Results 11 to 20 of about 42,170 (301)
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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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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On Hölder Projective Divergences
Entropy, 2017 We describe a framework to build distances by measuring the tightness of inequalities and introduce the notion of proper statistical divergences and improper pseudo-divergences.
Frank Nielsen +2 more
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$q$-Exponential Families [PDF]
The Electronic Journal of Combinatorics, 2004 We develop an analog of the exponential families of Wilf in which the label sets are finite dimensional vector spaces over a finite field rather than finite sets of positive integers. The essential features of exponential families are preserved, including the exponential formula relating the deck enumerator and the hand enumerator.
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Deformed Algebras and Generalizations of Independence on Deformed Exponential Families
Entropy, 2015 A deformed exponential family is a generalization of exponential families. Since the useful classes of power law tailed distributions are described by the deformed exponential families, they are important objects in the theory of complex systems.
Hiroshi Matsuzoe, Tatsuaki Wada
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Reproductive Exponential Families
The Annals of Statistics, 1983 Consider a full and steep exponential model $\mathscr{M}$ with model function $a(\theta)b(x)\exp\{\theta \cdot t(x)\}$ and a sample $x_1, \cdots, x_n$ from $\mathscr{M}$. Let $\bar{t} = \{t(x_1) + \cdots + t(x_n)\}/n$ and let $\bar{t} = (\bar{t}_1, \bar{t}_2)$ be a partition of the canonical statistic $\bar{t}$.
Barndorff-Nielsen, O., Blæsild, P.
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Simple Exponential Family PCA [PDF]
IEEE Transactions on Neural Networks and Learning Systems, 2013 Principal component analysis (PCA) is a widely used model for dimensionality reduction. In this paper, we address the problem of determining the intrinsic dimensionality of a general type data population by selecting the number of principal components for a generalized PCA model.
Jun, Li, Dacheng, Tao
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Exponential dichotomy for evolution families on the real line
Abstract and Applied Analysis, 2006 We give necessary and sufficient conditions for uniform exponential dichotomy of evolution families in terms of the admissibility of the pair (Lp(ℝ,X),Lq(ℝ,X)).
Adina Luminiţa Sasu
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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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Mathematics, 2023 The paper comprehensively studies the natural exponential family and its associated exponential dispersion model generated by the Landau distribution. These families exhibit probabilistic and statistical properties and are suitable for modeling skewed ...
Shaul K. Bar-Lev
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