Juli 202124 Juli 2021

Publikationsreihe

NameProceedings of Machine Learning Research
Band139
ISSN (elektronisch)2640-3498

Konferenz

Konferenz38th International Conference on Machine Learning, ICML 2021
OrtVirtual, Online
Zeitraum18/07/2124/07/21

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