Decentralize and Randomize: Faster Algorithm for Wasserstein Barycenters
Authors: Pavel Dvurechenskii, Darina Dvinskikh, Alexander Gasnikov, Cesar Uribe, Angelia Nedich
NeurIPS 2018 | Venue 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 EMAIL Alexander Gasnikov Moscow Institute of Physics and Technology, Institute for Information Transmission Problems RAS EMAIL César A. Uribe Massachusetts Institute of Technology EMAIL Angelia Nedi c Arizona State University, Moscow Institute of Physics and Technology EMAIL |
| 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. |