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Axiomatization of an exponential similarity function

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.
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Submitted on : Thursday, March 11, 2010 - 5:00:29 PM
Last modification on : Tuesday, June 14, 2022 - 8:54:48 AM

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Antoine Billot, Itzhak Gilboa, David Schmeidler. Axiomatization of an exponential similarity function. Mathematical Social Sciences, Elsevier, 2008, Vol.55,n°2, pp.107-115. ⟨10.1016/j.mathsocsci.2007.08.002⟩. ⟨hal-00463265⟩

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