Simplicity and likelihood: An axiomatic approach

Itzhak Gilboa; David Schmeidler

doi:10.1016/j.jet.2010.03.010

Simplicity and likelihood: An axiomatic approach

Itzhak Gilboa^*, David Schmeidler

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

We suggest a model in which theories are ranked given various databases. Certain axioms on such rankings imply a numerical representation that is the sum of the log-likelihood of the theory and a fixed number for each theory, which may be interpreted as a measure of its complexity. This additive combination of log-likelihood and a measure of complexity generalizes both the Akaike Information Criterion and the Minimum Description Length criterion, which are well known in statistics and in machine learning, respectively. The axiomatic approach is suggested as a way to analyze such theory-selection criteria and judge their reasonability based on finite databases.

Original language	English
Pages (from-to)	1757-1775
Number of pages	19
Journal	Journal of Economic Theory
Volume	145
Issue number	5
DOIs	https://doi.org/10.1016/j.jet.2010.03.010
State	Published - Sep 2010

Funding

Funders	Funder number
Pinhas Sapir Center for Development and Israel Science Foundation	355/06, 975/03

Keywords

Akaike Information Criterion
Axioms
Maximum likelihood
Minimum Description Length
Model selection
Simplicity

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10.1016/j.jet.2010.03.010

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title = "Simplicity and likelihood: An axiomatic approach",

abstract = "We suggest a model in which theories are ranked given various databases. Certain axioms on such rankings imply a numerical representation that is the sum of the log-likelihood of the theory and a fixed number for each theory, which may be interpreted as a measure of its complexity. This additive combination of log-likelihood and a measure of complexity generalizes both the Akaike Information Criterion and the Minimum Description Length criterion, which are well known in statistics and in machine learning, respectively. The axiomatic approach is suggested as a way to analyze such theory-selection criteria and judge their reasonability based on finite databases.",

keywords = "Akaike Information Criterion, Axioms, Maximum likelihood, Minimum Description Length, Model selection, Simplicity",

author = "Itzhak Gilboa and David Schmeidler",

note = "Funding Information: ✩ We thank Yoav Binyamini, Offer Lieberman, two anonymous referees and the associate editor for comments and suggestions. This project was supported by the Pinhas Sapir Center for Development and Israel Science Foundation Grant Nos. 975/03 and 355/06. * Corresponding author at: Tel-Aviv University, Israel. E-mail addresses: [email protected] (I. Gilboa), [email protected] (D. Schmeidler).",

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KW - Axioms

KW - Maximum likelihood

KW - Minimum Description Length

KW - Model selection

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Simplicity and likelihood: An axiomatic approach

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