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• W3213698509 abstract "We study first-order optimization algorithms for computing the barycenter of Gaussian distributions with respect to the optimal transport metric. Although the objective is geodesically non-convex, Riemannian GD empirically converges rapidly, in fact faster than off-the-shelf methods such as Euclidean GD and SDP solvers. This stands in stark contrast to the best-known theoretical results for Riemannian GD, which depend exponentially on the dimension. In this work, we prove new geodesic convexity results which provide stronger control of the iterates, yielding a dimension-free convergence rate. Our techniques also enable the analysis of two related notions of averaging, the entropically-regularized barycenter and the geometric median, providing the first convergence guarantees for Riemannian GD for these problems." @default.
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• W3213698509 date "2021-12-06" @default.
• W3213698509 modified "2023-10-18" @default.
• W3213698509 title "Averaging on the Bures-Wasserstein manifold: dimension-free convergence of gradient descent" @default.
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