Studying representations which are closed-form Monge mapping optimum with software to area adaptation
Authors: Oliver Struckmeier, Ievgen Redko, Anton Mallasto, Karol Arndt, Markus Heinonen, Ville Kyrki
Summary: Optimum transport (OT) is a strong geometric instrument used to check and align chance measures following the least effort precept. Regardless of its widespread use in machine studying (ML), OT downside nonetheless bears its computational burden, whereas on the similar time affected by the curse of dimensionality for measures supported on basic high-dimensional areas. On this paper, we suggest to deal with these challenges utilizing illustration studying. Particularly, we search to study an embedding house such that the samples of the 2 enter measures turn out to be alignable in it with a easy affine mapping that may be calculated effectively in closed-form. We then present that such strategy results in outcomes which are akin to fixing the unique OT downside 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 out there at url{https://github.com/Oleffa/LaOT}