Decentralize and Randomize: Faster Algorithm for Wasserstein Barycenters
Authors: Pavel Dvurechenskii, Darina Dvinskikh, Alexander Gasnikov, Cesar Uribe, Angelia Nedich
NeurIPS 2018 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Finally, we demonstrate the effectiveness of our algorithm on the distributed computation of the regularized Wasserstein barycenter of a set of von Mises distributions for various network topologies and network sizes. Moreover, we show some initial results on the problem of image aggregation for two datasets, namely, a subset of the MNIST digit dataset [29] and subset of the IXI Magnetic Resonance dataset [1]. |
| Researcher Affiliation | Collaboration | Pavel Dvurechensky, Darina Dvinskikh Weierstrass Institute for Applied Analysis and Stochastics, Institute for Information Transmission Problems RAS {pavel.dvurechensky,darina.dvinskikh}@wias-berlin.de Alexander Gasnikov Moscow Institute of Physics and Technology, Institute for Information Transmission Problems RAS gasnikov@yandex.ru César A. Uribe Massachusetts Institute of Technology cauribe@mit.edu Angelia Nedi c Arizona State University, Moscow Institute of Physics and Technology angelia.nedich@asu.edu |
| Pseudocode | Yes | Algorithm 1 Accelerated Primal-Dual Stochastic Gradient Method (APDSGD) Algorithm 2 Distributed computation of Wasserstein barycenter |
| Open Source Code | No | No explicit statement or link providing access to the source code for the methodology described in the paper was found. |
| Open Datasets | Yes | MNIST digit dataset [29] IXI Magnetic Resonance dataset [1] |
| Dataset Splits | No | No specific training/test/validation dataset splits (e.g., percentages, counts, or standard split references) are explicitly provided in the main text. |
| Hardware Specification | No | No specific hardware details (e.g., GPU/CPU models, memory) used for running experiments are provided. |
| Software Dependencies | No | No specific software dependencies with version numbers are provided. |
| Experiment Setup | Yes | We assume n = 100 and the support of p is a set of 100 equally spaced points on the segment [ 5, 5]. Figure 1 shows the performance of Algorithm 2 for four classes of networks: complete, cycle, star, and Erd os-Rényi. Moreover, we show the behavior for different network sizes, namely: m = 10, 100, 200, 500. Figure 1: Dual function value and distance to consensus for 200, 100, 10, 500 agents, Mk = 100 and γ = 0.1. |