On the Complexity of Approximating Wasserstein Barycenters
Authors: Alexey Kroshnin, Nazarii Tupitsa, Darina Dvinskikh, Pavel Dvurechensky, Alexander Gasnikov, Cesar Uribe
ICML 2019 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this section, we provide numerical analysis for the three algorithms for the computation of approximate Wasserstein barycenters. We compare their iteration performance for the problem of computing the barycenter of a set of 15 discrete and truncated Gaussian distributions. Figure 1 (Left) shows the distance to optimality versus the iteration count for the IBP method and the Prox IBP method. Figure 2 shows the performance of the primal-dual accelerated gradient descent method. Table 1 shows the numerical values of the optimality gap for a subset of the experiments shown above. |
| Researcher Affiliation | Academia | 1Institute for Information Transmission Problems RAS, Moscow, Russia 2National Research University Higher School of Economics, Moscow, Russia 3Universit e Claude Bernard Lyon 1, Villeurbanne, France 4Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany 5Moscow Institute of Physics and Technology, Moscow, Russia 6Massachusetts Institute of Technology, Cambridge, USA. |
| Pseudocode | Yes | Algorithm 1 Dual Iterative Bregman Projection; Algorithm 2 Finding Wasserstein barycenter by IBP; Algorithm 3 Finding Wasserstein barycenter by proximal IBP; Algorithm 4 Accelerated Distributed Computation of Wasserstein barycenter |
| Open Source Code | No | The paper does not provide an explicit link to source code for the described methods or state that the code is publicly available. |
| Open Datasets | No | The paper states 'We compare their iteration performance for the problem of computing the barycenter of a set of 15 discrete and truncated Gaussian distributions.' but does not provide access information (link, citation with authors/year, or repository name) for these distributions or any other dataset. |
| Dataset Splits | No | The paper does not specify any training, validation, or test splits for the data used in the numerical analysis. |
| Hardware Specification | No | The paper does not mention any specific hardware used for running the experiments (e.g., GPU/CPU models, memory, or cloud instances). |
| Software Dependencies | No | The paper does not list specific software dependencies with version numbers used for the experiments. |
| Experiment Setup | Yes | Figure 1 (Left) shows the distance to optimality versus the iteration count for the IBP method and the Prox IBP method. For the Prox IBP method, we show the performance for four different cases, namely: = 1, = 0.1, = 0.01, and varying with = /2, if 1e 3 ( 0 = 10). |