[Moved Online] Hot Topics: Optimal Transport And Applications To Machine Learning And Statistics - Computing Wasserstein barycenters using gradient descent algorithms
Presenter
May 4, 2020
Keywords:
- Barycenters
- gradient descent
- optimal transport
- Bures manifold
- Polyak-Lojasiewicz inequality
MSC:
- 74P20
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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.