Exponential Families with External Parameters [PDF]
Entropy, 2022 In this paper we introduce a class of statistical models consisting of exponential families depending on additional parameters, called external parameters.
Marco Favretti
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Revisiting Chernoff Information with Likelihood Ratio Exponential Families [PDF]
Entropy, 2022 The Chernoff information between two probability measures is a statistical divergence measuring their deviation defined as their maximally skewed Bhattacharyya distance.
Frank Nielsen
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Statistical Divergences between Densities of Truncated Exponential Families with Nested Supports: Duo Bregman and Duo Jensen Divergences [PDF]
Entropy, 2022 By calculating the Kullback–Leibler divergence between two probability measures belonging to different exponential families dominated by the same measure, we obtain a formula that generalizes the ordinary Fenchel–Young divergence.
Frank Nielsen
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On Representations of Divergence Measures and Related Quantities in Exponential Families [PDF]
Entropy, 2021 Within exponential families, which may consist of multi-parameter and multivariate distributions, a variety of divergence measures, such as the Kullback–Leibler divergence, the Cressie–Read divergence, the Rényi divergence, and the Hellinger metric, can ...
Stefan Bedbur, Udo Kamps
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Information Geometric Duality of ϕ-Deformed Exponential Families [PDF]
Entropy, 2019 In the world of generalized entropies—which, for example, play a role in physical systems with sub- and super-exponential phase space growth per degree of freedom—there are two ways for implementing constraints in the maximum entropy ...
Jan Korbel, Rudolf Hanel, Stefan Thurner
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On the Limiting Behaviour of the Fundamental Geodesics of Information Geometry [PDF]
Entropy, 2017 The Information Geometry of extended exponential families has received much recent attention in a variety of important applications, notably categorical data analysis, graphical modelling and, more specifically, log-linear modelling.
Frank Critchley, Paul Marriott
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Generalised Exponential Families and Associated Entropy Functions
Entropy, 2008 A generalised notion of exponential families is introduced. It is based on the variational principle, borrowed from statistical physics. It is shown that inequivalent generalised entropy functions lead to distinct generalised exponential families.
Jan Naudts
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Information Geometry of κ-Exponential Families: Dually-Flat, Hessian and Legendre Structures [PDF]
Entropy, 2018 In this paper, we present a review of recent developments on the κ -deformed statistical mechanics in the framework of the information geometry.
Antonio M. Scarfone +2 more
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Deep Exponential Families [PDF]
, 2014 We describe \textit{deep exponential families} (DEFs), a class of latent variable models that are inspired by the hidden structures used in deep neural networks.
Blei, David M. +3 more
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Two Families of Continuous Probability Distributions Generated by the Discrete Lindley Distribution
Mathematics, 2023 In this paper, we construct two new families of distributions generated by the discrete Lindley distribution. Some mathematical properties of the new families are derived. Some special distributions from these families can be constructed by choosing some
Srdjan Kadić +2 more
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