Deep Nonparametric Estimation of Operators between Infinite Dimensional Spaces
Authors: Hao Liu, Haizhao Yang, Minshuo Chen, Tuo Zhao, Wenjing Liao
JMLR 2024 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | This paper studies the nonparametric estimation of Lipschitz operators using deep neural networks. Non-asymptotic upper bounds are derived for the generalization error of the empirical risk minimizer over a properly chosen network class... Our contributions are summarized as follows: 1. We derive an upper bound on the generalization error... The proofs of all results are given in Section 7. We conclude this paper in Section 8. |
| Researcher Affiliation | Academia | 1 Department of Mathematics, Hong Kong Baptist University, Hong Kong 2 Department of Mathematics and Department of Computer Science, University of Maryland College 3 Department of Electrical and Computer Engineering, Princeton University, USA 4 School of Industrial and Systems Engineering, Georgia Institute of Technology, USA 5 School of Mathematics, Georgia Institute of Technology, USA |
| Pseudocode | No | The paper describes methods and theoretical derivations in prose and mathematical notation but does not contain any structured pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not provide concrete access to source code for the methodology described. It only mentions the license for the paper itself: 'License: CC-BY 4.0, see https://creativecommons.org/licenses/by/4.0/. Attribution requirements are provided at http://jmlr.org/papers/v25/22-0719.html.' |
| Open Datasets | No | The paper is theoretical and analyzes statistical properties and error bounds for learning operators. It discusses 'training sample size' and 'samples' in a theoretical context but does not use or refer to any specific named publicly available datasets for experimental evaluation. |
| Dataset Splits | No | The paper describes a theoretical data splitting strategy for its analysis: 'Given the training data S = {ui, vi}2n i=1, we split the data into two subsets S1 = {ui, vi}n i=1 and S2 = {ui, vi}2n i=n+1 1, where S1 is used to compute the encoders and decoders and S2 is used to learn the transformation Γ between the encoded vectors.' However, this is part of the theoretical framework and not a specification for reproducing experiments with real datasets. |
| Hardware Specification | No | This is a theoretical paper. There are no experiments conducted that would require specific hardware, and thus no hardware specifications are mentioned. |
| Software Dependencies | No | This is a theoretical paper. There are no experiments conducted that would require specific software, and thus no software dependencies with version numbers are mentioned. |
| Experiment Setup | No | This is a theoretical paper. No experiments are conducted, and therefore no experimental setup details, hyperparameters, or training configurations are provided. |