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Convex Analysis
, 1970
"... In this book we aim to present, in a unified framework, a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. The title Variational Analysis reflects this breadth. For a lo ..."
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Cited by 5350 (67 self)
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was the exploration of variations around a point, within the bounds imposed by the constraints, in order to help characterize solutions and portray them in terms of ‘variational principles’. Notions of perturbation, approximation and even generalized differentiability were extensively investigated. Variational theory
Least angle regression
 Ann. Statist
"... The purpose of model selection algorithms such as All Subsets, Forward Selection and Backward Elimination is to choose a linear model on the basis of the same set of data to which the model will be applied. Typically we have available a large collection of possible covariates from which we hope to s ..."
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Cited by 1308 (43 self)
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to select a parsimonious set for the efficient prediction of a response variable. Least Angle Regression (LARS), a new model selection algorithm, is a useful and less greedy version of traditional forward selection methods. Three main properties are derived: (1) A simple modification of the LARS algorithm
The Lifting Scheme: A Construction Of Second Generation Wavelets
, 1997
"... . We present the lifting scheme, a simple construction of second generation wavelets, wavelets that are not necessarily translates and dilates of one fixed function. Such wavelets can be adapted to intervals, domains, surfaces, weights, and irregular samples. We show how the lifting scheme leads to ..."
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Cited by 541 (16 self)
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. Essentially we can think of them as data building blocks. Their fundamental property is that they allow for representations which are efficient and which can be computed fast. In other words, wavelets are capable of quickly capturing the essence of a data set with only a small set of coefficients
Jumps and stochastic volatility: Exchange rate processes implicit in Deutsche Mark options
, 1993
"... ..."
KodairaSpencer theory of gravity and exact results for quantum string amplitudes
 Commun. Math. Phys
, 1994
"... We develop techniques to compute higher loop string amplitudes for twisted N = 2 theories with ĉ = 3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured to all orders by a master anomaly equation. In a particu ..."
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Cited by 545 (60 self)
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We develop techniques to compute higher loop string amplitudes for twisted N = 2 theories with ĉ = 3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured to all orders by a master anomaly equation. In a particular realization of the N = 2 theories, the resulting string field theory is equivalent to a topological theory in six dimensions, the Kodaira– Spencer theory, which may be viewed as the closed string analog of the Chern–Simon theory. Using the mirror map this leads to computation of the ‘number ’ of holomorphic curves of higher genus curves in Calabi–Yau manifolds. It is shown that topological amplitudes can also be reinterpreted as computing corrections to superpotential terms appearing in the effective 4d theory resulting from compactification of standard 10d superstrings on the corresponding N = 2 theory. Relations with c = 1 strings are also pointed out.
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.
The Future of Wires
, 1999
"... this paper we first discuss the wire metrics of interest and examine them in a contemporary 0.25m process. We then discuss technology scaling over the next several generations, from SIA and other predictions, and how our wire metrics trend over that time. We will examine the delay and bandwidth lim ..."
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Cited by 508 (7 self)
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this paper we first discuss the wire metrics of interest and examine them in a contemporary 0.25m process. We then discuss technology scaling over the next several generations, from SIA and other predictions, and how our wire metrics trend over that time. We will examine the delay and bandwidth limitations of both long global wires and short local wires and discuss architectural design techniques that help us avoid the limitations of scaled wires.
Wireless Communications
, 2005
"... Copyright c ○ 2005 by Cambridge University Press. This material is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University ..."
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Cited by 1129 (32 self)
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Copyright c ○ 2005 by Cambridge University Press. This material is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University
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