PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Step Size Adaptation in Reproducing Kernel Hilbert Space
S V N Vishwanathan, Nicol Schraudolph and Alex Smola
Journal of Machine Learning Research 2005.

Abstract

This paper presents an online Support Vector Machine (SVM) that uses the Stochastic Meta-Descent (SMD) algorithm to adapt its step size automatically. We formulate the online learning problem as a stochastic gradient descent in Reproducing Kernel Hilbert Space (RKHS) and translate SMD to the nonparametric setting, where its gradient trace parameter is no longer a coefficient vector but an element of the RKHS. We derive efficient updates that allow us to perform the step size adaptation in linear time. We apply the online SVM framework to a variety of loss functions, and in particular show how to handle structured output spaces and achieve efficient online multiclass classification. Experiments show that our algorithm outperforms more primitive methods for setting the gradient step size.

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EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:2043
Deposited By:S V N Vishwanathan
Deposited On:16 January 2006