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+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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- Itzhak Gilboa & Offer Lieberman & David Schmeidler, 2004.
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- Gilboa, I. & Schmeidler, D., 2001. "Inductive Inference: An Axiomatic Approach," Papers 2001-19, Tel Aviv.
- Itzhak Gilboa & David Schmeidler, 2002. "Inductive Inference: An Axiomatic Approach," NajEcon Working Paper Reviews 391749000000000544, www.najecon.org.
- Itzhak Gilboa & David Schmeidler, 2003. "Inductive Inference: An Axiomatic Approach," Post-Print hal-00481297, HAL.
- Antoine Billot & Itzhak Gilboa & Dov Samet & David Schmeidler, 2004.
"Probabilities as Similarity-Weighted Frequencies,"
122247000000000696, UCLA Department of Economics.
- Itzhak Gilboa & Antoine Billot & Dov Samet & David Schmeidler, 2005. "Probabilities as Similarity-Weighted Frequencies," Post-Print hal-00481235, HAL.
- Antoine Billot & Itzhak Gilboa & David Schmeidler & Dov Samet, 2004. "Probabilities as Similarity-Weighted Frequencies," Cowles Foundation Discussion Papers 1492, Cowles Foundation for Research in Economics, Yale University.
- Antoine Billot & Itzhak Gilboa & Dov Samet & David Schmeidler, 2003. "Probabilities: Frequencies Viewed in Perspective," Levine's Bibliography 666156000000000295, UCLA Department of Economics.
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