# How Many Machines Can We Use in Parallel Computing for Kernel Ridge Regression?

arXiv: https://arxiv.org/abs/1805.09948 · HTML: https://mlsanity.com/paper/1805.09948/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 May 2018.

## Built on by (most cited first, 1 of 1)

- [Oversampling Divide-and-conquer for Response-skewed Kernel Ridge Regression](https://mlsanity.com/paper/2107.05834/) (2021)

## Abstract (arXiv)

This paper aims to solve a basic problem in distributed statistical inference: how many machines can we use in parallel computing? In kernel ridge regression, we address this question in two important settings: nonparametric estimation and hypothesis testing. Specifically, we find a range for the number of machines under which optimal estimation/testing is achievable. The employed empirical processes method provides a unified framework, that allows us to handle various regression problems (such as thin-plate splines and nonparametric additive regression) under different settings (such as univariate, multivariate and diverging-dimensional designs). It is worth noting that the upper bounds of the number of machines are proven to be un-improvable (upto a logarithmic factor) in two important cases: smoothing spline regression and Gaussian RKHS regression. Our theoretical findings are backed by thorough numerical studies.