A General Framework for Consistency of Principal Component Analysis
Authors: Dan Shen, Haipeng Shen, J. S. Marron
JMLR 2016 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | A general asymptotic framework is developed for studying consistency properties of principal component analysis (PCA). Our framework includes several previously studied domains of asymptotics as special cases and allows one to investigate interesting connections and transitions among the various domains. More importantly, it enables us to investigate asymptotic scenarios that have not been considered before, and gain new insights into the consistency, subspace consistency and strong inconsistency regions of PCA and the boundaries among them. We also establish the corresponding convergence rate within each region. |
| Researcher Affiliation | Academia | Dan Shen EMAIL Interdisciplinary Data Sciences Consortium Department of Mathematics and Statistics University of South Florida Tampa, FL 33620-5700, USA Haipeng Shen EMAIL School of Business University of Hong Kong Pokfulam, Hong Kong J. S. Marron EMAIL Department of Statistics and Operations Research University of North Carolina at Chapel Hill Chapel Hill, NC 27599-3260, USA |
| Pseudocode | No | The paper focuses on developing a general asymptotic framework, presenting theorems, and providing proofs (e.g., Section 7: "We now provide the detailed proof for Theorem 1"). It describes mathematical models and theoretical concepts. There are no structured pseudocode or algorithm blocks presented in the text. |
| Open Source Code | No | The paper refers to supplementary materials for proofs and corollaries: "The supplementary materials contain the corresponding corollaries of Theorems 1 and 2, for multiple-spike models with distinct eigenvalues and single spike models, along with the proofs of Theorem 2 and all the corollaries." It does not explicitly state that source code for the methodology is provided in these materials or elsewhere. |
| Open Datasets | No | The paper focuses on theoretical models such as the "Single-component Spike Model", "Multiple-component Spike Model", and "The Factor Model of Fan et al. (2013)". It does not use or provide access information for any empirical, publicly available datasets. |
| Dataset Splits | No | The paper presents theoretical models and mathematical proofs. There are no experiments conducted using datasets, and therefore no mention of dataset splits for training, validation, or testing. |
| Hardware Specification | No | This paper is theoretical, focusing on mathematical frameworks and proofs. It does not describe any computational experiments or the hardware used to run them. |
| Software Dependencies | No | The paper is a theoretical work on statistical consistency of PCA. It does not describe any computational implementations or software used with specific version numbers. |
| Experiment Setup | No | The paper is theoretical and focuses on developing an asymptotic framework for PCA consistency. It does not involve experimental setups, hyperparameters, or training configurations. |