  This paper proposes a data-driven systematic, consistent and non-exhaustive
approach to Model Selection, that is an extension of the classical agnostic PAC
learning model. In this approach, learning problems are modeled not only by a
hypothesis space $\mathcal{H}$, but also by a Learning Space
$\mathbb{L}(\mathcal{H})$, a poset of subspaces of $\mathcal{H}$, which covers
$\mathcal{H}$ and satisfies a property regarding the VC dimension of related
subspaces, that is a suitable algebraic search space for Model Selection
algorithms. Our main contributions are a data-driven general learning algorithm
to perform implicitly regularized Model Selection on $\mathbb{L}(\mathcal{H})$
and a framework under which one can, theoretically, better estimate a target
hypothesis with a given sample size by properly modeling
$\mathbb{L}(\mathcal{H})$ and employing high computational power. A remarkable
consequence of this approach are conditions under which a non-exhaustive search
of $\mathbb{L}(\mathcal{H})$ can return an optimal solution. The results of
this paper lead to a practical property of Machine Learning, that the lack of
experimental data may be mitigated by a high computational capacity. In a
context of continuous popularization of computational power, this property may
help understand why Machine Learning has become so important, even where data
is expensive and hard to get.
