Fluctuations of the largest eigenvalues of transformed spiked Wigner matrices
Authors: Aro Lee, Ji Oon Lee
ICML 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In section 5, we conduct numerical experiments to compare theoretical results with numerical results for several examples. We conduct numerical experiments compare the theoretical results from Theorem 2.5 with empirical results using specific models. |
| Researcher Affiliation | Academia | 1Department of Mathematical Sciences, KAIST, Daejeon, Korea. Correspondence to: Aro Lee <EMAIL>, Ji Oon Lee <EMAIL>. |
| Pseudocode | No | The paper describes theoretical proofs and outlines, but does not contain any structured pseudocode or algorithm blocks (e.g., a figure or section explicitly labeled 'Algorithm' or 'Pseudocode'). |
| Open Source Code | No | The paper does not contain any explicit statement about releasing source code, nor does it provide a link to a code repository or mention code in supplementary materials for the described methodology. |
| Open Datasets | No | We first consider a transformed spiked Wigner matrix with non-Gaussian noise. The (rescaled) noise entries NWij (i j) are independently drawn from the sum of Gaussian and Rademacher random variables, whose density p is given by a centered bimodal distribution with unit variance. For the spike, we sample a random N-vector x so that Nxi s are i.i.d. Rademacher random variables, independent from the noise. We next consider a spiked Gaussian Wigner matrix, entrywise transformed by a polynomial. We let each noise entry be i.i.d. Gaussian and apply the mapping f(x) = (x2 + 3x 1)/ 11 entrywise. The paper describes generating synthetic data based on specified distributions and parameters, rather than using or providing access to pre-existing public datasets. |
| Dataset Splits | No | The paper describes generating synthetic data for its numerical experiments (e.g., 'We set N = 1024 and generate 5,000 independent transformed spiked Wigner matrices described above.') but does not specify training, testing, or validation splits for a pre-existing dataset. |
| Hardware Specification | No | The paper does not provide specific hardware details (e.g., GPU/CPU models, memory specifications, or types of computing clusters) used for running the numerical experiments. |
| Software Dependencies | No | The paper does not specify any software names with version numbers (e.g., programming languages, libraries, or frameworks) used to conduct the numerical experiments. |
| Experiment Setup | Yes | We set N = 1024 and generate 5,000 independent transformed spiked Wigner matrices described above. For a supercritical case, we set SNR λ = 0.8 with λe 2.902. For a subcritical case, we set SNR λ = 0.1 with λe 0.363. For a supercritical case, we set SNR λ = 2.5 with λe 1.294. For a subcritical case, we set SNR λ = 0.1 with λe 0.350. These details specify the matrix size, number of generated samples, and signal-to-noise ratio values used in the numerical experiments. |