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Graphical models, exponential families, and variational inference
, 2008
"... The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building largescale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fiel ..."
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Cited by 819 (28 self)
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of probability distributions — are best studied in the general setting. Working with exponential family representations, and exploiting the conjugate duality between the cumulant function and the entropy for exponential families, we develop general variational representations of the problems of computing
Exponential Families
, 1990
"... General methods for obtaining maximum likelihood estimates in exponential families are demonstrated using a constrained autologistic model for estimating relatedness from DNA fingerprint data. The novel features are the use of constrained optimization and two new algorithms for maximum likelihood es ..."
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Cited by 20 (4 self)
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General methods for obtaining maximum likelihood estimates in exponential families are demonstrated using a constrained autologistic model for estimating relatedness from DNA fingerprint data. The novel features are the use of constrained optimization and two new algorithms for maximum likelihood
Exponential family harmoniums with an application to . . .
"... Directed graphical models with one layer of observed random variablesand one or more layers of hidden random variables have been the dominant modelling paradigm in many research fields. Although this approach has met with considerable success, the causal semantics of these models can make it diffi ..."
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Cited by 150 (22 self)
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it difficult to infer the posterior distribution over thehidden variables. In this paper we propose an alternative twolayer model based on exponential family distributions and the semantics of undirected models. Inference in these "exponential family harmoniums " is fast while learning is performed
Exponential Families and Conjugate Priors 1 Exponential Families
, 2007
"... Inference with continuous distributions present an additional challenge compared to inference with discrete distributions: how to represent these continuous objects within finitememory computers? A common solution to this problem is to use a (much smaller) subset (or family) of distributions instea ..."
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of distribution that has special properties with respect to statistical inference is the exponential family, introduced by Pitman (father), Darmois and Koopman. As a preview, here are some important properties of the exponential family that explain their central role in statistics: • Suppose X1, X2,... are iid
Graphical models and exponential families
 In Proceedings of the 14th Annual Conference on Uncertainty in Arti cial Intelligence (UAI98
, 1998
"... We provide a classification of graphical models according to their representation as subfamilies of exponential families. Undirected graphical models with no hidden variables are linear exponential families (LEFs), directed acyclic graphical models and chain graphs with no hidden variables, includin ..."
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Cited by 22 (1 self)
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We provide a classification of graphical models according to their representation as subfamilies of exponential families. Undirected graphical models with no hidden variables are linear exponential families (LEFs), directed acyclic graphical models and chain graphs with no hidden variables
Expectation propagation for exponential families
, 2005
"... This is a tutorial describing the Expectation Propagation (EP) algorithm for a general exponential family. Our focus is on simplicity of exposition. Although the overhead of translating a specific model into its exponential family representation can be considerable, many apparent complications of EP ..."
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Cited by 26 (4 self)
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This is a tutorial describing the Expectation Propagation (EP) algorithm for a general exponential family. Our focus is on simplicity of exposition. Although the overhead of translating a specific model into its exponential family representation can be considerable, many apparent complications
qExponential Families
, 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 ..."
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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
FREE REAL EXPONENTIAL FAMILIES
, 2006
"... Free exponential families were introduced in [6]. We continue to study their properties following the analogy with classical reproductive exponential models [9]. ..."
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Free exponential families were introduced in [6]. We continue to study their properties following the analogy with classical reproductive exponential models [9].
Bayesian Exponential Family PCA
"... Principal Components Analysis (PCA) has become established as one of the key tools for dimensionality reduction when dealing with real valued data. Approaches such as exponential family PCA and nonnegative matrix factorisation have successfully extended PCA to nonGaussian data types, but these tec ..."
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Cited by 21 (7 self)
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Principal Components Analysis (PCA) has become established as one of the key tools for dimensionality reduction when dealing with real valued data. Approaches such as exponential family PCA and nonnegative matrix factorisation have successfully extended PCA to nonGaussian data types
Kernel methods and the exponential family
 Neurocomputing
, 2005
"... The success of Support Vector Machine (SVM) gave rise to the development of a new class of theoretically elegant learning machines which use a central concept of kernels and the associated reproducing kernel Hilbert space (RKHS). Exponential families, a standard tool in statistics, can be used to un ..."
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Cited by 14 (0 self)
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The success of Support Vector Machine (SVM) gave rise to the development of a new class of theoretically elegant learning machines which use a central concept of kernels and the associated reproducing kernel Hilbert space (RKHS). Exponential families, a standard tool in statistics, can be used
Results 1  10
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2,706