  In part \textit{I} we proposed a structure for a general Hypotheses Space
$\mathcal{H}$, the Learning Space $\mathbb{L}(\mathcal{H})$, which can be
employed to avoid \textit{overfitting} when estimating in a complex space with
relative shortage of examples. Also, we presented the U-curve property, which
can be taken advantage of in order to select a Hypotheses Space without
exhaustively searching $\mathbb{L}(\mathcal{H})$. In this paper, we carry
further our agenda, by showing the consistency of a model selection framework
based on Learning Spaces, in which one selects from data the Hypotheses Space
on which to learn. The method developed in this paper adds to the
state-of-the-art in model selection, by extending Vapnik-Chervonenkis Theory to
\textit{random} Hypotheses Spaces, i.e., Hypotheses Spaces learned from data.
In this framework, one estimates a random subspace $\hat{\mathcal{M}} \in
\mathbb{L}(\mathcal{H})$ which converges with probability one to a target
Hypotheses Space $\mathcal{M}^{\star} \in \mathbb{L}(\mathcal{H})$ with desired
properties. As the convergence implies asymptotic unbiased estimators, we have
a consistent framework for model selection, showing that it is feasible to
learn the Hypotheses Space from data. Furthermore, we show that the
generalization errors of learning on $\hat{\mathcal{M}}$ are lesser than those
we commit when learning on $\mathcal{H}$, so it is more efficient to learn on a
subspace learned from data.
