3 Review(s)

The book presents an axiomatic approach to the problems of prediction, classification, and statistical learning. Using methodologies from axiomatic decision theory, and, in particular, the authors' case-based decision theory, the present studies attempt to ask what inductive conclusions can be derived from existing databases. It is shown that simple consistency rules lead to similarity-weighted aggregation, akin to kernel-based methods. It is suggested that the similarity function be estimated from the data. The incorporation of rule-based reasoning is discussed. Table of Contents Case-Based Decision Theory Act Similarity in Case-Based Decision Theory Cognitive Foundations of Probability Inductive Inference: An Axiomatic Approach A Derivation of Expected Utility Maximization in the Context of a Game Subjective Distributions Probabilities as Similarity-Weighted Frequencies Fact-Free Learning Empirical Similarity Axiomatization of an Exponential Similarity Function On the Definition of Objective Probabilities by Empirical Similarity Simplicity and Likelihood: An Axiomatic Approach