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3 edition of Oracle inequalities in empirical risk minimization and sparse recovery problems found in the catalog.

Oracle inequalities in empirical risk minimization and sparse recovery problems

Vladimir Koltchinskii

Oracle inequalities in empirical risk minimization and sparse recovery problems

École d"été de probabilités de Saint-Flour XXXVIII-2008

by Vladimir Koltchinskii

  • 218 Want to read
  • 35 Currently reading

Published by Springer Verlag in Berlin, Heidelberg, New York .
Written in English

    Subjects:
  • Probabilities,
  • Congresses,
  • Regression analysis,
  • Inequalities (Mathematics),
  • Sparse matrices,
  • Estimation theory,
  • Nonparametric statistics

  • Edition Notes

    Includes bibliographical references and index.

    Other titlesÉcole d"été de probabilités de Saint-Flour XXXVIII-2008
    StatementVladimir Koltchinskii
    SeriesLecture notes in mathematics -- 2033, Lecture notes in mathematics (Springer-Verlag) -- 2033.
    ContributionsEcole d"été de probabilités de Saint-Flour (38th : 2008)
    Classifications
    LC ClassificationsQA278.2 .K65 2011
    The Physical Object
    Paginationix, 254 p. ;
    Number of Pages254
    ID Numbers
    Open LibraryOL25146428M
    ISBN 103642221467
    ISBN 109783642221460
    LC Control Number2011934366
    OCLC/WorldCa733246860

    Principles of Risk Minimization for Learning Theory constructed on the basis of the training set (1). The induction principle of empirical risk minimization (ERM) assumes that the function I(x, wi),which minimizes E(w) over the set w E W, results in a risk R(wi) which is close to its minimum. C. Mitchelland S. van de Geer/Optimal oracle inequalities for model selection 4 2. Bernstein’s inequality Bernstein’s inequality for a single average is well known, and the extension of Bernstein’s probability inequality to a uniform probability inequality over p averages is completely straightforward. The result can be seen as the simplest.

    Sec. 5 contains the proofs of oracle inequalities for model selection problems with nested classes F i. 2. Setup and algorithms In this section, we will describe our statistical and computational assumptions about the problem, giving examples of classes of problems and Cited by: Empirical risk minimization algorithms are based on the philosophy that it is possible to approximate the expectation of the loss functions using their empiri-calmean,andchooseinsteadofh thefunction ^h 2 H forwhich 1 n Pn i=1 l^h(xi;yi) ˇ infh2H 1 n Pn i=1 lh(xi;yi). Such a function is called the empirical minimizer.

    This section includes several special cases that deal with risk minimization, such as Ordinary Least Squares, Ridge Regression, Lasso, and Logistic Regression. Table provides information on their loss functions, regularizers, as well as solutions. In statistics and machine learning, classification studies how to automatically learn to make good qualitative predictions (i.e., assign class labels) based on past observations. Examples of classification Cited by: 8.


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Oracle inequalities in empirical risk minimization and sparse recovery problems by Vladimir Koltchinskii Download PDF EPUB FB2

Sparse recovery based on l_1-type penalization and low rank matrix recovery based on the nuclear norm penalization are other active areas of research, where the main problems can be stated in the framework of penalized empirical risk minimization, and concentration inequalities and empirical processes tools have proved to be very useful.

Oracle Inequalities in Empirical Risk Minimization and Sparse Recovery Problems: École d’Été de Probabilités de Saint-Flour XXXVIII (Lecture Notes in Mathematics Book ) - Kindle edition by Koltchinskii, Vladimir.

Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading Oracle Inequalities Manufacturer: Springer.

Sparse recovery based on l_1-type penalization and low rank matrix recovery based on the nuclear norm penalization are other active areas of research, where the main problems can be stated in the framework of penalized empirical risk minimization, and concentration inequalities and empirical processes tools have proved to be very : Springer-Verlag Berlin Heidelberg.

Sparse recovery based on l_1-type penalization and low rank matrix recovery based on the nuclear norm penalization are other active areas of research, where the main problems can be stated in the framework of penalized empirical risk minimization, and concentration inequalities and empirical processes tools have proved to be very by: Oracle Inequalities in Empirical Risk Minimization and Sparse Recovery Problems We then discuss penalized empirical risk minimization and oracle inequalities and conclude with sparse recovery and low rank matrix recovery problems.

Abstract Empirical Risk Minimization. Get this from a library. Oracle inequalities in empirical risk minimization and sparse recovery problems: École d'Été de Probabilités de Saint-Flour XXXVIII - [Vladimir Koltchinskii;]. Oracle Inequalities in Empirical Risk Minimization and Sparse Recovery Problems Vladimir Koltchinskii School of Mathematics Georgia Institute of Technology Atlanta GA USA [email protected] Septem 1File Size: 1MB.

