Case-based Predictions: An Axiomatic Approach to Prediction, Classification and Statistical Learning (World Scientific Series in Economic Theory)

Gilboa, Itzhak/ Schmeidler, David

World Scientific Publishing Co Pte Ltd（2012/04発売）

• 製本 Hardcover:ハードカバー版／ページ数 348 p.
• 言語 ENG
• 商品コード 9789814366175
• DDC分類 330.01

Full Description

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.

Contents

Case-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.