Learning the hypotheses space from data through a U-curve algorithm
This addresses model selection in machine learning, particularly for domains with expensive data, but it appears incremental as it builds on existing PAC learning frameworks.
The paper tackles model selection by proposing a data-driven approach that extends PAC learning with a learning space poset, leading to conditions where non-exhaustive search can find optimal solutions and suggesting that high computational power can mitigate limited data.
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.