Statistical Optimality of Divide and Conquer Kernel-based Functional Linear Regression
Authors: Jiading Liu, Lei Shi
JMLR 2024 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | This paper studies the convergence performance of divide-and-conquer estimators in the scenario that the target function does not necessarily reside in the underlying RKHS. As a decomposition-based scalable approach, the divide-and-conquer estimators of functional linear regression can substantially reduce the algorithmic complexities in time and memory. We develop an integral operator approach to establish sharp finite sample upper bounds for prediction with divide-and-conquer estimators under various regularity conditions of explanatory variables and target function. We also prove the asymptotic optimality of the derived rates by building the mini-max lower bounds. Finally, we consider the convergence of noiseless estimators and show that the rates can be arbitrarily fast under mild conditions. |
| Researcher Affiliation | Academia | Jiading Liu EMAIL School of Mathematical Sciences Fudan University, Shanghai 200433, China Lei Shi EMAIL School of Mathematical Sciences and Shanghai Key Laboratory for Contemporary Applied Mathematics Fudan University, Shanghai 200433, China Shanghai Artificial Intelligence Laboratory 701 Yunjin Road, Shanghai 200232, China |
| Pseudocode | No | The paper does not contain any clearly labeled pseudocode or algorithm blocks. It describes mathematical methods and theoretical analyses without structured code-like procedures. |
| Open Source Code | No | The paper does not provide any statements or links indicating that source code for the described methodology is publicly available. |
| Open Datasets | No | The paper is theoretical and focuses on statistical optimality and convergence rates for functional linear regression. It does not use or provide access to any specific datasets for empirical evaluation. |
| Dataset Splits | No | The paper is theoretical and does not perform experiments on specific datasets, therefore, no dataset splits are mentioned. |
| Hardware Specification | No | The paper is theoretical and focuses on mathematical proofs and statistical optimality. It does not describe any experiments that would require specific hardware, and thus no hardware specifications are mentioned. |
| Software Dependencies | No | The paper is theoretical and focuses on mathematical derivations and proofs. It does not describe any computational experiments that would require specific software dependencies with version numbers. |
| Experiment Setup | No | The paper is theoretical and focuses on statistical optimality and convergence rates. It does not describe any experimental setups, hyperparameters, or training configurations. |