We consider adaptive sequential lossy coding of bounded individual sequences when the performance is measured by the sequentially accumulated mean squared distortion. The encoder and the decoder are connected via a noiseless channel of capacity $R$ and both are assumed to have zero delay. No...

We derive a new inequality for uniform deviations of averages from their means. The inequality is a common generalization of previous results of Vapnik and Chervonenkis (1974) and Pollard (1986). Using the new inequality we obtain tight bounds for empirical loss minimization learning.

We derive a new inequality for uniform deviations of averages from their means. The inequality is a common generalization of previous results of Vapnik and Chervonenkis [1974, Theory of Pattern Recognition. Nauka, Moscow] and Pollard [1995, Uniform ratio limit theorems for empirical processes,...

Given an i.i.d. sample drawn from a density "f" on the real line, the problem of testing whether "f" is in a given class of densities is considered. Testing procedures constructed on the basis of minimizing the "L"₁-distance between a kernel density estimate and any density in the hypothesized...

We obtain Vapnik-Chervonenkis type upper bounds for the uniform deviation of probabilities from their expectations. The bounds sharpen previously known probability inequalities.