Axiomatization of an Exponential Similarity Function

Antoine Billot, Itzhak Gilboa and David Schmeidler

Chapter 10 in Case-Based Predictions:An Axiomatic Approach to Prediction, Classification and Statistical Learning, 2012, pp 245-257 from World Scientific Publishing Co. Pte. Ltd.

Abstract: An individual is asked to assess a real-valued variable y based on certain characteristics x = (x1, …, xm), and on a database consisting of n observations of (x1, …, xm, y). A possible approach to combine past observations of x and y with the current values of x to generate an assessment of y is similarity-weighted averaging. It suggests that the predicted value of y, yn+1s, be the weighted average of all previously observed values yi, where the weight of yi is the similarity between the vector xn+11,…,xn+1m, associated with yn+1, and the previously observed vector, xi1,…,xim. This paper axiomatizes, in terms of the prediction yn+1, a similarity function that is a (decreasing) exponential in a norm of the difference between the two vectors compared.

Keywords: Case-Based Reasoning; Case-Based Decision Theory; Statistics; Decision Under Uncertainty (search for similar items in EconPapers)
Date: 2012
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Related works:
Journal Article: Axiomatization of an exponential similarity function (2008)
Working Paper: Axiomatization of an exponential similarity function (2008)
Working Paper: Axiomatization of an exponential similarity function (2008)
Working Paper: An Axiomatization of an Exponential Similarity Function (2004)
Working Paper: Axiomatization of an Exponential Similarity Function (2004)
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