  We present a study of generalization for data-dependent hypothesis sets. We
give a general learning guarantee for data-dependent hypothesis sets based on a
notion of transductive Rademacher complexity. Our main result is a
generalization bound for data-dependent hypothesis sets expressed in terms of a
notion of hypothesis set stability and a notion of Rademacher complexity for
data-dependent hypothesis sets that we introduce. This bound admits as special
cases both standard Rademacher complexity bounds and algorithm-dependent
uniform stability bounds. We also illustrate the use of these learning bounds
in the analysis of several scenarios.
