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Computing Wasserstein barycenters using gradient descent algorithms

[Moved Online] Hot Topics: Optimal transport and applications to machine learning and statistics May 04, 2020 - May 08, 2020

May 04, 2020 (02:00 PM PDT - 03:00 PM PDT)
Speaker(s): Philippe Rigollet (Massachusetts Institute of Technology)
Location: SLMath: Online/Virtual
Tags/Keywords

  • Barycenters

  • gradient descent

  • optimal transport

  • Bures manifold

  • Polyak-Lojasiewicz inequality

Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification
Video

Computing Wasserstein Barycenters Using Gradient Descent Algorithms
Abstract

In this talk, I will present rates of convergence for Wasserstein barycenters using gradient descent and stochastic gradient descent. While the barycenter functional is not geodesically convex, this result hinges on a Polyak-Lojasiewicz (PL) inequality in the case where the underlying distribution is supported on a subset of Gaussian distributions.
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Computing Wasserstein Barycenters Using Gradient Descent Algorithms

H.264 Video 928_28410_8313_Computing_Wasserstein_Barycenters_Using_Gradient_Descent_Algorithms.mp4
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