Sinkhorn Barycenters with Free Support via Frank-Wolfe Algorithm
Authors: Giulia Luise, Saverio Salzo, Massimiliano Pontil, Carlo Ciliberto
NeurIPS 2019 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Experiments validate the effectiveness of our method in practice.We empirically evaluate the performance of the proposed algorithm. |
| Researcher Affiliation | Academia | Giulia Luise1, Saverio Salzo2, Massimiliano Pontil1,2, Carlo Ciliberto3 g.luise.16@ucl.ac.uk, saverio.salzo@iit.it, m.pontil@cs.ucl.ac.uk,c.ciliberto@ic.ac.uk 1 Department of Computer Science, University College London, UK 2 CSML, Istituto Italiano di Tecnologia, Genova, Italy 3 Department of Electrical and Electronic Engineering, Imperial College London, UK |
| Pseudocode | Yes | Algorithm 1 FRANK-WOLFE IN DUAL BANACH SPACES |
| Open Source Code | Yes | Code has been made publicly available1. 1 https://github.com/GiulsLu/Sinkhorn-Barycenters |
| Open Datasets | Yes | k-means on MNIST digits. We consider a subset of 500 random images from the MNIST dataset. Continuous measures: barycenter of Gaussians. We compute the barycenter of 5 Gaussian distributions N(mi, Ci) i = 1, . . . , 5 in R2, with mean mi 2 R2 and covariance Ci randomly generated. |
| Dataset Splits | No | The information is insufficient. The paper mentions datasets like MNIST and Gaussian distributions but does not provide specific train/validation/test dataset splits (percentages, sample counts, or explicit standard split references) for reproducibility. |
| Hardware Specification | No | The information is insufficient. The paper does not provide specific hardware details (e.g., exact GPU/CPU models, processor types, or memory amounts) used for running its experiments. |
| Software Dependencies | No | The information is insufficient. The paper does not provide specific ancillary software details (e.g., library or solver names with version numbers) needed to replicate the experiment. |
| Experiment Setup | Yes | We compute the barycenter of 30 randomly generated nested ellipses on a 50 50 grid similarly to [14]. We apply Alg. 2 to empirical measures obtained by sampling n = 500 points from each N(mi, Ci), i = 1, . . . , 5. We initialize 20 centroids according to the k-means++ strategy [4]. |