Efficient Robust Optimal Transport with Application to Multi-Label Classification
@article{Jawanpuria2020EfficientRO, title={Efficient Robust Optimal Transport with Application to Multi-Label Classification}, author={Pratik Jawanpuria and N T V Satyadev and Bamdev Mishra}, journal={2021 60th IEEE Conference on Decision and Control (CDC)}, year={2020}, pages={1490-1495} }
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…
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On Riemannian Optimization over Positive Definite Matrices with the Bures-Wasserstein Geometry
- Mathematics, Computer ScienceNeurIPS
- 2021
It is shown that the Bures-Wasserstein geometry has a non-negative curvature, which further improves convergence rates of algorithms over the non-positively curved AI geometry, and it is verified that several popular cost functions are also geodesic convex under the BW geometry.
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