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Titlebook: Empirical Inference; Festschrift in Honor Bernhard Schölkopf,Zhiyuan Luo,Vladimir Vovk Book 2013 Springer-Verlag Berlin Heidelberg 2013 Bay

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Pivotal Estimation in High-Dimensional Regression via Linear Programmingroscedasticity, and does not require knowledge of the variance of random errors. The method is based on linear programming only, so that its numerical implementation is faster than for previously known techniques using conic programs, and it allows one to deal with higher-dimensional models. We prov
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https://doi.org/10.1007/978-3-662-36877-0uation of fixed design and i.i.d. Gaussian errors with known variance. Following Gautier and Tsybakov (High-dimensional instrumental variables regression and confidence sets. ArXiv e-prints 1105.2454, 2011), we obtain the results under weaker sensitivity assumptions than the restricted eigenvalue or assimilated conditions.
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Some Remarks on the Statistical Analysis of SVMs and Related Methodscade witnessed a shift towards consistencyConsistency, oracle inequalities, and learning ratesLearning rate. We discuss some of these developments in view of binary classificationBinary classification and least squares regressionLeast squares regression.
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Explaining AdaBoostsed and studied, with applications in numerous fields. This chapter aims to review some of the many perspectives and analyses of AdaBoost that have been applied to explain or understand it as a learning method, with comparisons of both the strengths and weaknesses of the various approaches.
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