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Thermodynamics, Statistical Mechanics and Entropy
Open AccessFeature PaperArticle

On Maximum Entropy and Inference

by Luigi Gresele 1,2 and Matteo Marsili 3,*
1
Empirical Inference Department, Max Planck Institute for Intelligent Systems, Max-Planck-Ring 4, 72076 Tübingen, Germany
2
High-field Magnetic Resonance Department, Max Planck Institute for Biological Cybernetics, Max-Planck-Ring 11, 72076 Tübingen, Germany
3
Quantitative Life Sciences Section, The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
*
Author to whom correspondence should be addressed.
Entropy 2017, 19(12), 642; https://doi.org/10.3390/e19120642
Received: 9 October 2017 / Revised: 18 November 2017 / Accepted: 20 November 2017 / Published: 28 November 2017
(This article belongs to the Special Issue Entropy and Its Applications across Disciplines)
Maximum entropy is a powerful concept that entails a sharp separation between relevant and irrelevant variables. It is typically invoked in inference, once an assumption is made on what the relevant variables are, in order to estimate a model from data, that affords predictions on all other (dependent) variables. Conversely, maximum entropy can be invoked to retrieve the relevant variables (sufficient statistics) directly from the data, once a model is identified by Bayesian model selection. We explore this approach in the case of spin models with interactions of arbitrary order, and we discuss how relevant interactions can be inferred. In this perspective, the dimensionality of the inference problem is not set by the number of parameters in the model, but by the frequency distribution of the data. We illustrate the method showing its ability to recover the correct model in a few prototype cases and discuss its application on a real dataset. View Full-Text
Keywords: maximum entropy; model selection; spin models; singular value decomposition; high order interactions maximum entropy; model selection; spin models; singular value decomposition; high order interactions
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Gresele, L.; Marsili, M. On Maximum Entropy and Inference. Entropy 2017, 19, 642.

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