On the Rademacher maximal function

Maximal Discrepancy vs. Rademacher Complexity for error estimation

The Maximal Discrepancy and the Rademacher Complexity are powerful statistical tools that can be exploited to obtain reliable, albeit not tight, upper bounds of the generalization error of a classifier. We study the different behavior of the two methods when applied to linear classifiers and suggest a practical procedure to tighten the bounds. The resulting generalization estimation can be succ...

compactifications and function spaces on weighted semigruops

chapter one is devoted to a moderate discussion on preliminaries, according to our requirements. chapter two which is based on our work in (24) is devoted introducting weighted semigroups (s, w), and studying some famous function spaces on them, especially the relations between go (s, w) and other function speces are invesigated. in fact this chapter is a complement to (32). one of the main fea...

On the Adjoint of the Maximal Function

Rademacher Processes and Bounding the Risk of Function Learning

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

ON THE MAXIMAL SPECTRUM OF A MODULE

Let $R$ be a commutative ring with identity. The purpose of this paper is to introduce and study two classes of modules over $R$, called $mbox{Max}$-injective and $mbox{Max}$-strongly top modules and explore some of their basic properties. Our concern is to extend some properties of $X$-injective and strongly top modules to these classes of modules and obtain some related results.