Fiche du document
- handle: 10670/1.tn80oh
- hal: hal-00463265
- doi: 10.1016/j.mathsocsci.2007.08.002
Ce document est lié à :
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.mathsocsci.2007.08.002
Mots-clés
Similarity function Axiom Exponential decaySujets proches
SimilarityCiter ce document
Antoine Billot et al., « Axiomatization of an exponential similarity function », HAL-SHS : économie et finance, ID : 10.1016/j.mathsocsci.2007.08.002
Métriques
Partage / Export
Résumé
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.