CATEGORIZATION AS PROBABILITY DENSITY-ESTIMATION

A category can be represented as a probability density function (pdf), that is, as a set of exemplars along with the probability or likelihood that each is selected as a stimulus. This article examines the relation between categorization and pdf estimation. We first discuss the differences between classifiers that know the true category pdfs and classifiers that must estimate these functions from trial-by-trial feedback. Consistency is shown to be the key statistical property that guarantees two such classifiers will reasonably agree. Parametric and nonparametric pdf estimators are interpreted from the perspective of the categorization process. It is shown that the prototype model and several decision-bound models of categorization are parametric, whereas most exemplar models are nonparametric. The exemplar models are shown to be equivalent to a classifier that uses the minimum variance unbiased estimator of the category baserates and a nonparametric pdf estimator that is one of the most commonly used estimators of professional statisticians (i.e., the kernel estimator). It is also shown that in most applications, the exemplar models predict essentially optimal performance. Finally, the implications of these results are discussed and an alternative approach to the study of categorization is suggested. (C) 1995 Academic Press, Inc.