  We quantify the separation between the numbers of labeled examples required
to learn in two settings: Settings with and without the knowledge of the
distribution of the unlabeled data. More specifically, we prove a separation by
$\Theta(\log n)$ multiplicative factor for the class of projections over the
Boolean hypercube of dimension $n$. We prove that there is no separation for
the class of all functions on domain of any size.
  Learning with the knowledge of the distribution (a.k.a. fixed-distribution
learning) can be viewed as an idealized scenario of semi-supervised learning
where the number of unlabeled data points is so great that the unlabeled
distribution is known exactly. For this reason, we call the separation the
value of unlabeled data.
