52 citations · 54 across the 8 of their papers we have counts for
8 papers
Deviation inequality for monotonic Boolean functions with application to a number of k-cycles in a random graph
Dmitry Panchenko
Using Talagrand's concentration inequality on the discrete cube {0,1}^m we show that given a real-valued function Z(x)on {0,1}^m that satisfies certain monotonicity conditions one…
Symmetrization approach to concentration inequalities for empirical processes
Dmitry Panchenko
We introduce a symmetrization technique that allows us to translate a problem of controlling the deviation of some functionals on a product space from their mean into a problem of…
Empirical margin distributions and bounding the generalization error of combined classifiers
Vladimir Koltchinskii, Dmitry Panchenko
We prove new probabilistic upper bounds on generalization error of complex classifiers that are combinations of simple classifiers. Such combinations could be implemented by neural…
Some extensions of an inequality of Vapnik and Chervonenkis
Dmitry Panchenko
The inequality of Vapnik and Chervonenkis controls the expectation of the function by its sample average uniformly over a VC-major class of functions taking into account the size o…
Some Local Measures of Complexity of Convex Hulls and Generalization Bounds
Olivier Bousquet, Vladimir Koltchinskii, Dmitry Panchenko
We investigate measures of complexity of function classes based on continuity moduli of Gaussian and Rademacher processes. For Gaussian processes, we obtain bounds on the continuit…
Rademacher processes and bounding the risk of function learning
Vladimir Koltchinskii, Dmitry Panchenko
We construct data dependent 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 c…