Categorization as probability density estimation
type: Item
instance of: scholarly article
title: Categorization as probability density estimation
zbMATH Open document ID: 0840.62098
author: F. Gregory Ashby
author: Leola A. Alfonso-Reese
published in: Journal of Mathematical Psychology
publication date: 1995-10-17T00:00:00Z
review text: First, the basic structure of categorization models is described in terms of their representation, category access, and response selection assumptions. Next, we elaborate on the notion of categorization as probability density estimation. We discuss the differences between classifiers that know the true category pdfs and classifiers that must estimate these functions from the trial-by-trial feedback provided by the experimenter. It is shown that consistency is the key statistical property that guarantees two such classifiers will reasonably agree. The third section defines parametric and nonparametric pdf estimation and relates these statistical terms to the categorization process. The fourth section discusses parametric categorization models. In particular, it is shown that the prototype model and several decision-bound models are parametric. The fifth section shows that most popular exemplar models of categorization are nonparametric. In particular, we show that they are equivalent to a classifier that uses the minimum variance unbiased estimator of the category base rates and a nonparametric pdf estimator that is one of the most widely used estimators of professional statisticians. We also show that in most applications these models predict essentially optimal performance. Finally, the last section discusses implications of these results and suggests an alternative approach to studying human categorization performance.
Mathematics Subject Classification ID: 62P15
Mathematics Subject Classification ID: 91E99
Mathematics Subject Classification ID: 62F10
Mathematics Subject Classification ID: 62G05
zbMATH DE Number: 806633
zbMATH Keywords: representation
zbMATH Keywords: category access
zbMATH Keywords: density estimation
zbMATH Keywords: categorization models
zbMATH Keywords: response selection
zbMATH Keywords: consistency
zbMATH Keywords: prototype model
zbMATH Keywords: decision-bound models
zbMATH Keywords: minimum variance unbiased estimator
MaRDI profile type: Publication
full work available at URL: jmps.1995.1021
OpenAlex ID: W2082929796
DOI: 10.1006/JMPS.1995.1021
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description: scientific article; zbMATH DE number 806633