PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

On Boolean combinations of definitive classifiers
Martin Anthony
(2003) Technical Report. Centre for Discrete and Applicable Mathematics, LSE, London, UK.

Abstract

We consider the sample complexity of concept learning when we classify by using a fixed Boolean function of the outputs of a number of different classifiers. Here, we take into account the `margins' of each of the constituent classifiers. A special case is that in which the constituent classifiers are linear threshold functions (or perceptrons) and the fixed Boolean function is the majority function. This corresponds to a `committee of perceptrons', an artificial neural network (or circuit) consisting of a single layer of perceptrons (or linear threshold units) in which the output of the network is defined to be the majority output of the perceptrons. Recent work of Auer et al. studied the computational properties of such networks (where they were called `parallel perceptrons'), proposed an incremental learning algorithm for them, and demonstrated empirically that the learning rule is effective. As a corollary of the sample complexity result presented here, generalization error bounds are derived for this special case that provide further motivation for the use of this learning rule.

EPrint Type:Monograph (Technical Report)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Theory & Algorithms
ID Code:114
Deposited By:Martin Anthony
Deposited On:22 May 2004