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Combinatorial Tools

  • Luc Devroye
  • Gábor Lugosi
Part of the Springer Series in Statistics book series (SSS)

Abstract

Consider a class A of subsets of R d , and let x 1,…,x n R d be arbitrary points. Recall from the previous chapter that properties of the finite set A(x 1 n ) ⊂ {0, 1} n defined by
$$ A(x_1^n) = \{ b = ({b_1}, \ldots ,{b_n}) \in {\{ 0,1\} ^n}:\exists A \in A:{b_i} = {1_{[{x_i} \in A]}},i = 1, \ldots ,n\}$$
play an essential role in bounding uniform deviations of the empirical measure.

Keywords

Dimension Versus Binomial Theorem Packing Number Combinatorial Tool Uniform Deviation 
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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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Luc Devroye
    • 1
  • Gábor Lugosi
    • 2
  1. 1.Computer Science DepartmentMcGill UniversityMontrealCanada
  2. 2.Facultat de Ciencies EconomiquesUniversitat Pompeu FabraBarcelonaSpain

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