Results 1  10
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95
Bounds on the sample complexity of Bayesian learning using information theory and the VC dimension
, 1992
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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 108 (18 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.
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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Introduction to Statistical Learning Theory
 In , O. Bousquet, U.v. Luxburg, and G. Rsch (Editors
, 2004
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A Few Notes on Statistical Learning Theory
 Advanced Lectures on Machine Learning: Machine Learning Summer School 2002
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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 46 (2 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.
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 42 (1 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.
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 42 (4 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
Improved Bounds on the Sample Complexity of Learning
 Journal of Computer and System Sciences
, 2000
"... We present two improved bounds on the sample complexity of learning. First, we present a new general upper bound on the number of examples required to estimate all of the expectations of a set of random variables uniformly well. The quality of the estimates is measured using a variant of the relativ ..."
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Cited by 39 (1 self)
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We present two improved bounds on the sample complexity of learning. First, we present a new general upper bound on the number of examples required to estimate all of the expectations of a set of random variables uniformly well. The quality of the estimates is measured using a variant of the relative error proposed by Haussler and Pollard. We also show that our bound is within a constant factor of the best possible. Our upper bound implies improved bounds on the sample complexity of learning according to Haussler's decision theoretic model. Next, we prove a lower bound on the sample complexity for learning according to the prediction model that is optimal to within a factor of 1+o(1). 1 Introduction Many important applied problems can be modeled as learning from random examples. Examples include text categorization [21], handwritten character recognition [15, 4, 26], speech recognition [2, 1], and virtual circuit holding times in IPoverATM networks [20, 17, 14]. In this paper, we p...
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 30 (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.