Studying representations which can be closed-form Monge mapping optimum with utility to area adaptation
Authors: Oliver Struckmeier, Ievgen Redko, Anton Mallasto, Karol Arndt, Markus Heinonen, Ville Kyrki
Summary: Optimum transport (OT) is a strong geometric device used to check and align likelihood measures following the least effort precept. Regardless of its widespread use in machine studying (ML), OT drawback nonetheless bears its computational burden, whereas on the identical time affected by the curse of dimensionality for measures supported on normal high-dimensional areas. On this paper, we suggest to deal with these challenges utilizing illustration studying. Specifically, we search to be taught an embedding house such that the samples of the 2 enter measures develop into alignable in it with a easy affine mapping that may be calculated effectively in closed-form. We then present that such method results in outcomes which can be corresponding to fixing the unique OT drawback when utilized to the switch studying process on which many OT baselines the place beforehand evaluated in each homogeneous and heterogeneous DA settings. The code for our contribution is on the market at url{https://github.com/Oleffa/LaOT}
