Distributed Learning with Regularized Least Squares
Authors: Shao-Bo Lin, Xin Guo, Ding-Xuan Zhou
JMLR 2017 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | We study distributed learning with the least squares regularization scheme in a reproducing kernel Hilbert space (RKHS). By a divide-and-conquer approach, the algorithm partitions a data set into disjoint data subsets, applies the least squares regularization scheme to each data subset to produce an output function, and then takes an average of the individual output functions as a final global estimator or predictor. We show with error bounds and learning rates in expectation in both the L2-metric and RKHS-metric that the global output function of this distributed learning is a good approximation to the algorithm processing the whole data in one single machine. Our derived learning rates in expectation are optimal and stated in a general setting without any eigenfunction assumption. The analysis is achieved by a novel second order decomposition of operator differences in our integral operator approach. Even for the classical least squares regularization scheme in the RKHS associated with a general kernel, we give the best learning rate in expectation in the literature. |
| Researcher Affiliation | Academia | Shao-Bo Lin EMAIL Department of Mathematics City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong Xin Guo EMAIL Department of Applied Mathematics The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong Ding-Xuan Zhou EMAIL Department of Mathematics City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong |
| Pseudocode | No | The paper describes algorithms and mathematical procedures using standard mathematical notation and text, but it does not include any clearly labeled 'Pseudocode' or 'Algorithm' blocks, nor does it present structured steps formatted like code. |
| Open Source Code | No | The paper does not contain an unambiguous statement that the authors are releasing their code, nor does it provide a direct link to a source-code repository or mention code in supplementary materials for the methodology described. |
| Open Datasets | No | The paper discusses a theoretical learning framework that involves conceptual 'data sets' or 'samples' (e.g., 'a sample D = {(xi, yi)}N i=1 X Y independently drawn according to ρ'). However, it does not use or provide concrete access information (links, citations, repository names) for any specific publicly available or open dataset used in empirical experiments. |
| Dataset Splits | No | The paper is theoretical and does not describe any empirical experiments involving specific datasets. While it discusses 'partitioning the data set D into m disjoint subsets {Dj}m j=1' as part of the distributed learning algorithm's conceptual description, this is not a specification of training/test/validation splits for an actual dataset used in an experiment. |
| Hardware Specification | No | The paper is theoretical and does not describe any experiments or their implementation details that would necessitate mentioning specific hardware specifications like GPU/CPU models, processors, or cloud resources. |
| Software Dependencies | No | The paper is theoretical and focuses on mathematical derivations and error analysis. It does not mention any specific software, libraries, or their version numbers that would be required to reproduce experimental results. |
| Experiment Setup | No | The paper is theoretical and focuses on error analysis and learning rates. It does not describe any empirical experiments, and therefore, no specific experimental setup details such as hyperparameter values, training configurations, or system-level settings are provided. |