Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in [1].
Kernel Distribution Embeddings: Universal Kernels, Characteristic Kernels and Kernel Metrics on Distributions
Authors: Carl-Johann Simon-Gabriel, Bernhard Schölkopf
JMLR 2018 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | The contributions of this paper are three-fold. First, by slightly extending the usual definitions of universal, characteristic and strictly positive definite kernels, we show that these three concepts are essentially equivalent. Second, we give the first complete characterization of those kernels whose associated MMD-distance metrizes the weak convergence of probability measures. Third, we show that kernel mean embeddings can be extended from probability measures to generalized measures called Schwartz-distributions and analyze a few properties of these distribution embeddings. |
| Researcher Affiliation | Academia | Carl-Johann Simon-Gabriel EMAIL Bernhard Sch olkopf EMAIL MPI for Intelligent Systems Spemannstrasse 41, 72076 T ubingen, Germany |
| Pseudocode | No | The paper presents theoretical definitions, theorems, and proofs related to kernel distribution embeddings, but it does not include any structured pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not contain any explicit statements about releasing source code or links to code repositories. |
| Open Datasets | No | The paper is theoretical and does not conduct experiments on any specific datasets. Example 1 uses theoretical Gaussian probability measures for illustration but not for empirical validation with a dataset. |
| Dataset Splits | No | The paper does not involve empirical experiments with datasets, and therefore no dataset splits are discussed or provided. |
| Hardware Specification | No | The paper is theoretical and does not describe any experimental setup that would require specific hardware. No hardware specifications are mentioned. |
| Software Dependencies | No | The paper focuses on theoretical mathematical concepts and does not describe any specific software implementations or dependencies with version numbers. |
| Experiment Setup | No | The paper is theoretical and does not contain details about experimental setups, hyperparameters, or training configurations. There are no empirical experiments described in the main text. |