33 Pages Posted: 21 Feb 2006
Date Written: January 2006
We present a model of induction, where the decision maker (DM) infers the unknown properties of an object from information about other objects. We show that categorization is an optimal solution to the prediction problem: The DM classifies objects into groups and her predictions of the object's properties are based on typical properties in the group. The DM prefers to use relatively fewer and larger categories to avoid the problem of overfitting. Since the DM is fully rational, it is an argument that bounded rationality is not necessary for categorization, and categorization does not need to lead to a persistent bias in information processing. In a technical sense, our model studies exchangeability in a multi-dimensional setting. This leads to a generalization of methods related to de Finetti's theorem.
Keywords: Learning, Statistical Decision Theory
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