An analysis of learning in weightless neural systems

Abstract

This thesis brings together two strands of neural networks research - weightless systems and statistical learning theory - in an attempt to understand better the learning and generalisation abilities of a class of pattern classifying machines. The machines under consideration are n-tuple classifiers. While their analysis falls outside the domain of more widespread neural networks methods the method has found considerable application since its first publication in 1959. The larger class of learning systems to which the n-tuple classifier belongs is known as the set of weightless or RAM-based systems, because of the fact that they store all their modifiable information in the nodes rather than as weights on the connections. The analytical tools used are those of statistical learning theory. Learning methods and machines are considered in terms of a formal learning problem which allows the precise definition of terms such as learning and generalisation (in this context). Results relating the empirical error of the machine on the training set, the number of training examples and the complexity of the machine (as measured by the Vapnik- Chervonenkis dimension) to the generalisation error are derived. In the thesis this theoretical framework is applied for the first time to weightless systems in general and to n-tuple classifiers in particular. Novel theoretical results are used to inspire the design of related learning machines and empirical tests are used to assess the power of these new machines. Also data-independent theoretical results are compared with data-dependent results to explain the apparent anomalies in the n-tuple classifier's behaviour. The thesis takes an original approach to the study of weightless networks, and one which gives new insights into their strengths as learning machines. It also allows a new family of learning machines to be introduced and a method for improving generalisation to be applied.