1. Suppose that a list contains the values 20 44 48 55 62 66 74 88 93 99 at index positions 0 through 9. Trace the values of the variables….

## Prove that the class of all polynomial classifiers over R has infinite VCdimension.

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 of*H *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*}.