Learning representations that are closed-form Monge mapping optimal with application to domain adaptation

• URL: http://arxiv.org/abs/2305.07500v2
• Date: Fri, 11 Aug 2023 10:49:52 GMT
• Title: Learning representations that are closed-form Monge mapping optimal with application to domain adaptation
• Authors: Oliver Struckmeier, Ievgen Redko, Anton Mallasto, Karol Arndt, Markus Heinonen, Ville Kyrki
• Abstract summary: Optimal transport (OT) is a powerful tool used to compare and align probability measures following the least effort principle. Despite its widespread use in machine learning (ML), OT problem still bears its computational burden. We propose to tackle these challenges using representation learning.
• Score: 24.258758784011572
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Optimal transport (OT) is a powerful geometric tool used to compare and align probability measures following the least effort principle. Despite its widespread use in machine learning (ML), OT problem still bears its computational burden, while at the same time suffering from the curse of dimensionality for measures supported on general high-dimensional spaces. In this paper, we propose to tackle these challenges using representation learning. In particular, we seek to learn an embedding space such that the samples of the two input measures become alignable in it with a simple affine mapping that can be calculated efficiently in closed-form. We then show that such approach leads to results that are comparable to solving the original OT problem when applied to the transfer learning task on which many OT baselines where previously evaluated in both homogeneous and heterogeneous DA settings. The code for our contribution is available at \url{https://github.com/Oleffa/LaOT}.

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