论文标题
从数据中学习假设空间：学习空间和U-Curve属性
Learning the Hypotheses Space from data: Learning Space and U-curve Property
论文作者
论文摘要
本文介绍了经典不可知论的PAC学习模型的扩展，其中学习问题不仅是由假设空间$ \ Mathcal {h} $建模的，而且还通过学习空间$ \ Mathbb {l}（\ Mathcal {h}）$模型算法。我们的主要贡献是一种数据驱动的通用学习算法，以在$ \ mathbb {l}（\ Mathcal {h}）$上执行正则模型选择。这种方法的一种显着的，正式证明的结果是$ \ mathbb {l}（\ Mathcal {h}）$的条件以及导致估计的样本外错误表面的损耗功能，这些误差表面是$ \ m athbb {l}（l Mathcal {h}）（\ Mathcal {h}）$ chins $ chains $ chains $ curves in $ \ mathbb { $ \ mathbb {l}（\ Mathcal {h}）$。据我们所知，这是第一个严格的结果，认为对候选模型家庭的非详尽搜索可以返回最佳解决方案。在这个新框架中，U-Curve优化算法成为模型选择的自然组成部分，因此是学习算法的。这里提出的抽象一般框架可能对现代学习模型以及神经架构搜索等领域具有重要意义。
This paper presents an extension of the classical agnostic PAC learning model in which learning problems are modelled not only by a Hypothesis Space $\mathcal{H}$, but also by a Learning Space $\mathbb{L}(\mathcal{H})$, which is a cover of $\mathcal{H}$, constrained by a VC-dimension property, that is a suitable domain for Model Selection algorithms. Our main contribution is a data driven general learning algorithm to perform regularized Model Selection on $\mathbb{L}(\mathcal{H})$. A remarkable, formally proved, consequence of this approach are conditions on $\mathbb{L}(\mathcal{H})$ and on the loss function that lead to estimated out-of-sample error surfaces which are true U-curves on $\mathbb{L}(\mathcal{H})$ chains, enabling a more efficient search on $\mathbb{L}(\mathcal{H})$. To our knowledge, this is the first rigorous result asserting that a non exhaustive search of a family of candidate models can return an optimal solution. In this new framework, an U-curve optimization algorithm becomes a natural component of Model Selection, hence of learning algorithms. The abstract general framework proposed here may have important implications on modern learning models and on areas such as Neural Architecture Search.
