A Perturbation-Based Kernel Approximation Framework
Authors: Roy Mitz, Yoel Shkolnisky
JMLR 2022 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We support our theoretical results numerically and demonstrate the advantages of our approximation framework on both synthetic and real-world data. |
| Researcher Affiliation | Academia | Roy Mitz EMAIL Yoel Shkolnisky EMAIL School of Mathematical Sciences Tel-Aviv University Tel-Aviv, Israel |
| Pseudocode | No | The paper describes mathematical formulas and derivations, but it does not contain any explicitly labeled pseudocode or algorithm blocks with structured steps. |
| Open Source Code | Yes | The MATLAB code to reproduce the graphs in this section is found in github.com/roymitz/perturbation_kernel_approximation. |
| Open Datasets | Yes | In this subsection, we use real-world datasets taken from the UCI Machine Learning Repository (Dua and Graff, 2017), as described in Table 1. For each dataset, we repeat the experiment described in the introduction of Section 7.2 multiple times, each time on a random subset of 1000 points from the dataset, and for several values of σ, reflecting the transition between a sparse matrix (small σ) and a dense matrix (large σ). |
| Dataset Splits | Yes | For each dataset, we repeat the experiment described in the introduction of Section 7.2 multiple times, each time on a random subset of 1000 points from the dataset, and for several values of σ, reflecting the transition between a sparse matrix (small σ) and a dense matrix (large σ). |
| Hardware Specification | No | The paper does not provide specific hardware details (e.g., CPU, GPU models, or memory specifications) used for running the experiments. |
| Software Dependencies | No | The MATLAB code to reproduce the graphs in this section is found in github.com/roymitz/perturbation_kernel_approximation. (While MATLAB is mentioned, no specific version number is provided, nor are any specific libraries or packages with their versions.) |
| Experiment Setup | Yes | In all the numerical examples to follow, we use µ = 0 for all approximation schemes. We note that we typically witness a marginal difference between the performance of µ = 0 and µ = µmean for real-world data, as such data are usually close to being low-rank. Thus, we do not include the µ-shifted kernel approximation in the experiments of this section. We also set n = 1000 in all experiments. We choose m to be the number of components that account for 90% of the energy of K, with a maximum value of 5. For the block-diagonal kernel approximation, we always use two blocks of the same size. Each experiment is performed as follows. For each kernel type, we generate several kernels of that type, each with a different kernel parameter (to be explained later for each example). Then, we approximate each of the kernels using each of the approximation methods, where in any case the matrix Ks used in the approximation consists of 20% of the entries of the approximated kernel. |