Georgia Institute of Technology College of Sciences

I will be presenting the paper by S. Mendelson titled 'Rademacher Averages and Phase Transitions in Glivenko–Cantelli Classes'. Fat-shattering dimension and its use in characterizing GC classes will be introduced. Then a new quantity based on the growth rate of the Rademacher averages will be introduced. This parameter enables one to provide improved complexity estimates for the agnostic learning problem with respect to any norm. A phase transition phenomenon that appears in the sample complexity estimates, covering numbers estimates, and in the growth rate of the Rademacher averages will be discussed. Further (i) estimates on the covering numbers of a class when considered as a subset of spaces and (ii) estimate the fat-shattering dimension of the convex hull of a given class will be discussed.