Learning with nested generalized exemplars

This thesis presents a theory of learning called nested generalized exemplar theory (NGE), in which learning is accomplished by strong objects in Euclidean n-space, $E\sp{n},$ as hyper-rectangles. The hyper-rectangles may be nested inside one another or arbitrary depth. In contrast to most generalization processes, which replace symbolic formulae by more general formulae, the generalization process for NGE learning modifies hyper-rectangles by growing and reshaping them in a well-defined fashion. The axes of these hyper-rectangles are defined by the variables measured for each example. Each variable can have any range on the real line; thus the theory is not restricted to symbolic or binary values.

The basis of this theory is a psychological model called exemplar-based learning, in which examples are stored strictly as points in $E\sp{n}$. This thesis describes some advantages and disadvantages of NGE theory, positions it as a form of exemplar-based learning, and compares it to other inductive learning theories. An implementation has been tested on several different domains, four of which are presented in this thesis: predicting the recurrence of breast cancer, classifying iris flowers, predicting survival times for heart attack patients, and a discrete event simulation of a prediction task. The results in these domains are at least as good as, and in some cases significantly better than other learning algorithms applied to the same data.

Exemplar-based learning is emerging as a new direction for machine learning research. The main contribution of this thesis is to show how an exemplar-based theory, using nested generalizations to deal with exceptions, can be used to create very compact representations with excellent modelling capability.