Simplicity and Likelihood: An Axiomatic Approach

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

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 loglikelihood 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 languageEnglish
Title of host publicationCase-Based Predictions
Subtitle of host publicationAn Axiomatic Approach to Prediction, Classification and Statistical Learning
PublisherTaylor and Francis
Pages281-309
Number of pages29
ISBN (Electronic)9789814366182
ISBN (Print)981436617X, 9789814366175
DOIs
StatePublished - 1 Jan 2012

Keywords

  • Akaike information criterion
  • Axioms
  • Maximum likelihood
  • Minimum description length
  • Model selection
  • Simplicity

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