Formal Approaches in Categorization by Wills A. J. Pothos Emmanuel M. & Andy J. Wills

Formal Approaches in Categorization by Wills A. J. Pothos Emmanuel M. & Andy J. Wills

Author:Wills, A. J.,Pothos, Emmanuel M. & Andy J. Wills
Language: eng
Format: epub
Publisher: Cambridge University Press
Published: 2011-03-14T16:00:00+00:00


8 Nonparametric Bayesian models of categorization

Thomas L. Griffiths, Adam N. Sanborn, Kevin R. Canini, Daniel J. Navarro and Joshua B. Tenenbaum

Motivation

Models of human categorization often focus on the psychological processes by which people form and use knowledge of categories, appealing to concepts such as memory traces, activation, and similarity. An alternative approach is to take a step back from these psychological processes, and instead consider the abstract computational problem being solved when we learn categories, exploring how ideal solutions to that problem might shed light on human behaviour. This kind of investigation – conducted at Marr’s (1982) computational level, or via Anderson’s (1990) principles of rational analysis – has been particularly successful for categorization, identifying some surprising connections between psychological process models and methods used in machine learning and statistics. This chapter explores some of these connections in detail, and may present technical ideas that are new to many readers. Those who are interested in the mathematical details can find readable introductions from the perspectives of machine learning and cognitive science in Bishop (2006) and Griffiths, Kemp, and Tenenbaum (2008a) respectively.

Categorization is an instance of an inductive problem, requiring category membership to be inferred from the limited information provided by the features of a stimulus. As such, an ideal solution to this problem is provided by Bayesian inference, and in particular by computing a probability distribution over categories given the stimulus. If the joint probability of the features x and category label c of a stimulus is p(x, c), then the probability that x belongs to category c is given by



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