As it was pointed out in the Introduction, many important sparse recovery methods 3 are based on empirical risk minimization with convex loss and convex complexity 4 penalty.

Some interesting algorithms, for instance, the Dantzig selector by Candes 5 and Tao [44] can be formulated as Author: Vladimir Koltchinskii. Oracle Inequalities in Empirical Risk Minimization and Sparse Recovery Problems的话题 (全部 条) 什么是话题 无论是一部作品、一个人,还是一件事,都往往可以衍生出许多不同的话题。. The purpose of these lecture notes is to provide an introduction to the general theory of empirical risk minimization with an emphasis on excess risk bounds and oracle inequalities in penalized Author: Sara Van de Geer.

Oracle Inequalities in Empirical Risk Minimization and Sparse Recovery Problems: École d'Été de Probabilités de Saint-Flour XXXVIII– Springer, ISBN: [Preview with Google Books] Shalev-Shwartz, Shai, and Shai Ben-David.

Understanding Machine Learning: From Theory to Algorithms. Cambridge University Press, The purpose of these lecture notes is to provide an introduction to the general theory of empirical risk minimization with an emphasis on excess risk bounds and oracle inequalities in penalized Author: Vladimir Koltchinskii.

Online shopping from a great selection at Books Store. Oracle Inequalities in Empirical Risk Minimization and Sparse Recovery Problems: École d’Été de Probabilités de Saint-Flour XXXVIII Vladimir Koltchinskii, Oracle Inequalities in Empirical Risk Minimization and Sparse Recovery Problems.

Stéphane Boucheron, Gábor Lugosi and Pascal Massart, Concentration Inequalities: A Non-Asymptotic Theory of Independence. Sara van de Geer, Empirical processes in M-estimation.

Syllabus. Sparse oracle inequalities for variable selection via regularized quantization CLEMENT LEVRARD Universit e Paris Diderot, 8 place Aur elie Nemours, Paris E-mail: [email protected] We give oracle inequalities on procedures which combines quantization and variable selection via a weighted Lasso k-means type algorithm.

Oracle Inequalities in Empirical Risk Minimization and Sparse Recovery Problems, Springer Lecture Notes in Mathematics, Laszlo Gyorfi, Michael Kohler, Adam Krzyzak, Harro Walk ().

A Distribution-Free Theory of Nonparametric Regression, Springer. First, we investigate model M1 with θ 0 = (3,0, 0, 2, 0, 0,0 ︸ d − 5). The number of predictors d is orand there are 3 relevant predictors in the model.

The results of experiments are given in Table can notice that for M1 the accuracy of the Lasso estimators in predicting the ordering between objects is by: 2.

Concentration inequalities and asymptotic results for ratio type empirical processes Giné, Evarist and Koltchinskii, Vladimir, The Annals of Probability, ; Sparse recovery in convex hulls via entropy penalization Koltchinskii, Vladimir, The Annals of Statistics, ; On minimax density estimation on \mathbb{R}} Juditsky, Anatoli and Lambert-Lacroix, Sophie, Bernoulli,   P.

Bickel, Y. Ritov, A. Tsybakov, Simultaneous analysis of Lasso and Dantzig selector. Ann. Stat. 37, – () MathSciNet CrossRef zbMATH Google Scholar. Empirical risk minimization for a classification problem with a loss function is known to be an NP-hard problem even for such a relatively simple class of functions as linear classifiers.

Though, it can be solved efficiently when the minimal empirical risk is zero, i.e. data is linearly separable. F. Bunea et al./Sparsity oracle inequalities for the Lasso where pen(λ) = 2 XM j=1 ωn,j|λj| with ωn,j = rn,Mkfjkn, () where we write kgk2 n = n−1 Pn i=1 g 2(X i) for the squared empirical L2 norm of any function g: X → R.

The corresponding estimate of fis fb= PM j=1 λb choice of the tuning sequence rn,M >0 will be.minimization of penalized empirical risk with complexity penalty depending on the dimension of the model d(J):=#(J).

It is not hard to analyze the performance of this method in sparse problems using general theory of excess risk bounds and model selection in empirical risk minimization (see, e.g., [1,16,19,20]). However, if N is very large, solving.Sparse recovery in large ensembles of kernel machines.

In 21 st Annual Conference on Learning Theory—COLTHelsinki, Finland, July(R. A. Servedio and T. Zhang, eds.) –