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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 800 (26 self)
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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 fields, including bioinformatics, communication theory, statistical physics, combinatorial optimization, signal and image processing, information retrieval and statistical machine learning. Many problems that arise in specific instances — including the key problems of computing marginals and modes 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 likelihoods, marginal probabilities and most probable configurations. We describe how a wide varietyof algorithms — among them sumproduct, cluster variational methods, expectationpropagation, mean field methods, maxproduct and linear programming relaxation, as well as conic programming relaxations — can all be understood in terms of exact or approximate forms of these variational representations. The variational approach provides a complementary alternative to Markov chain Monte Carlo as a general source of approximation methods for inference in largescale statistical models.
Strategies of Discourse Comprehension
, 1983
"... El Salvador, Guatemala is a, study in black and white. On the left is a collection of extreme MarxistLeninist groups led by what one diplomat calls “a pretty faceless bunch of people.’ ’ On the right is an entrenched elite that has dominated Central America’s most populous country since a CIAbacke ..."
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Cited by 601 (27 self)
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El Salvador, Guatemala is a, study in black and white. On the left is a collection of extreme MarxistLeninist groups led by what one diplomat calls “a pretty faceless bunch of people.’ ’ On the right is an entrenched elite that has dominated Central America’s most populous country since a CIAbacked coup deposed the reformist government of Col. Jacobo Arbenz Guzmán in 1954. Moderates of the political center. embattled but alive in E1 Salvador, have virtually disappeared in Guatemalajoining more than 30.000 victims of terror over the last tifteen vears. “The situation in Guatemala is much more serious than in EI Salvador, ” declares one Latin American diplomat. “The oligarchy is that much more reactionary. and the choices are far fewer. “ ‘Zero’: The Guatemalan oligarchs hated Jimmy Carter for cutting off U.S. military aid in 1977 to protest humanrights abusesand the rightwingers hired marimba bands and set off firecrackers on the night Ronald Reagan was elected. They considered Reagan an ideological kinsman and believed they had a special
The Parisi formula
, 2006
"... Using Guerra’s interpolation scheme, we compute the free energy of the SherringtonKirkpatrick model for spin glasses at any temperature, confirming a celebrated prediction of G. Parisi. ..."
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Cited by 131 (4 self)
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Using Guerra’s interpolation scheme, we compute the free energy of the SherringtonKirkpatrick model for spin glasses at any temperature, confirming a celebrated prediction of G. Parisi.
Regularization Theory and Neural Networks Architectures
 Neural Computation
, 1995
"... We had previously shown that regularization principles lead to approximation schemes which are equivalent to networks with one layer of hidden units, called Regularization Networks. In particular, standard smoothness functionals lead to a subclass of regularization networks, the well known Radial Ba ..."
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Cited by 396 (33 self)
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We had previously shown that regularization principles lead to approximation schemes which are equivalent to networks with one layer of hidden units, called Regularization Networks. In particular, standard smoothness functionals lead to a subclass of regularization networks, the well known Radial Basis Functions approximation schemes. This paper shows that regularization networks encompass a much broader range of approximation schemes, including many of the popular general additive models and some of the neural networks. In particular, we introduce new classes of smoothness functionals that lead to different classes of basis functions. Additive splines as well as some tensor product splines can be obtained from appropriate classes of smoothness functionals. Furthermore, the same generalization that extends Radial Basis Functions (RBF) to Hyper Basis Functions (HBF) also leads from additive models to ridge approximation models, containing as special cases Breiman's hinge functions, som...
A New Proof of Parisi’s Conjecture for the Finite Random Assignment Problem
, 2004
"... Abstract — Consider the problem of minimizing cost when assigning n jobs to n machines. An assignment is a onetoone mapping of jobs onto the machines. Assume that the cost of executing job i on machine j is cij, i,j =1,...,n. When the cij are i.i.d. exponentials of mean 1, Parisi conjectured that ..."
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Abstract — Consider the problem of minimizing cost when assigning n jobs to n machines. An assignment is a onetoone mapping of jobs onto the machines. Assume that the cost of executing job i on machine j is cij, i,j =1,...,n. When the cij are i.i.d. exponentials of mean 1, Parisi conjectured
Proofs of the Parisi and CoppersmithSorkin random assignment conjectures
, 2005
"... Suppose that there are n jobs and n machines and it costs cij to execute job i on machine j. The assignment problem concerns the determination of a onetoone assignment of jobs onto machines so as to minimize the cost of executing all the jobs. When the cij are independent and identically distribu ..."
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Cited by 14 (0 self)
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distributed exponentials of mean 1, Parisi [Technical Report condmat/9801176, xxx LANL Archive, 1998] made the beautiful conjecture that the expected cost of the minimum assignment equals ∑n i=1 (1/i2). Coppersmith and Sorkin [Random Structures Algorithms 15 (1999), 113–144] generalized Parisi’s conjecture
A proof of Parisi’s conjecture on the random assignment problem
 PROBAB. THEORY RELAT. FIELDS
, 2003
"... ..."
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