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Bounding Expected Sup-Norms of Empirical and Rademacher Processes

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Part of the Lecture Notes in Mathematics book series (LNMECOLE,volume 2033)

Abstract

In what follows, we will use a number of bounds on expectation of suprema of empirical and Rademacher processes. Because of symmetrization inequalities, the problems of bounding expected suprema for these two stochastic processes are equivalent. The bounds are usually based on various complexity measures of function classes (such as linear dimension, VC-dimension, shattering numbers, uniform covering numbers, random covering numbers, bracketing numbers, generic chaining complexities, etc). It would be of interest to develop the bounds with precise dependence on such geometric parameters as the L2.P /-diameter of the class. Combining the bounds on expected suprema with Talagrand’s concentration inequalities yields exponential inequalities for the tail probabilities of sup-norms.

Keywords

  • Empirical Process
  • Reproduce Kernel Hilbert Space
  • Entropy Bound
  • Symmetrization Inequality
  • Contraction Inequality

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Correspondence to Vladimir Koltchinskii .

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© 2011 Springer-Verlag Berlin Heidelberg

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Koltchinskii, V. (2011). Bounding Expected Sup-Norms of Empirical and Rademacher Processes. In: Oracle Inequalities in Empirical Risk Minimization and Sparse Recovery Problems. Lecture Notes in Mathematics(), vol 2033. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22147-7_3

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