PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Using generalization error bounds to train the set covering machine
Zakria Hussain and John Shawe-Taylor
International Conference on Neural Information Processing 2007.

Abstract

In this paper we eliminate the need for parameter estimation associated with the set covering machine (SCM) by directly minimizing generalization error bounds. Firstly, we consider a sub-optimal greedy heuristic algorithm termed the bound set covering machine (BSCM). Next, we propose the branch and bound set covering machine (BBSCM) and prove that it finds a classifier producing the smallest generalization error bound. We further justify empirically the BBSCM algorithm with a heuristic relaxation, called BBSCM($\tau$), which guarantees a solution whose bound is within a factor $\tau$ of the optimal. Experiments comparing against the support vector machine (SVM) and SCM algorithms demonstrate that the approaches proposed can lead to some or all of the following: 1) faster running times, 2) sparser classifiers and 3) competitive generalization error, all while avoiding the need for parameter estimation.

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EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:3145
Deposited By:Zakria Hussain
Deposited On:26 December 2007