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Summary: Sampling Techniques for Kernel Methods
Dimitris Achlioptas
Microsoft Research
optas@microsoft.com
Frank McSherry
University of Washington
mcsherry@cs.washington.edu
Bernhard Sch¨olkopf
Biowulf Technologies NY
bs@conclu.de
Abstract
We propose randomized techniques for speeding up Kernel Principal
Component Analysis on three levels: sampling and quantization of the
Gram matrix in training, randomized rounding in evaluating the kernel
expansions, and random projections in evaluating the kernel itself. In all
three cases, we give sharp bounds on the accuracy of the obtained ap-
proximations. Rather intriguingly, all three techniques can be viewed as
instantiations of the following idea: replace the kernel function by a
"randomized kernel" which behaves like in expectation.
1 Introduction
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