1. Use the Dudley representation to figure out the VC-dimension of the class Pd 1 – the class of all d-degree polynomials over R.
2. Prove that the class of all polynomial classifiers over R has infinite VCdimension.
3. Use the Dudley representation to figure out the VC-dimension of the class Pd n (as a function of d and n).
4. Prove that for any finite class H, and any description language d : H → {0,1}∗, the VC-dimension ofH is at most 2sup{|d(h)| : h ∈H} – the maximum description length of a predictor in H. Furthermore, if d is a prefix-free description then VCdim(H) ≤ sup{|d(h)| : h ∈ H}.
