An unbiased hypothesis space $H$ is one that shatters
instance space $X$. (and remember, unbiased is bad).
But, what if $H$ can instead shatter a large subset of
$X$?
The Vapnik-Chervonenkis dimension, $VC(H)$, of
hypothesis space $H$ defined over instance space $X$ is the
size of the largest finite subset of $X$ shattered by $H$. If
arbitrarily large finite sets of $X$ can be shattered by $H$,
then $VC(H) \equiv \infty$.
For any finite $H$ we have that
\[
\array{
VC(H) &= d \\
|H| &\geq 2^d \\
VC(H) &\leq \log_2|H|
} \]