Spectral Phase Transition and Optimal PCA in Block-Structured Spiked Models
Authors: Pierre Mergny, Justin Ko, Florent Krzakala
ICML 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In Fig. 1, we illustrated the behavior of the theoretical limiting spectral distribution and top eigenvalue of the matrix Y /N before, at, and after the critical value λ1(ΩK) = 1 for specific values of the parameters. In Fig. 2, we plotted the value of the overlaps for different models and different values of the λ1(ΩK). The colored histogram corresponds to the empirical distribution of a sample Y /N with N = 3000...the dots represent an average over 30 samples of the empirical value of the overlaps for N = 4000... |
| Researcher Affiliation | Academia | Pierre Mergny 1 Justin Ko 2 3 Florent Krzakala 1 1Ide PHICS laboratory, Ecole F ed erale Polytechnique de Lausanne, Switzerland 2Department of Statistics and Actuarial Science, University of Waterloo, Canada 3UMPA, ENS Lyon, France. |
| Pseudocode | No | The paper focuses on theoretical analysis and mathematical derivations, and does not include any pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not contain any statement about making its source code publicly available or provide a link to a code repository. |
| Open Datasets | No | The paper describes empirical evaluations using generated data samples (e.g., 'empirical distribution of a sample Y /N with N = 3000', 'x sampled from a standard Gaussian distribution') but does not refer to or provide access information for any publicly available or open dataset. |
| Dataset Splits | No | The paper includes empirical illustrations from generated samples but does not specify any training, validation, or test dataset splits or cross-validation details for reproducibility. |
| Hardware Specification | No | The paper mentions empirical results from simulations (e.g., 'N = 3000', 'N = 4000') but provides no specific details about the hardware (e.g., CPU, GPU models, memory) used to run these simulations. |
| Software Dependencies | No | The paper describes theoretical and empirical work but does not list any specific software dependencies with version numbers (e.g., programming languages, libraries, frameworks) required to reproduce the results. |
| Experiment Setup | No | The paper presents theoretical results validated with empirical plots, but it does not include specific details about the experimental setup such as hyperparameter values, optimizer settings, or other training configurations. |