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 paper, we study the problem of fair sparse regression on a biased dataset where bias depends upon a hidden binary attribute. The presence of a hidden attribute adds an extra layer of complexity to the problem by combining sparse regression and clustering with unknown binary labels. The corresponding optimization problem is combinatorial, but we propose a novel relaxation of it as an invex optimization problem. To the best of our knowledge, this is the first invex relaxation for a combinatorial problem. We show that the inclusion of the debi-asing/fairness constraint in our model has no adverse effect on the performance. Rather, it enables the recovery of the hidden attribute.

Choosing optimal PT hyperparameter values is challenging, and existing methods do not work well.

Choosing optimal PT hyperparameter values is challenging, and existing methods do not work well.

It is common for data structures such as images and shapes of 2D objects to be represented as points on a manifold.

The results of our survey are shown in Table 10.