Simplicity and Likelihood: An Axiomatic Approach
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.
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- Itzhak Gilboa & David Schmeidler, 2001.
"Inductive Inference: An Axiomatic Approach,"
Cowles Foundation Discussion Papers
1339, Cowles Foundation for Research in Economics, Yale University.
- Itzhak Gilboa & David Schmeidler, 2002. "Inductive Inference: An Axiomatic Approach," NajEcon Working Paper Reviews 391749000000000544, www.najecon.org.
- 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," Levine's Working Paper Archive 391749000000000544, David K. Levine.
- Gilboa, I. & Schmeidler, D., 1999. "Inductive Inference: an Axiomatic Approach," Papers 29-99, Tel Aviv.
- repec:cup:cbooks:9780521003117 is not listed on IDEAS
- Itzhak Gilboa & Offer Lieberman & David Schmeidler, 2004.
122247000000000684, UCLA Department of Economics.
- Antoine Billot & Itzhak Gilboa & Dov Samet & David Schmeidler, 2004.
"Probabilities as Similarity-Weighted Frequencies,"
122247000000000696, UCLA Department of Economics.
- repec:cup:cbooks:9780521802345 is not listed on IDEAS
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