Reproducing Kernels and New Approaches in Compositional Data Analysis
Authors: Binglin Li, Changwon Yoon, Jeongyoun Ahn
JMLR 2023 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We demonstrate the wide applicability of the proposed theoretical framework with examples of nonparametric density estimation, kernel exponential family, and support vector machine for compositional data. An empirical example with support vector machines will also be presented to showcase its practical relevance in real-world problems. Figure 2: Toy compositional data on the simplex 2 in (a) are spread out to a sphere S2 in (b). The density estimate on S2 in (c) are pulled back to 2 in (d). In this section, we showcase the effectiveness of our compositional kernel in conjunction with a kernel support vector machine (SVM) using a toy dataset depicted in Figure 5. |
| Researcher Affiliation | Academia | Binglin Li EMAIL Department of Mathematics and Statistics North Carolina A&T State University Greensboro, NC 27411, USA Changwon Yoon EMAIL Jeongyoun Ahn EMAIL Department of Industrial and Systems Engineering Korea Advanced Institute of Science and Technology Daejeon, 34141, Korea |
| Pseudocode | No | The paper describes methods and mathematical constructions in prose and equations, but does not include any clearly labeled pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not provide an explicit statement about releasing source code for the described methodology, nor does it include a link to a code repository. |
| Open Datasets | No | Figure 2: Toy compositional data on the simplex 2... In this section, we showcase the effectiveness of our compositional kernel in conjunction with a kernel support vector machine (SVM) using a toy dataset depicted in Figure 5. The paper does not provide concrete access information for a publicly available dataset, instead using 'toy datasets' for its examples. |
| Dataset Splits | No | The paper uses a 'toy dataset' (Figure 5) with '100 observations from two classes' in Section 4.1.2 but does not provide specific details on how this dataset was split for training, validation, or testing. |
| Hardware Specification | Yes | For instance, the kernel SVM experiment discussed in Section 4.1.2 took between 52.15 to 92.41 seconds to compute on an M1 Mac Book Pro with 16 GB of memory, while other competing methods took much less computation times. |
| Software Dependencies | No | To implement the proposed compositional kernel, we utilized the gegenbauer C function in Matlab to compute ki( , ) and the fitcsvm function for SVM. The paper mentions Matlab and specific functions within it, but does not provide version numbers for any software components. |
| Experiment Setup | No | While we varied the hyperparameters of each kernel function, we kept the penalty parameter in SVM fixed at its default value. The paper mentions adjusting hyperparameters and using a default penalty parameter but does not provide any specific values for these settings. |