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.
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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.
Itzhak Gilboa is Professor of Economics and Decision Sciences at HEC (Ecole des Hautes Etudes Commerciales), Paris, and Professor of Economics at Berglas School of Economics, Tel Aviv University. He is the coauthor (with David Schmeidler) of "Theory of Case-Based Decisions" and the author of "Theory of Decision under Uncertainty".
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