Home Page

Papers

Submissions

News

Editorial Board

Announcements

Proceedings

Open Source Software

Search

Statistics

Login

Frequenty Asked Questions

Contact Us



RSS Feed

Parallelizing Spectrally Regularized Kernel Algorithms

Nicole Mücke, Gilles Blanchard; 19(30):1−29, 2018.

Abstract

We consider a distributed learning approach in supervised learning for a large class of spectral regularization methods in an reproducing kernel Hilbert space (RKHS) framework. The data set of size $n$ is partitioned into $m=O(n^\alpha)$, $\alpha < \frac{1}{2}$, disjoint subsamples. On each subsample, some spectral regularization method (belonging to a large class, including in particular Kernel Ridge Regression, $L^2$-boosting and spectral cut-off) is applied. The regression function $f$ is then estimated via simple averaging, leading to a substantial reduction in computation time. We show that minimax optimal rates of convergence are preserved if $m$ grows sufficiently slowly (corresponding to an upper bound for $\alpha$) as $n \to \infty$, depending on the smoothness assumptions on $f$ and the intrinsic dimensionality. In spirit, the analysis relies on a classical bias/stochastic error analysis.

[abs][pdf][bib]       
© JMLR 2018. (edit, beta)