Unbalanced Optimal Transport through Non-negative Penalized Linear Regression

Author name not available (Why is that?)

Publication date: 8 June 2021

Abstract: This paper addresses the problem of Unbalanced Optimal Transport (UOT) in which the marginal conditions are relaxed (using weighted penalties in lieu of equality) and no additional regularization is enforced on the OT plan. In this context, we show that the corresponding optimization problem can be reformulated as a non-negative penalized linear regression problem. This reformulation allows us to propose novel algorithms inspired from inverse problems and nonnegative matrix factorization. In particular, we consider majorization-minimization which leads in our setting to efficient multiplicative updates for a variety of penalties. Furthermore, we derive for the first time an efficient algorithm to compute the regularization path of UOT with quadratic penalties. The proposed algorithm provides a continuity of piece-wise linear OT plans converging to the solution of balanced OT (corresponding to infinite penalty weights). We perform several numerical experiments on simulated and real data illustrating the new algorithms, and provide a detailed discussion about more sophisticated optimization tools that can further be used to solve OT problems thanks to our reformulation.

Has companion code repository: https://github.com/lchapel/UOT-though-penalized-linear-regression

This page was built for publication: Unbalanced Optimal Transport through Non-negative Penalized Linear Regression

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6369734)