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].
On Stationary-Point Hitting Time and Ergodicity of Stochastic Gradient Langevin Dynamics
Authors: Xi Chen, Simon S. Du, Xin T. Tong
JMLR 2020 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | Our analysis is straightforward. It only relies on basic linear algebra and probability theory tools. Our direct analysis also leads to tighter bounds comparing to Zhang et al. (2017) and shows the explicit dependence of the hitting time on different factors, including dimensionality, smoothness, noise strength, and step size effects. Moreover, we apply our analysis to study several important online estimation problems in machine learning, including linear regression, matrix factorization, and online PCA. Proofs for technical lemmas and the results in Section 6 are deferred to the appendix. |
| Researcher Affiliation | Academia | Xi Chen EMAIL Stern School of Business New York University, New York, NY 10012, USA; Simon S. Du EMAIL School of Mathematics Institute for Advanced Study, Princeton, NJ 08540, USA; Xin T. Tong EMAIL Department of Mathematics National University of Singapore, Singapore 119076 , Singapore. All listed institutions are universities or public research institutions. |
| Pseudocode | No | The paper discusses 'Algorithm (1.4)' which refers to the Unadjusted Langevin Algorithm (ULA), an existing method, rather than providing new pseudocode or an algorithm block for the methodology developed in this paper. The content is primarily theoretical with mathematical derivations and proofs. |
| Open Source Code | No | The paper does not contain any explicit statements about releasing source code for the described methodology, nor does it provide any links to code repositories. The focus of the paper is on theoretical analysis. |
| Open Datasets | No | The paper discusses applications to 'linear regression, matrix factorization, and online PCA'. For these applications, it describes theoretical data generation processes (e.g., 'Let the n-th sample be ωn = (an, bn), where the input an Rd is a sequence of random vectors independently drawn from the same distribution N(0, A)') rather than using or providing access to specific public datasets. |
| Dataset Splits | No | The paper focuses on theoretical analysis and does not involve empirical experiments with specific datasets. Therefore, there are no mentions of dataset splits like training, validation, or test sets. |
| Hardware Specification | No | The paper presents a theoretical analysis of Stochastic Gradient Langevin Dynamics (SGLD) and does not describe any experimental setup or results that would require specific hardware. Consequently, no hardware specifications are provided. |
| Software Dependencies | No | The paper is theoretical in nature, focusing on mathematical analysis and proofs. It does not describe any computational implementations or experiments that would necessitate listing specific software dependencies with version numbers. |
| Experiment Setup | No | The paper is a theoretical work providing analysis and bounds for SGLD. It does not describe any empirical experiments, and therefore, no experimental setup details, hyperparameters, or training configurations are provided. |