Diffusion Approximations for Online Principal Component Estimation and Global Convergence
Authors: Chris Junchi Li, Mengdi Wang, Han Liu, Tong Zhang
NeurIPS 2017 | Conference PDF | Archive PDF | Plain Text | 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 finite-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 {junchil,mengdiw,hanliu}@princeton.edu Tong Zhang Tencent AI Lab Shennan Ave, Nanshan District, Shenzhen, Guangdong Province 518057, China tongzhang@tongzhang-ml.org |
| 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. |