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 specific properties of the function class. Using Talagrand's type concentration inequalities for empirical and Rade...

We provide a generalisation of Pinelis’ Rademacher-Gaussian tail comparison to complex coefficients. also establish uniform bounds on the probability that magnitude weighted sums independent random vectors Euclidean spheres with matrix coefficients exceeds its second moment.

It has recently been shown that supervised learning linear classifiers with two of the most popular losses, the logistic and square loss, is equivalent to optimizing an equivalent loss over sufficient statistics about the class: Rademacher observations (rados). It has also been shown that learning over rados brings solutions to two prominent problems for which the state of the art of learning f...

Given a sequence (X n ) of real or complex random variables and numbers (a ), an interesting problem is to determine the conditions under which series ∑ n=1 ∞ X almost surely convergent. This paper extends classical Menshov–Rademacher theorem on convergence orthogonal general dependent derives sufficient for everywhere trigonometric with respect singular measures whose Fourier transform decays ...