Recovery Bounds on Class-Based Optimal Transport: A Sum-of-Norms Regularization Framework

• URL: http://arxiv.org/abs/1903.03850v3
• Date: Mon, 22 May 2023 16:00:53 GMT
• Title: Recovery Bounds on Class-Based Optimal Transport: A Sum-of-Norms Regularization Framework
• Authors: Arman Rahbar, Ashkan Panahi, Morteza Haghir Chehreghani, Devdatt Dubhashi, Hamid Krim
• Abstract summary: We propose a convex OT program with a sum-of-norms regularization term, which provably recovers the underlying class structure under geometric assumptions. We provide a novel argument for the uniqueness of the optimum even in the absence of strong convexity. Our experiments show that the new regularizer not only results in a better preservation of the class structure in the data but also yields additional robustness to the data geometry.
• Score: 21.037720934987483
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We develop a novel theoretical framework for understating OT schemes respecting a class structure. For this purpose, we propose a convex OT program with a sum-of-norms regularization term, which provably recovers the underlying class structure under geometric assumptions. Furthermore, we derive an accelerated proximal algorithm with a closed-form projection and proximal operator scheme, thereby affording a more scalable algorithm for computing optimal transport plans. We provide a novel argument for the uniqueness of the optimum even in the absence of strong convexity. Our experiments show that the new regularizer not only results in a better preservation of the class structure in the data but also yields additional robustness to the data geometry, compared to previous regularizers.

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