We investigate the behaviour of global and local Rademacher averages. We present new error bounds which are based on the local averages and indicate how data-dependent local averages can be estimated without a priori knowledge of the class at hand.

Last time we introduced the VC dimension and saw one of the fundamental results in statistical learning theory. Recall that for a hypothesis space H : X → {0, 1}, we say that H shatters a sample C ⊂ X if the H can realize all possible binary labelings of C. The VC dimension is the size of the largest set C that can be shattered by H. For binary classification with 0/1 loss, if the hypothesis sp...

We consider the problem of approximately reconstructing a partially-observed, approximately low-rank matrix. This problem has received much attention lately, mostly using the trace-norm as a surrogate to the rank. Here we study low-rank matrix reconstruction using both the trace-norm, as well as the less-studied max-norm, and present reconstruction guarantees based on existing analysis on the R...