Non-asymptotic convergence bounds for Wasserstein approximation using point clouds
Authors: Quentin Mérigot, Filippo Santambrogio, Clément SARRAZIN
NeurIPS 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this section, we report some experimental results in dimension d = 2. Gray-scale image As we mentioned in the introduction, uniform optimal quantization allows to sparsely represent a (gray scale) image via points, clustered more closely in areas where the image is darker [5, 3]. On figure 2, we ploted the point clouds obtained after one step of Lloyd s algorithm, starting from regular grids. The rate of convergence observed on the right-hand side chart, namely N 1.00, is coherent with the theoretical estimate log(N)/N of Remark 1. |
| Researcher Affiliation | Academia | Quentin Mérigot Université Paris-Saclay, CNRS, Laboratoire de mathématiques d Orsay, 91405, Orsay, France Institut Universitaire de France Filippo Santambrogio Univ Lyon, Université Claude Bernard Lyon 1, CNRS UMR 5208, Institut Camille Jordan F-69622 Villeurbanne Institut Universitaire de France Clément Sarrazin Université Paris-Saclay, CNRS, Laboratoire de mathématiques d Orsay 91405, Orsay, France |
| Pseudocode | No | The paper describes algorithms (Lloyd's algorithm, gradient descent) in mathematical equations and prose, but does not include structured pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not provide any explicit statement about releasing source code or a link to a code repository for the methodology described. |
| Open Datasets | No | The paper mentions using a 'gray-scale image' (Puffin from Wikimedia Commons) and a 'Gaussian density truncated to the unit square' for numerical results, but does not provide concrete access information (link, DOI, or formal citation for a dataset) for a publicly available or open dataset used for training. |
| Dataset Splits | No | The paper does not provide specific information about training, validation, or test dataset splits, percentages, or sample counts needed to reproduce the data partitioning. |
| Hardware Specification | No | The paper does not provide any specific hardware details such as GPU/CPU models, processor types, or memory used for running its experiments. |
| Software Dependencies | No | The paper does not specify any software dependencies with version numbers (e.g., Python, PyTorch, specific solvers) needed to replicate the experiment. |
| Experiment Setup | No | The paper describes initial conditions for the point clouds (e.g., regular grid, random distribution) but does not provide specific hyperparameter values (like learning rates, batch sizes, or number of epochs) or detailed training configurations for the experiments. |