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AN INFINITE FAMILY OF BOUNDS ON ZEROS OF ANALYTIC FUNCTIONS AND RELATIONSHIP TO SMALE’S BOUND
"... Abstract. Smale’s analysis of Newton’s iteration function induce a lower bound on the gap between two distinct zeros of a given complexvalued analytic function f(z). In this paper we make use of a fundamental family of iteration functions Bm(z), m ≥ 2, to derive an infinite family of lower bounds o ..."
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Cited by 6 (3 self)
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Abstract. Smale’s analysis of Newton’s iteration function induce a lower bound on the gap between two distinct zeros of a given complexvalued analytic function f(z). In this paper we make use of a fundamental family of iteration functions Bm(z), m ≥ 2, to derive an infinite family of lower bounds
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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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
Modeling Strategic Relationships for Process Reengineering
, 1995
"... Existing models for describing a process (such as a business process or a software development process) tend to focus on the \what " or the \how " of the process. For example, a health insurance claim process would typically be described in terms of a number of steps for assessing and appr ..."
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Cited by 545 (40 self)
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in terms of intentional dependency relationships among agents. Agents depend on each other for goals to be achieved, tasks to be performed, and resources to be furnished. Agents are intentional in that they have desires and wants, and strategic in that they are concerned about opportunities
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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long time, ‘variational ’ problems have been identified mostly with the ‘calculus of variations’. In that venerable subject, built around the minimization of integral functionals, constraints were relatively simple and much of the focus was on infinitedimensional function spaces. A major theme
Boosting a Weak Learning Algorithm By Majority
, 1995
"... We present an algorithm for improving the accuracy of algorithms for learning binary concepts. The improvement is achieved by combining a large number of hypotheses, each of which is generated by training the given learning algorithm on a different set of examples. Our algorithm is based on ideas pr ..."
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Cited by 516 (15 self)
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presented by Schapire in his paper "The strength of weak learnability", and represents an improvement over his results. The analysis of our algorithm provides general upper bounds on the resources required for learning in Valiant's polynomial PAC learning framework, which are the best general
Cilk: An Efficient Multithreaded Runtime System
 JOURNAL OF PARALLEL AND DISTRIBUTED COMPUTING
, 1995
"... Cilk (pronounced "silk") is a Cbased runtime system for multithreaded parallel programming. In this paper, we document the efficiency of the Cilk workstealing scheduler, both empirically and analytically. We show that on real and synthetic applications, the "work" and "cri ..."
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Cited by 750 (40 self)
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Cilk (pronounced "silk") is a Cbased runtime system for multithreaded parallel programming. In this paper, we document the efficiency of the Cilk workstealing scheduler, both empirically and analytically. We show that on real and synthetic applications, the "work" and "
Regression Shrinkage and Selection Via the Lasso
 Journal of the Royal Statistical Society, Series B
, 1994
"... We propose a new method for estimation in linear models. The "lasso" minimizes the residual sum of squares subject to the sum of the absolute value of the coefficients being less than a constant. Because of the nature of this constraint it tends to produce some coefficients that are exactl ..."
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Cited by 4055 (51 self)
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an interesting relationship with recent work in adaptive function estimation by Donoho and Johnstone. The lasso idea is quite general and can be applied in a variety of statistical models: extensions to generalized regression models and treebased models are briefly described. Keywords: regression, subset
Estimating the Support of a HighDimensional Distribution
, 1999
"... Suppose you are given some dataset drawn from an underlying probability distribution P and you want to estimate a "simple" subset S of input space such that the probability that a test point drawn from P lies outside of S is bounded by some a priori specified between 0 and 1. We propo ..."
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Cited by 766 (29 self)
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Suppose you are given some dataset drawn from an underlying probability distribution P and you want to estimate a "simple" subset S of input space such that the probability that a test point drawn from P lies outside of S is bounded by some a priori specified between 0 and 1. We
A unified theory of underreaction, momentum trading and overreaction in asset markets
, 1999
"... We model a market populated by two groups of boundedly rational agents: “newswatchers” and “momentum traders.” Each newswatcher observes some private information, but fails to extract other newswatchers’ information from prices. If information diffuses gradually across the population, prices underre ..."
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Cited by 577 (31 self)
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We model a market populated by two groups of boundedly rational agents: “newswatchers” and “momentum traders.” Each newswatcher observes some private information, but fails to extract other newswatchers’ information from prices. If information diffuses gradually across the population, prices
A perspective on judgment and choice: Mapping bounded rationality
 American psychologist
, 2003
"... Early studies of intuitive judgment and decision making conducted with the late Amos Tversky are reviewed in the context of two related concepts: an analysis of accessibility, the ease with which thoughts come to mind; a distinction between effortless intuition and deliberate reasoning. Intuitive th ..."
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Cited by 393 (0 self)
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Early studies of intuitive judgment and decision making conducted with the late Amos Tversky are reviewed in the context of two related concepts: an analysis of accessibility, the ease with which thoughts come to mind; a distinction between effortless intuition and deliberate reasoning. Intuitive thoughts, like percepts, are highly accessible. Determinants and consequences of accessibility help explain the central results of prospect theory, framing effects, the heuristic process of attribute substitution, and the characteristic biases that result from the substitution of nonextensional for extensional attributes. Variations in the accessibility of rules explain the occasional corrections of intuitive judgments. The study of biases is compatible with a view of intuitive thinking and decision making as generally skilled and successful.
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