Covering Numbers , Pseudo - Dimension , and Fat - Shattering Dimension

So far we have seen how to obtain high confidence bounds on the generalization error er D [hS ] of a binary classifier hS learned by an algorithm from a function class H ⊆ {−1, 1}X of limited capacity, using the ideas of uniform convergence. We saw the use of the growth function ΠH(m) to measure the capacity of the class H, as well as the VC-dimension VCdim(H), which provides a one-number summary of the capacity of H.