Blind Source Separation with Optimal Transport Non-negative Matrix Factorization

no code implementations • 15 Feb 2018 • Antoine Rolet, Vivien Seguy, Mathieu Blondel, Hiroshi Sawada

Optimal transport as a loss for machine learning optimization problems has recently gained a lot of attention.

blind source separation

Large Scale Optimal Transport and Mapping Estimation

no code implementations • ICLR 2018 • Vivien Seguy, Bharath Bhushan Damodaran, Remi Flamary, Nicolas Courty, Antoine Rolet, Mathieu Blondel

First, we learn an optimal transport (OT) plan, which can be thought as a one-to-many map between the two distributions.

Domain Adaptation

Large-Scale Optimal Transport and Mapping Estimation

2 code implementations • 7 Nov 2017 • Vivien Seguy, Bharath Bhushan Damodaran, Rémi Flamary, Nicolas Courty, Antoine Rolet, Mathieu Blondel

We prove two theoretical stability results of regularized OT which show that our estimations converge to the OT plan and Monge map between the underlying continuous measures.

Domain Adaptation

Smooth and Sparse Optimal Transport

1 code implementation • 17 Oct 2017 • Mathieu Blondel, Vivien Seguy, Antoine Rolet

In this paper, we explore regularizing the primal and dual OT formulations with a strongly convex term, which corresponds to relaxing the dual and primal constraints with smooth approximations.

Principal Geodesic Analysis for Probability Measures under the Optimal Transport Metric

no code implementations • NeurIPS 2015 • Vivien Seguy, Marco Cuturi

Given a family of probability measures in P(X), the space of probability measures on a Hilbert space X, our goal in this paper is to highlight one ore more curves in P(X) that summarize efficiently that family.