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Estimating divergence functionals and the likelihood ratio by penalized convex risk minimization
 In Advances in Neural Information Processing Systems (NIPS
, 2007
"... by convex risk minimization ..."
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
Just Relax: Convex Programming Methods for Identifying Sparse Signals in Noise
, 2006
"... This paper studies a difficult and fundamental problem that arises throughout electrical engineering, applied mathematics, and statistics. Suppose that one forms a short linear combination of elementary signals drawn from a large, fixed collection. Given an observation of the linear combination that ..."
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Cited by 496 (2 self)
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. This paper studies a method called convex relaxation, which attempts to recover the ideal sparse signal by solving a convex program. This approach is powerful because the optimization can be completed in polynomial time with standard scientific software. The paper provides general conditions which ensure
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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propose a method to approach this problem by trying to estimate a function f which is positive on S and negative on the complement. The functional form of f is given by a kernel expansion in terms of a potentially small subset of the training data; it is regularized by controlling the length
Risk as Feelings
, 2001
"... Virtually all current theories of choice under risk or uncertainty are cognitive and consequentialist. They assume that people assess the desirability and likelihood of possible outcomes of choice alternatives and integrate this information through some type of expectationbased calculus to arrive a ..."
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Cited by 458 (19 self)
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Virtually all current theories of choice under risk or uncertainty are cognitive and consequentialist. They assume that people assess the desirability and likelihood of possible outcomes of choice alternatives and integrate this information through some type of expectationbased calculus to arrive
Estimating divergence functionals and the likelihoodratio by penalized convex risk minimization
"... Abstract We develop and analyze an algorithm for nonparametric estimation of divergencefunctionals and the density ratio of two probability distributions. Our method is based on a variational characterization of fdivergences, which turns the estimation into a penalized convex risk minimization pro ..."
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Abstract We develop and analyze an algorithm for nonparametric estimation of divergencefunctionals and the density ratio of two probability distributions. Our method is based on a variational characterization of fdivergences, which turns the estimation into a penalized convex risk minimization
Bid, ask and transaction prices in a specialist market with heterogeneously informed traders
 Journal of Financial Economics
, 1985
"... The presence of traders with superior information leads to a positive bidask spread even when the specialist is riskneutral and makes zero expected profits. The resulting transaction prices convey information, and the expectation of the average spread squared times volume is bounded by a number th ..."
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Cited by 1217 (5 self)
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that is independent of insider activity. The serial correlation of transaction price differences is a function of the proportion of the spread due to adverse selection. A bidask spread implies a divergence between observed returns and realizable returns. Observed returns are approximately realizable returns plus
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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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
Additive Logistic Regression: a Statistical View of Boosting
 Annals of Statistics
, 1998
"... Boosting (Freund & Schapire 1996, Schapire & Singer 1998) is one of the most important recent developments in classification methodology. The performance of many classification algorithms can often be dramatically improved by sequentially applying them to reweighted versions of the input dat ..."
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Cited by 1719 (25 self)
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data, and taking a weighted majority vote of the sequence of classifiers thereby produced. We show that this seemingly mysterious phenomenon can be understood in terms of well known statistical principles, namely additive modeling and maximum likelihood. For the twoclass problem, boosting can
Bundle Adjustment  A Modern Synthesis
 VISION ALGORITHMS: THEORY AND PRACTICE, LNCS
, 2000
"... This paper is a survey of the theory and methods of photogrammetric bundle adjustment, aimed at potential implementors in the computer vision community. Bundle adjustment is the problem of refining a visual reconstruction to produce jointly optimal structure and viewing parameter estimates. Topics c ..."
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Cited by 555 (12 self)
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This paper is a survey of the theory and methods of photogrammetric bundle adjustment, aimed at potential implementors in the computer vision community. Bundle adjustment is the problem of refining a visual reconstruction to produce jointly optimal structure and viewing parameter estimates. Topics
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