A General Framework for the Analysis of Kernel-based Tests
Authors: Tamara Fernández, Nicolás Rivera
JMLR 2024 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | To demonstrate the efficacy of our approach, we thoroughly examine two categories of kernel tests, along with three specific examples of kernel tests, including a novel kernel test for conditional independence testing. ... For completeness, we include two experiments with simulated data to evaluate the empirical performance of the kernelised GCM, hereafter referred to as KGCM, as introduced in Section 4.3.1. |
| Researcher Affiliation | Academia | Tamara Fern andez EMAIL Faculty of Engineering and Science Universidad Adolfo Ib a nez, Chile; Nicol as Rivera EMAIL Facultad de Ciencias Universidad de Valpara ıso, Chile |
| Pseudocode | No | The paper describes methods and proposes a framework but does not contain any explicitly labeled 'Pseudocode' or 'Algorithm' blocks. |
| Open Source Code | No | In our experiments, we use the code provided by the authors1, which automatically chooses the k weight functions ωa, and performs the test. Footnote 1: https://cran.r-project.org/web/packages/weightedGCM/index.html. This refers to a third-party R package used for comparison, not the authors' own source code for the methodology described in this paper. |
| Open Datasets | No | For completeness, we include two experiments with simulated data to evaluate the empirical performance of the kernelised GCM, hereafter referred to as KGCM, as introduced in Section 4.3.1. Data 1. Let U1 N(0, 1) and U2 N(0, 1) be independent. Given a parameter γ [0, 1], we generate data as Z N(0, 1), X = Z + U1 sin(5Z) and Y = Z2 + γU1 + (1 γ)U2. Data 2. Let d 2, and let Id be the d d identity matrix. Then we generate data Z = (Z1, . . . , Zd) N(0, Id), X = Z1 + 1/sqrt(d) P_i=1^d Ui Zi, and Y = Z2 + 1/sqrt(d) P_i=1^d Ui, where U = (U1, . . . , Ud) N(0, Id) is independent of Z. |
| Dataset Splits | No | Our experiments consider n = 100 data points, and we repeat the experiment 1000 times to estimate the rejection rate. The paper mentions the total number of data points and repetitions but does not specify any training, validation, or test splits. |
| Hardware Specification | No | The paper describes experimental procedures and methods used (e.g., polynomial regression) but does not provide any specific details about the hardware (e.g., CPU, GPU models, memory) used to run the experiments. |
| Software Dependencies | No | In our experiments, we use the code provided by the authors1, which automatically chooses the k weight functions ωa, and performs the test. Footnote 1: https://cran.r-project.org/web/packages/weightedGCM/index.html. The paper mentions using the 'weightedGCM' package, implicitly referring to the R language, but does not provide specific version numbers for R or the package itself. |
| Experiment Setup | No | The paper mentions employing 'polynomial regression with a degree of 3 in our first experiment and a degree of 1 in the second' and setting 'α = 0.05 as the level of the test' and using 'M = 1000 bootstrap samples'. However, it does not provide detailed hyperparameters or system-level training settings for the core methodologies. |