## 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 language | English |
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Title of host publication | Case-Based Predictions |

Subtitle of host publication | An Axiomatic Approach to Prediction, Classification and Statistical Learning |

Publisher | Taylor and Francis |

Pages | 281-309 |

Number of pages | 29 |

ISBN (Electronic) | 9789814366182 |

ISBN (Print) | 981436617X, 9789814366175 |

DOIs | |

State | Published - 1 Jan 2012 |

## Keywords

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