Metrizing Weak Convergence with Maximum Mean Discrepancies
Authors: Carl-Johann Simon-Gabriel, Alessandro Barp, Bernhard Schölkopf, Lester Mackey
JMLR 2023 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | This paper characterizes the maximum mean discrepancies (MMD) that metrize the weak convergence of probability measures for a wide class of kernels. More precisely, we prove that, on a locally compact, non-compact, Hausdorffspace, the MMD of a bounded continuous Borel measurable kernel k, whose RKHS-functions vanish at infinity (i.e., Hk C0), metrizes the weak convergence of probability measures if and only if k is continuous and integrally strictly positive definite ( R s.p.d.) over all signed, finite, regular Borel measures. |
| Researcher Affiliation | Collaboration | Carl-Johann Simon-Gabriel EMAIL Institute for Machine Learning ETH Zürich, Switzerland Alessandro Barp EMAIL Department of Engineering University of Cambridge, Alan Turing Institute, United Kingdom Bernhard Schölkopf EMAIL Empirical Inference Department MPI for Intelligent Systems, Tübingen, Germany Lester Mackey EMAIL Microsoft Research Cambridge, MA, USA |
| Pseudocode | No | The paper contains theoretical discussions, definitions, theorems, lemmas, and proofs, but no structured pseudocode or algorithm blocks are present. |
| Open Source Code | No | The paper does not contain any explicit statement about providing access to source code for the methodology described, nor does it provide any links to a code repository. |
| Open Datasets | No | The paper is a theoretical work focusing on mathematical properties and proofs; it does not describe or use any datasets for empirical evaluation. |
| Dataset Splits | No | The paper is a theoretical work and does not involve experimental evaluation with datasets, thus there is no mention of dataset splits. |
| Hardware Specification | No | The paper describes theoretical contributions and does not report on any experimental work that would require specific hardware specifications. |
| Software Dependencies | No | This is a theoretical paper and does not mention any software dependencies with specific version numbers, as no experimental setup is described. |
| Experiment Setup | No | The paper presents theoretical work, including proofs and mathematical characterizations, and therefore does not describe any experimental setup or hyperparameters. |