379 citations · 1.2k across the 30 of their papers we have counts for
6 papers · 1 filter
Weighted uniform consistency of kernel density estimators
Evarist Gine, Vladimir Koltchinskii, Joel Zinn
Let f_n denote a kernel density estimator of a continuous density f in d dimensions, bounded and positive. Let Ψ(t) be a positive continuous function such that \|Ψf^β\|_{\infty}<\i…
Bounding the generalization error of convex combinations of classifiers: balancing the dimensionality and the margins
Vladimir Koltchinskii, Dmitry Panchenko, Fernando Lozano
A problem of bounding the generalization error of a classifier f in H, where H is a "base" class of functions (classifiers), is considered. This problem frequently occurs in comput…
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 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…
Complexities of convex combinations and bounding the generalization error in classification
Vladimir Koltchinskii, Dmitry Panchenko
We introduce and study several measures of complexity of functions from the convex hull of a given base class. These complexity measures take into account the sparsity of the weigh…