Efficient Robust Optimal Transport with Application to Multi-Label Classification

TL;DR

This paper introduces a novel optimal transport formulation that incorporates feature correlations via a Mahalanobis metric, simplifying optimization and improving performance in multi-label classification tasks.

Contribution

It proposes a new OT method that models feature relationships with a Mahalanobis metric, enabling efficient optimization and application to high-dimensional data.

Findings

Effective in multi-label classification tasks

Simplifies optimization through problem structure

Performs well on tag prediction and multi-class classification

Abstract

Optimal transport (OT) is a powerful geometric tool for comparing two distributions and has been employed in various machine learning applications. In this work, we propose a novel OT formulation that takes feature correlations into account while learning the transport plan between two distributions. We model the feature-feature relationship via a symmetric positive semi-definite Mahalanobis metric in the OT cost function. For a certain class of regularizers on the metric, we show that the optimization strategy can be considerably simplified by exploiting the problem structure. For high-dimensional data, we additionally propose suitable low-dimensional modeling of the Mahalanobis metric. Overall, we view the resulting optimization problem as a non-linear OT problem, which we solve using the Frank-Wolfe algorithm. Empirical results on the discriminative learning setting, such as tag prediction and multi-class classification, illustrate the good performance of our approach.