Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in [1].
Diffusion Approximations for Online Principal Component Estimation and Global Convergence
Authors: Chris Junchi Li, Mengdi Wang, Han Liu, Tong Zhang
NeurIPS 2017 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | In this paper, we propose to adopt the diffusion approximation tools to study the dynamics of Oja s iteration... We show that the Oja s iteration for the top eigenvector generates a continuous-state discrete-time Markov chain over the unit sphere. We characterize the Oja s iteration in three phases using diffusion approximation and weak convergence tools. Our three-phase analysis further provides a ο¬nite-sample error bound for the running estimate, which matches the minimax information lower bound for principal component analysis under the additional assumption of bounded samples. |
| Researcher Affiliation | Collaboration | Chris Junchi Li Mengdi Wang Han Liu Princeton University Department of Operations Research and Financial Engineering, Princeton, NJ 08544 EMAIL Tong Zhang Tencent AI Lab Shennan Ave, Nanshan District, Shenzhen, Guangdong Province 518057, China EMAIL |
| Pseudocode | No | The paper describes the Oja's iteration using mathematical notation (Equation 1.3) but does not provide any explicitly labeled 'Algorithm' or 'Pseudocode' block. |
| Open Source Code | No | The paper does not contain any statement about releasing source code or provide a link to a code repository for the methodology described. |
| Open Datasets | No | The paper is a theoretical analysis of an algorithm and does not describe experiments performed on specific public datasets for training. |
| Dataset Splits | No | The paper is theoretical and does not describe an experimental setup with dataset splits for training, validation, or testing. |
| Hardware Specification | No | The paper does not provide any specific details about the hardware used for any computational work, which is consistent with its theoretical focus. |
| Software Dependencies | No | The paper does not list any specific software dependencies with version numbers, such as programming languages, libraries, or frameworks used for implementation or analysis. |
| Experiment Setup | No | The paper does not detail specific experimental setup parameters such as hyperparameter values, training configurations, or system-level settings, as it is a theoretical work. |