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This paper proposes a data-driven systematic, consistent and non-exhaustiveapproach to Model Selection, that is an extension of the classical agnostic PAClearning model. In this approach, learning problems are modeled not only by ahypothesis 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 relatedsubspaces, that is a suitable algebraic search space for Model Selectionalgorithms. Our main contributions are a data-driven general learning algorithmto perform implicitly regularized Model Selection on $\mathbb{L}(\mathcal{H})$and a framework under which one can, theoretically, better estimate a targethypothesis with a given sample size by properly modeling$\mathbb{L}(\mathcal{H})$ and employing high computational power. A remarkableconsequence of this approach are conditions under which a non-exhaustive searchof $\mathbb{L}(\mathcal{H})$ can return an optimal solution. The results ofthis paper lead to a practical property of Machine Learning, that the lack ofexperimental data may be mitigated by a high computational capacity. In acontext of continuous popularization of computational power, this property mayhelp understand why Machine Learning has become so important, even where datais expensive and hard to get.

Learning the hypotheses space from data through a U-curve algorithm