On Distance and Kernel Measures of Conditional Dependence
Authors: Tianhong Sheng, Bharath K. Sriperumbudur
JMLR 2023 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | In this work, we explore the connection between conditional dependence measures induced by distances on a metric space and reproducing kernels associated with a reproducing kernel Hilbert space (RKHS). For certain distance and kernel pairs, we show the distance-based conditional dependence measures to be equivalent to that of kernel-based measures. On the other hand, we also show that some popular kernel conditional dependence measures based on the Hilbert-Schmidt norm of a certain crossconditional covariance operator, do not have a simple distance representation, except in some limiting cases. |
| Researcher Affiliation | Academia | Tianhong Sheng EMAIL Department of Statistics Pennsylvania State University University Park, PA 16802, USA Bharath K. Sriperumbudur EMAIL Department of Statistics Pennsylvania State University University Park, PA 16802, USA |
| Pseudocode | No | The paper does not contain any pseudocode or algorithm blocks. It focuses on mathematical definitions, theorems, and proofs. |
| Open Source Code | No | The paper makes no explicit statement about releasing source code for the methodology described. It refers to other works for related concepts but does not provide code for its own contributions. |
| Open Datasets | No | The paper is theoretical and does not use any datasets for experiments or analysis, therefore no information regarding public availability of datasets is provided. |
| Dataset Splits | No | The paper is theoretical and does not involve experiments using datasets, so there is no mention of dataset splits. |
| Hardware Specification | No | The paper is theoretical and does not describe any experimental setup or computational tasks that would require specific hardware specifications. |
| Software Dependencies | No | The paper is theoretical and focuses on mathematical concepts and proofs, thus it does not mention any software dependencies or version numbers. |
| Experiment Setup | No | The paper is theoretical and does not include any experimental results or setups, therefore no details on hyperparameters or training settings are provided. |