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Maximum Entropy Model

In: Minimum Divergence Methods in Statistical Machine Learning

Author

Listed:
  • Shinto Eguchi

    (Institute of Statistical Mathematic)

  • Osamu Komori

    (Seikei University)

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.

Suggested Citation

  • Shinto Eguchi & Osamu Komori, 2022. "Maximum Entropy Model," Springer Books, in: Minimum Divergence Methods in Statistical Machine Learning, chapter 0, pages 71-95, Springer.
    • Handle: RePEc:spr:sprchp:978-4-431-56922-0_3
    DOI: 10.1007/978-4-431-56922-0_3
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