# Learning Theory of Distributed Regression with Bias Corrected Regularization Kernel Network

arXiv: https://arxiv.org/abs/1708.01960 · HTML: https://mlsanity.com/paper/1708.01960/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Aug 2017.

## Built on by (most cited first, 4 of 4)

- [Robust Kernel-based Distribution Regression](https://mlsanity.com/paper/2104.10637/) (2021)
- [Adaptive Distributed Kernel Ridge Regression: A Feasible Distributed Learning Scheme for Data Silos](https://mlsanity.com/paper/2309.04236/) (2023)
- [Distributed Semi-Supervised Sparse Statistical Inference](https://mlsanity.com/paper/2306.10395/) (2023)
- [Oversampling Divide-and-conquer for Response-skewed Kernel Ridge Regression](https://mlsanity.com/paper/2107.05834/) (2021)

## Abstract (arXiv)

Distributed learning is an effective way to analyze big data. In distributed regression, a typical approach is to divide the big data into multiple blocks, apply a base regression algorithm on each of them, and then simply average the output functions learnt from these blocks. Since the average process will decrease the variance, not the bias, bias correction is expected to improve the learning performance if the base regression algorithm is a biased one. Regularization kernel network is an effective and widely used method for nonlinear regression analysis. In this paper we will investigate a bias corrected version of regularization kernel network. We derive the error bounds when it is applied to a single data set and when it is applied as a base algorithm in distributed regression. We show that, under certain appropriate conditions, the optimal learning rates can be reached in both situations.