Open AccessProceedings Article
Screening Sinkhorn Algorithm for Regularized Optimal Transport
Mokhtar Z. Alaya,Maxime Berar,Gilles Gasso,Alain Rakotomamonjy +3 more
- 20 Jun 2019
Vol. 32, pp 12169-12179
TL;DR: The Screenkhorn algorithm, a novel strategy for efficiently approximating the Sinkhorn distance between two discrete measures, is introduced, based on a new formulation of dual of Sinkinghorn divergence problem and on the KKT optimality conditions of this problem, which enable identification of dual components to be screened.
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Abstract: We introduce in this paper a novel strategy for efficiently approximating the Sinkhorn distance between two discrete measures. After identifying neglectable components of the dual solution of the regularized Sinkhorn problem, we propose to screen those components by directly setting them at that value before entering the Sinkhorn problem. This allows us to solve a smaller Sinkhorn problem while ensuring approximation with provable guarantees. More formally, the approach is based on a new formulation of dual of Sinkhorn divergence problem and on the KKT optimality conditions of this problem, which enable identification of dual components to be screened. This new analysis leads to the Screenkhorn algorithm. We illustrate the efficiency of Screenkhorn on complex tasks such as dimensionality reduction and domain adaptation involving regularized optimal transport.
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Citations
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Overrelaxed Sinkhorn-Knopp Algorithm for Regularized Optimal Transport
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Overrelaxed Sinkhorn-Knopp Algorithm for Regularized Optimal Transport
TL;DR: In this article, the Sinkhorn-Knopp algorithm is used to over-relax the Bregman projection operators, allowing for faster convergence, which corresponds to elevating the diagonal scaling factors to a given power at each step of the algorithm.
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Meta-learning meets the Internet of Things: Graph prototypical models for sensor-based human activity recognition
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