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4,523
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
FARKASTYPE RESULTS WITH CONJUGATE FUNCTIONS
"... We present some new Farkastype results for inequality systems involving a finite as well as an infinite number of convex constraints. For this, we use two kinds of conjugate dual problems, namely an extended Fencheltype dual problem and the recently introduced FenchelLagrange dual problem. For t ..."
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Cited by 12 (4 self)
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We present some new Farkastype results for inequality systems involving a finite as well as an infinite number of convex constraints. For this, we use two kinds of conjugate dual problems, namely an extended Fencheltype dual problem and the recently introduced FenchelLagrange dual problem
Monotone operators and “bigger conjugate” functions
, 2011
"... We study a question posed by Stephen Simons in his 2008 monograph involving “bigger conjugate ” (BC) functions and the partial infimal convolution. As Simons demonstrated in his monograph, these function have been crucial to the understanding and advancement of the stateoftheart of harder problem ..."
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Cited by 2 (2 self)
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We study a question posed by Stephen Simons in his 2008 monograph involving “bigger conjugate ” (BC) functions and the partial infimal convolution. As Simons demonstrated in his monograph, these function have been crucial to the understanding and advancement of the stateoftheart of harder
Monotone operators and “bigger conjugate ” functions
, 2011
"... We study a question posed by Stephen Simons in his 2008 monograph involving “bigger conjugate ” (BC) functions and the partial infimal convolution. As Simons demonstrated in his monograph, these function have been crucial to the understanding and advancement of the stateoftheart of harder probl ..."
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We study a question posed by Stephen Simons in his 2008 monograph involving “bigger conjugate ” (BC) functions and the partial infimal convolution. As Simons demonstrated in his monograph, these function have been crucial to the understanding and advancement of the stateoftheart of harder
Subdifferential of the conjugate function in general Banach spaces
, 2011
"... We give explicit formulas for the subdifferential set of the conjugate of non necessarily convex functions defined on general Banach spaces. Even if such a subdifferential mapping takes its values in the bidual space, we show that up to a weak** closure operation it is still described by using onl ..."
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We give explicit formulas for the subdifferential set of the conjugate of non necessarily convex functions defined on general Banach spaces. Even if such a subdifferential mapping takes its values in the bidual space, we show that up to a weak** closure operation it is still described by using
Sparse semisupervised learning using conjugate functions
, 2010
"... In this paper, we propose a general framework for sparse semisupervised learning, which concerns using a small portion of unlabeled data and a few labeled data to represent target functions and thus has the merit of accelerating function evaluations when predicting the output of a new example. This ..."
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Cited by 12 (4 self)
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In this paper, we propose a general framework for sparse semisupervised learning, which concerns using a small portion of unlabeled data and a few labeled data to represent target functions and thus has the merit of accelerating function evaluations when predicting the output of a new example
New formulas for the Fenchel subdifferential of the conjugate function
, 2010
"... Following [13] we provide new formulas for the Fenchel subdifferential of the conjugate of functions defined on locally convex spaces. In particular, this allows deriving expressions for the minimizers set of the lower semicontinuous convex hull of such functions. These formulas are written by means ..."
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Cited by 1 (1 self)
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Following [13] we provide new formulas for the Fenchel subdifferential of the conjugate of functions defined on locally convex spaces. In particular, this allows deriving expressions for the minimizers set of the lower semicontinuous convex hull of such functions. These formulas are written
Best constants in Zygmund's inequality for conjugate functions.
"... . A new proof is given of Zygmund's inequality which gives sharp constants both in the main term and in the first error term. 2000 AMS classification: Primary 42A50; Secondary 30D55, 31A05 KEY WORDS: conjugate functions, H 1 norm estimates. 0. The main result. Let F = f + i ..."
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. A new proof is given of Zygmund's inequality which gives sharp constants both in the main term and in the first error term. 2000 AMS classification: Primary 42A50; Secondary 30D55, 31A05 KEY WORDS: conjugate functions, H 1 norm estimates. 0. The main result. Let F = f + i
Results 1  10
of
4,523