Characterization of translation invariant MMD on Rd and connections with Wasserstein distances
Authors: Thibault Modeste, Clément Dombry
JMLR 2024 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | A short numerical experiment illustrates our findings in the framework of the one-sample-test. We propose a simple numerical experiment illustrating the behaviour of the various MMDs considered in this paper in the context of the One-Sample-Test. We report in Figure 1 the rejection rates of the tests corresponding to these different distances for DGP1 and DGP2 respectively. |
| Researcher Affiliation | Academia | Thibault Modeste EMAIL Institut Camille Jordan Universit e Claude Bernard Lyon 1 CNRS UMR 5208, F-69622 Villeurbanne, France Cl ement Dombry EMAIL Universit e de Franche-Comt e, CNRS, Lm B (UMR 6623), F-25000 Besan con, France |
| Pseudocode | No | The paper describes methodologies and proofs using mathematical notation and prose but does not include any explicitly labeled pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not contain an unambiguous statement or a direct link indicating that the authors have released source code for the methodology described in this paper. It mentions existing work with open-source implications (e.g., MMD and Wasserstein GANs) but not code specific to their contributions. |
| Open Datasets | No | The paper uses simulated data from well-known theoretical distributions (standard Gaussian distribution, Student distribution) for its numerical experiments. It does not provide concrete access information (links, DOIs, repositories, or specific citations) for a publicly available or open dataset in the typical sense of machine learning datasets. |
| Dataset Splits | No | The paper describes using a sample of size n=100 and a simulated independent sample of size m=500 for a one-sample test. These are sample sizes for simulated data generation and comparison, not traditional dataset splits (e.g., train/test/validation) of an existing dataset for model training or evaluation. |
| Hardware Specification | No | The paper describes numerical experiments but does not provide specific details about the hardware (e.g., GPU/CPU models, memory, or cluster specifications) used to run these experiments. |
| Software Dependencies | No | The paper describes mathematical frameworks and statistical tests but does not specify any ancillary software or library names with version numbers that would be needed to replicate the experiments. |
| Experiment Setup | Yes | We consider the tests as described above with n = 100, m = 500, B = 1000 and α = 0.05 and the following distances: GK: the MMD associated with the Gaussian kernel with variance σ2 = d, i.e. k(x, y) = exp( x y 2/(2d)) (similar to Example 1); ESK1-ESK3: the MMD associated with energy score kernel with power α = 0.25, 0.5 and 0.75 respectively (see Example 4); MGK: the MMD associated with the modified Gaussian kernel k(x, y) = exp( x y 2/(2d)) + d 1x y (see Example 6). W1: the Wasserstein distance of order 1. |