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Exponential Families with External Parameters. [PDF]
Entropy (Basel), 2022 In this paper we introduce a class of statistical models consisting of exponential families depending on additional parameters, called external parameters. The main source for these statistical models resides in the Maximum Entropy framework where we have thermal parameters, corresponding to the natural parameters of an exponential family, and ...
Favretti M.
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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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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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Stationary Exponential Families
The Annals of Statistics, 1995 An exponential family for stationary sequences of random vectors in \(\mathbb{R}^ d\) is defined by making use of the Ionesco Tulcea theorem [\textit{C. T. Ionesco Tulcea}, Atti Accad. Naz. Lincei, Rend., Cl. Sci. Fis. Mat. Natur., VIII. S. 7, 208-211 (1950; Zbl 0035.152)].
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Satisfiability with Exponential Families [PDF]
, 2007 Fix a set S ⊆ {0, 1}* of exponential size, e.g. |S ∩ {0, 1}n| ∈ Ω(αn), α > 1. The S-SAT problem asks whether a propositional formula F over variables v1, . . . , vn has a satisfying assignment (v1, . . . , vn) ∈ {0, 1}n ∩ S. Our interest is in determining the complexity of S-SAT.
Scheder, Dominik, Zumstein, Philipp
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, 2022 AbstractThis chapter introduces and discusses the exponential family (EF) and the exponential dispersion family (EDF). The EF and the EDF are by far the most important classes of distribution functions for regression modeling. They include, among others, the Gaussian, the binomial, the Poisson, the gamma, the inverse Gaussian distributions, as well as ...
Mario V. Wüthrich, Michael Merz
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Rank verification for exponential families [PDF]
The Annals of Statistics, 2019 Many statistical experiments involve comparing multiple population groups. For example, a public opinion poll may ask which of several political candidates commands the most support; a social scientific survey may report the most common of several responses to a question; or, a clinical trial may compare binary patient outcomes under several treatment ...
Hung, Kenneth, Fithian, William
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Signal & Image Processing : An International Journal, 2013 In this paper we propose a new class of 2-parameter adjustable windows, namely Exponential window, based on the exponential function [1,2]. The Exponential window is derived in the same way as Kaiser window was derived, but our proposed window is more computationally efficient because in its time domain function it has no power series expansion. First,
Kemal Avci, Arif Nacaroglu
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FREE EXPONENTIAL FAMILIES AS KERNEL FAMILIES
Demonstratio Mathematica, 2009 AbstractFree exponential families have been previously introduced as a special case of ...
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