Re: Q10 higher bound
I am still confused on how to piece everything together. I like your much cleaner version, but I do have one comment. Having disjoint hypothesis sets does not necessarily mean that the set of dichotomies they create will also be disjoint.
For example, let H1 and H2 be the positive and negative 1d rays, respectively. These two hypothesis sets are disjoint. However, given any data set they can both create the dichotomies of all +1 or all 1. They won't have much overlap beyond that (and maybe THAT is the point), but they won't be entirely disjoint as far as our inequalities are concerned.
