Uniform Convergence and Growth Function / VC - Entropy 3 4 Uniform Convergence in a General / Infinite Function Class H

In the previous lecture we reviewed the SVM learning algorithm, which when given a training sample S ∈ (X × {−1, 1}), selects a (linear or kernel-based) classifier hS : X→{−1, 1} that maximizes the margin on S, possibly with some errors. We know (by design) exactly what the algorithm does on the training sample, but how will it perform on future data, which is what we are really interested in? In particular, if the examples in S are drawn randomly and independently according to some distribution D, what can we say about how the learned function will perform on a new example drawn from D?