Distributional Convergence of the Sliced Wasserstein Process

Authors: Jiaqi Xi, Jonathan Niles-Weed

NeurIPS 2022 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental 4 Simulation Studies We illustrate our distributional limit results in Monte Carlo simulations. Specifically, we investigate the speed of convergence of the sliced Wasserstein distance and the max-sliced Wasserstein distance. We also investigate the convergence speed of the amplitude, which provides an example of a functional not covered in prior work.
Researcher Affiliation Academia Jiaqi Xi1 and Jonathan Niles-Weed1,2 1Courant Institute of Mathematical Sciences, New York University, NY 10012 2Center for Data Science, New York University, NY 10011
Pseudocode No No structured pseudocode or algorithm blocks were found.
Open Source Code Yes 3. (a) Did you include the code, data, and instructions needed to reproduce the main experimental results (either in the supplemental material or as a URL)? [Yes] We have included the code and instructions in the supplemental material.
Open Datasets No The paper describes distributions P and Q (e.g., 'uniform on unit sphere S2', 'uniform on the surface of ellipsoid') for its simulations but does not provide access information (link, DOI, specific repository, or formal citation with authors/year) for a publicly available dataset that adheres to the strict criteria.
Dataset Splits No The paper describes sampling i.i.d. observations with specified sizes (e.g., 'n = 50, 100, 500') and repetition counts for Monte Carlo simulations, but it does not specify explicit training/validation/test dataset splits with percentages, sample counts, or citations to predefined splits.
Hardware Specification No No specific hardware details (such as GPU/CPU models, processor types, or memory amounts) used for running experiments were provided.
Software Dependencies No The paper mentions using 'the Python package POT [18]' and a 'Riemannian optimization method proposed in [23]' but does not provide specific version numbers for these or any other software dependencies.
Experiment Setup Yes The paper specifies experimental parameters such as sample sizes ('n = 50, 100, 500' and 'n = 1000') and the number of repetitions for Monte Carlo simulations ('500 times', '2000 times', 'B = 500 replications').