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2008
IEEE

Axiomatization of an exponential similarity function

8 years 3 months ago
Axiomatization of an exponential similarity function
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+1 s , be the weighted average of all previously observed values yi, where the weight of yi is the similarity between the vector xn+1 1 ,..., xn+1 m , associated with yn+1, and the previously observed vector, xi 1 ,..., xi m . 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.
Antoine Billot, Itzhak Gilboa, David Schmeidler
Added 13 Dec 2010
Updated 13 Dec 2010
Type Journal
Year 2008
Where MSS
Authors Antoine Billot, Itzhak Gilboa, David Schmeidler
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