Dmitriy Panchenko

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In this paper we revisit Talagrand’s proof of concentration inequality for empirical processes. We give a different proof of the main technical lemma that garantees the existence of a certain kernel. Moreover, we generalize the result of Talagrand to a family of kernels which in one particular case allows us to produce the Poissonian bound without using the(More)
We construct data dependent upper bounds on the risk in function learning problems. The bounds are based on the local norms of the Rademacher process indexed by the underlying function class and they do not require prior knowledge about the distribution of training examples or any speci c properties of the function class. Using Talagrand's type(More)