Maximum Entropy Model

Shinto Eguchi () and Osamu Komori ()
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Shinto Eguchi: Institute of Statistical Mathematic
Osamu Komori: Seikei University

Chapter Chapter 3 in Minimum Divergence Methods in Statistical Machine Learning, 2022, pp 71-95 from Springer

Abstract: Abstract The classical theory for the maximum likelihood method has been established in an exponential modelExponential model with a notion of sufficient statistics. The exponential modelExponential model is characterized as the maximum entropy model with a mean regularization for the sufficient statistic in terms of the Boltzmann-Gibbs-Shannon entropy. In this chapter, we extend it to a generalized version of the maximum entropy and the minimum divergence employing the U-divergence, which is subsequently decomposed into the difference between the U-entropy and the U-cross entropy. We introduce a model of maximum entropy distributionsMaximum entropy distribution with the mean equal regularization in terms of the U-entropy. The maximum U-entropy model is characterized to be totally geodesic. The minimum U-divergence estimation is characterized by a single statistic in the framework associated with the U-divergence as discussed in Chap. 2 . As a result, we demonstrate a natural extension for the classical theory of the maximum likelihood method under the exponential modelExponential model.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-4-431-56922-0_3

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DOI: 10.1007/978-4-431-56922-0_3

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