We propose Rademacher complexity bounds for multiclass classifiers trained with a two-step semi-supervised model. In the first step, the algorithm partitions the partially labeled data and then identifies dense clusters containing κ predominant classes using the labeled training examples such that the proportion of their non-predominant classes is below a fixed threshold. In the second step, a ...

We propose two new generalization error bounds for multiple kernel learning (MKL). First, using the bound of Srebro and BenDavid (2006) as a starting point, we derive a new version which uses a simple counting argument for the choice of kernels in order to generate a tighter bound when 1-norm regularization (sparsity) is imposed in the kernel learning problem. The second bound is a Rademacher c...

It is shown how a special family of unitary operators, called the Rademacher permutations and related to the Clifford algebra, can be used to reduce the level of randomness in several results in asymptotic geometric analysis. §

We extend some sharp inequalities for martingale-differences to general multiplicative systems of random variables. The key ingredient in the proofs is a technique reducing case Rademacher variables without change constants inequalities.

These are lecturenotes for two lectures delivered at the Les Houches workshop on Number Theory, Physics, and Geometry, March 2003. They review two examples of interesting interactions between number theory and string compactification, and raise some new questions and issues in the context of those examples. The first example concerns the role of the Rademacher expansion of coefficients of modul...