Growth Function and VC - dimension

1 Review of VC theory Our primary interest so far is deriving the generalization bound for the binary classifiers. We have studied the Rademacher complexity techniques, and shown that the VC bound is an upper bound of the Rademacher complexity bound. For a binary classification with 0-1 loss l, we have R m (l • H) ≤ 2 log g H (m) m (1) where H = {h : X → {+1, −1}} is a hypothesis space. The growth function g H (m) is defined to be the number of ways the hypothesis space H assign an arbitrary m point sample set (Definition 1).