399 research outputs found
A chain rule for the expected suprema of Gaussian processes
The expected supremum of a Gaussian process indexed by the image of an index
set under a function class is bounded in terms of separate properties of the
index set and the function class. The bound is relevant to the estimation of
nonlinear transformations or the analysis of learning algorithms whenever
hypotheses are chosen from composite classes, as is the case for multi-layer
models
A Chain Rule for the Expected Suprema of Bernoulli Processes
We obtain an upper bound on the expected supremum of a Bernoulli process
indexed by the image of an index set under a uniformly Lipschitz function class
in terms of properties of the index set and the function class, extending an
earlier result of Maurer for Gaussian processes. The proof makes essential use
of recent results of Bednorz and Latala on the boundedness of Bernoulli
processes.Comment: 14 page
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