On Boolean Combinations of Definitive Classifiers

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. ∗Department of Mathematics and Centre for Discrete and Applicable Mathematics, London School of Economics, London WC2A 2AE, UK. [email protected]