Efficient Robust Optimal Transport with Application to Multi-Label Classification

• URL: http://arxiv.org/abs/2010.11852v2
• Date: Thu, 7 Oct 2021 07:04:47 GMT
• Title: Efficient Robust Optimal Transport with Application to Multi-Label Classification
• Authors: Pratik Jawanpuria, N T V Satyadev, and Bamdev Mishra
• Abstract summary: We model the feature-feature relationship via a symmetric positive semi-definite Mahalanobis metric in the OT cost function. 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.
• Score: 12.521494095948068
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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