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112
Local Rademacher complexities
 Annals of Statistics
, 2002
"... We propose new bounds on the error of learning algorithms in terms of a datadependent notion of complexity. The estimates we establish give optimal rates and are based on a local and empirical version of Rademacher averages, in the sense that the Rademacher averages are computed from the data, on a ..."
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Cited by 163 (21 self)
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We propose new bounds on the error of learning algorithms in terms of a datadependent notion of complexity. The estimates we establish give optimal rates and are based on a local and empirical version of Rademacher averages, in the sense that the Rademacher averages are computed from the data, on a subset of functions with small empirical error. We present some applications to classification and prediction with convex function classes, and with kernel classes in particular.
Bounds on the sample complexity of Bayesian learning using information theory and the VC dimension.
 Machine Learning
, 1994
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Learning nearoptimal policies with Bellmanresidual minimization based fitted policy iteration and a single sample path
 MACHINE LEARNING JOURNAL (2008) 71:89129
, 2008
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Theory of classification: A survey of some recent advances
, 2005
"... The last few years have witnessed important new developments in the theory and practice of pattern classification. We intend to survey some of the main new ideas that have led to these recent results. ..."
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Cited by 96 (3 self)
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The last few years have witnessed important new developments in the theory and practice of pattern classification. We intend to survey some of the main new ideas that have led to these recent results.
Introduction to Statistical Learning Theory
 In , O. Bousquet, U.v. Luxburg, and G. Rsch (Editors
, 2004
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Learning with Matrix Factorization
, 2004
"... Matrices that can be factored into a product of two simpler matrices can serve as a useful and often natural model in the analysis of tabulated or highdimensional data. Models based on matrix factorization (Factor Analysis, PCA) have been extensively used in statistical analysis and machine learning ..."
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Cited by 71 (6 self)
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Matrices that can be factored into a product of two simpler matrices can serve as a useful and often natural model in the analysis of tabulated or highdimensional data. Models based on matrix factorization (Factor Analysis, PCA) have been extensively used in statistical analysis and machine learning for over a century, with many new formulations and models suggested in recent
A few notes on statistical learning theory
 In S. Mendelson & A. Smola (Eds. ), Lecture Notes in Computer Science
, 2003
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Risk bounds for Statistical Learning
"... We propose a general theorem providing upper bounds for the risk of an empirical risk minimizer (ERM).We essentially focus on the binary classi…cation framework. We extend Tsybakov’s analysis of the risk of an ERM under margin type conditions by using concentration inequalities for conveniently weig ..."
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Cited by 59 (2 self)
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We propose a general theorem providing upper bounds for the risk of an empirical risk minimizer (ERM).We essentially focus on the binary classi…cation framework. We extend Tsybakov’s analysis of the risk of an ERM under margin type conditions by using concentration inequalities for conveniently weighted empirical processes. This allows us to deal with other ways of measuring the ”size”of a class of classi…ers than entropy with bracketing as in Tsybakov’s work. In particular we derive new risk bounds for the ERM when the classi…cation rules belong to some VCclass under margin conditions and discuss the optimality of those bounds in a minimax sense.
Nonparametric time series prediction through adaptive model selection
 Machine Learning
, 2000
"... Abstract. We consider the problem of onestep ahead prediction for time series generated by an underlying stationary stochastic process obeying the condition of absolute regularity, describing the mixing nature of process. We make use of recent results from the theory of empirical processes, and ada ..."
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Cited by 57 (0 self)
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Abstract. We consider the problem of onestep ahead prediction for time series generated by an underlying stationary stochastic process obeying the condition of absolute regularity, describing the mixing nature of process. We make use of recent results from the theory of empirical processes, and adapt the uniform convergence framework of Vapnik and Chervonenkis to the problem of time series prediction, obtaining finite sample bounds. Furthermore, by allowing both the model complexity and memory size to be adaptively determined by the data, we derive nonparametric rates of convergence through an extension of the method of structural risk minimization suggested by Vapnik. All our results are derived for general L p error measures, and apply to both exponentially and algebraically mixing processes.
Geometric Range Searching
, 1994
"... In geometric range searching, algorithmic problems of the following type are considered: Given an npoint set P in the plane, build a data structure so that, given a query triangle R, the number of points of P lying in R can be determined quickly. Problems of this type are of crucial importance in c ..."
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Cited by 54 (3 self)
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In geometric range searching, algorithmic problems of the following type are considered: Given an npoint set P in the plane, build a data structure so that, given a query triangle R, the number of points of P lying in R can be determined quickly. Problems of this type are of crucial importance in computational geometry, as they can be used as subroutines in many seemingly unrelated algorithms. We present a survey of results and main techniques in this area.