Cloud Hosting

Author :

Abstract : In this paper, we focus on computational aspects of the Wasserstein barycenter problem. We propose two algorithms to compute Wasserstein barycenters of m discrete measures of size n with accuracy $e$. The first algorithm, based on mirror prox with a specific norm, meets the complexity of celebrated accelerated iterative Bregman projections (IBP), namely $widetilde O(mnsqrt n/e)$, however, with no limitations in contrast to the (accelerated) IBP, which is numerically unstable under small regularization parameter. The second algorithm, based on area-convexity and dual extrapolation, improves the previously best-known convergence rates for the Wasserstein barycenter problem enjoying $widetilde O(mn/e)$ complexity.

2. Distributed Optimization with Quantization for Computing Wasserstein BarycentersarXiv)

Author : Roman Krawtschenko, Csar A. Uribe, Alexander Gasnikov, Pavel Dvurechensky

Abstract : We study the problem of the decentralized computation of entropy-regularized semi-discrete Wasserstein barycenters over a network. Building upon recent primal-dual approaches, we propose a sampling gradient quantization scheme that allows efficient communication and computation of approximate barycenters where the factor distributions are stored distributedly on arbitrary networks. The communication and algorithmic complexity of the proposed algorithm are shown, with explicit dependency on the size of the support, the number of distributions, and the desired accuracy. Numerical results validate our algorithmic analysis.

Go here to see the original:
Updates on Wasserstein barycenter part11(Machine Learning) | by ... - Medium