Towards optimal transport with global invariances
Name
1806.09277.pdf
Description
Accepted version
Size
3.94 MB
Format
Adobe PDF
Checksum (MD5)
7dd3e4ec89295a83a0694866a60dab10
Author(s)
Alvarez Melis, David
Jegelka, Stefanie Sabrina
Jaakkola, Tommi S
Date Issued
February 2019
Journal
Proceedings of Machine Learning Research PMLR
Publisher
JMLR
Citation
Alvarez-Melis, David, Stefanie Jegelka and Tommi S. Jaakkola. “Towards optimal transport with global invariances.” Proceedings of Machine Learning Research PMLR, 89 (February 2019): 1870-1879 © 2019 The Author(s)
Version
Author's final manuscript
Abstract
Many problems in machine learning involve calculating correspondences between sets of objects, such as point clouds or images. Discrete optimal transport provides a natural and successful approach to such tasks whenever the two sets of objects can be represented in the same space, or at least distances between them can be directly evaluated. Unfortunately neither requirement is likely to hold when object representations are learned from data. Indeed, automatically derived representations such as word embeddings are typically fixed only up to some global transformations, for example, reflection or rotation. As a result, pairwise distances across two such instances are ill-defined without specifying their relative transformation. In this work, we propose a general framework for optimal transport in the presence of latent global transformations. We cast the problem as a joint optimization over transport couplings and transformations chosen from a flexible class of invariances, propose algorithms to solve it, and show promising results in various tasks, including a popular unsupervised word translation benchmark.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
http://proceedings.mlr.press/v89/
