• Corpus ID: 252408706

Instance-dependent uniform tail bounds for empirical processes

  title={Instance-dependent uniform tail bounds for empirical processes},
  author={Sohail Bahmani},
We formulate a uniform tail bound for empirical processes indexed by a class of functions, in terms of the individual deviations of the functions rather than the worst-case deviation in the considered class. The tail bound is established by introducing an initial “deflation” step to the standard generic chaining argument. The resulting tail bound has a main complexity component, a variant of Talagrand’s γ functional for the deflated function class, as well as an instance-dependent deviation term… 



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Upper and Lower Bounds for Stochastic Processes

  • M. Talagrand
  • Mathematics
    Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
  • 2021