TY  - JOUR
A1  - Mücke, Nicole
A1  - Blanchard, Gilles
T1  - Parallelizing spectrally regularized kernel algorithms
JF  - Journal of machine learning research
N2  - 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 < 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 -> infinity, depending on the smoothness assumptions on f and the intrinsic dimensionality. In spirit, the analysis relies on a classical bias/stochastic error analysis.
KW  - Distributed Learning
KW  - Spectral Regularization
KW  - Minimax Optimality
Y1  - 2018
SN  - 1532-4435
VL  - 19
PB  - Microtome Publishing
CY  - Cambridge, Mass.
ER  -