Solving (partial) unbalanced optimal transport via transform coefficients and beyond
Primary Area: general machine learning (i.e., none of the above)
Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics.
Keywords: Optimal Transport
Submission Guidelines: I certify that this submission complies with the submission instructions as described on https://iclr.cc/Conferences/2024/AuthorGuide.
TL;DR: We propose transform coefficients methods for solving UOT, PUOT and OT in a general perspective.
Abstract: Unbalanced Optimal Transport (UOT) has gained increasing attention due to its ability to relax marginal constraints, thereby expanding its application potential. Previous solvers often incorporate an entropy regularization term, which can result in dense matching solutions. Meanwhile directly modeling UOT using penalized linear regression can be computationally expensive. To address the above issue, we turn to consider determining the marginal probability distribution of UOT with KL divergence via proposed \textbf{\textit{transform coefficient}} method. The transform coefficient approach is not only computationally friendly but also reveals the essence of UOT, which involves adjusting the sample weights accordingly. We further extend the transform coefficient method into exploiting the marginal probability distribution of Partial Unbalanced Optimal Transport (PUOT) with KL divergence for validating its generalization. Since the marginal probability of UOT/PUOT are determined, we are excited to discover that UOT/PUOT can be transformed into classical Optimal Transport (OT) problem for finding the transportation plan. Therefore, the transform coefficient method can be considered as the bridge that establishes the connection between UOT/PUOT and OT. Moreover, we discover the additional results of Lagrange multipliers when solving transform coefficient can offer valuable guidance for achieving more sparse and accurate mapping with Cost-Reweighted OT (CROT). We perform several numerical experiments to illustrate our proposed new algorithms on dealing with UOT, PUOT and OT problem.
Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors' identity.
No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.
Submission Number: 295
Loading