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122,097
A View Of The Em Algorithm That Justifies Incremental, Sparse, And Other Variants
 Learning in Graphical Models
, 1998
"... . The EM algorithm performs maximum likelihood estimation for data in which some variables are unobserved. We present a function that resembles negative free energy and show that the M step maximizes this function with respect to the model parameters and the E step maximizes it with respect to the d ..."
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Cited by 993 (18 self)
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to the distribution over the unobserved variables. From this perspective, it is easy to justify an incremental variant of the EM algorithm in which the distribution for only one of the unobserved variables is recalculated in each E step. This variant is shown empirically to give faster convergence in a mixture
Global Optimization with Polynomials and the Problem of Moments
 SIAM JOURNAL ON OPTIMIZATION
, 2001
"... We consider the problem of finding the unconstrained global minimum of a realvalued polynomial p(x) : R R, as well as the global minimum of p(x), in a compact set K defined by polynomial inequalities. It is shown that this problem reduces to solving an (often finite) sequence of convex linear ma ..."
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Cited by 577 (48 self)
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matrix inequality (LMI) problems. A notion of KarushKuhnTucker polynomials is introduced in a global optimality condition. Some illustrative examples are provided.
A Note on the Confinement Problem
, 1973
"... This not explores the problem of confining a program during its execution so that it cannot transmit information to any other program except its caller. A set of examples attempts to stake out the boundaries of the problem. Necessary conditions for a solution are stated and informally justified. ..."
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Cited by 532 (0 self)
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This not explores the problem of confining a program during its execution so that it cannot transmit information to any other program except its caller. A set of examples attempts to stake out the boundaries of the problem. Necessary conditions for a solution are stated and informally justified.
Optimal approximation by piecewise smooth functions and associated variational problems
 Commun. Pure Applied Mathematics
, 1989
"... (Article begins on next page) The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters. Citation Mumford, David Bryant, and Jayant Shah. 1989. Optimal approximations by piecewise smooth functions and associated variational problems. ..."
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Cited by 1294 (14 self)
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(Article begins on next page) The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters. Citation Mumford, David Bryant, and Jayant Shah. 1989. Optimal approximations by piecewise smooth functions and associated variational problems
No Free Lunch Theorems for Optimization
, 1997
"... A framework is developed to explore the connection between effective optimization algorithms and the problems they are solving. A number of “no free lunch ” (NFL) theorems are presented which establish that for any algorithm, any elevated performance over one class of problems is offset by performan ..."
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Cited by 961 (10 self)
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A framework is developed to explore the connection between effective optimization algorithms and the problems they are solving. A number of “no free lunch ” (NFL) theorems are presented which establish that for any algorithm, any elevated performance over one class of problems is offset
Some optimal inapproximability results
, 2002
"... We prove optimal, up to an arbitrary ffl? 0, inapproximability results for MaxEkSat for k * 3, maximizing the number of satisfied linear equations in an overdetermined system of linear equations modulo a prime p and Set Splitting. As a consequence of these results we get improved lower bounds for ..."
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Cited by 751 (11 self)
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for the efficient approximability of many optimization problems studied previously. In particular, for MaxE2Sat, MaxCut, MaxdiCut, and Vertex cover. Warning: Essentially this paper has been published in JACM and is subject to copyright restrictions. In particular it is for personal use only.
Learnability in Optimality Theory
, 1995
"... In this article we show how Optimality Theory yields a highly general Constraint Demotion principle for grammar learning. The resulting learning procedure specifically exploits the grammatical structure of Optimality Theory, independent of the content of substantive constraints defining any given gr ..."
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Cited by 529 (35 self)
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grammatical module. We decompose the learning problem and present formal results for a central subproblem, deducing the constraint ranking particular to a target language, given structural descriptions of positive examples. The structure imposed on the space of possible grammars by Optimality Theory allows
A Limited Memory Algorithm for Bound Constrained Optimization
 SIAM JOURNAL ON SCIENTIFIC COMPUTING
, 1994
"... An algorithm for solving large nonlinear optimization problems with simple bounds is described. It is based ..."
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Cited by 572 (9 self)
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An algorithm for solving large nonlinear optimization problems with simple bounds is described. It is based
SNOPT: An SQP Algorithm For LargeScale Constrained Optimization
, 2002
"... Sequential quadratic programming (SQP) methods have proved highly effective for solving constrained optimization problems with smooth nonlinear functions in the objective and constraints. Here we consider problems with general inequality constraints (linear and nonlinear). We assume that first deriv ..."
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Cited by 597 (24 self)
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Sequential quadratic programming (SQP) methods have proved highly effective for solving constrained optimization problems with smooth nonlinear functions in the objective and constraints. Here we consider problems with general inequality constraints (linear and nonlinear). We assume that first
Multiobjective Optimization Using Nondominated Sorting in Genetic Algorithms
 Evolutionary Computation
, 1994
"... In trying to solve multiobjective optimization problems, many traditional methods scalarize the objective vector into a single objective. In those cases, the obtained solution is highly sensitive to the weight vector used in the scalarization process and demands the user to have knowledge about t ..."
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Cited by 539 (5 self)
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In trying to solve multiobjective optimization problems, many traditional methods scalarize the objective vector into a single objective. In those cases, the obtained solution is highly sensitive to the weight vector used in the scalarization process and demands the user to have knowledge about
Results 1  10
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122,097