Description
Book SynopsisThe 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 ContentsCase-Based Decision Theory; Act Similarity in Case-Based Decision Theory; A Cognitive Foundation of Probability; Inductive Inference: An Axiomatic Approach; Expected Utility 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; Likelihood and Simplicity: An Axiomatic Approach.
