近似性和推广
Approximability and Generalisation
摘要：
近似学习机器在小型设备时代已经变得流行，包括量化、因子分解、散列或其他压缩预测器，而解释和保证这些方法良好泛化能力的探索才刚刚开始。在本文中，我们研究的作用，学习的近似性，无论是在全精度和近似设置的预测是从数据中学习，通过一个概念的灵敏度预测的近似算子的行动在手。我们证明了这样的预测的泛化上限，产生以下主要结果，任何PAC学习类和任何给定的近似算子。1)我们表明，在温和的条件下，近似的目标概念是从一个较小的标记样本，提供足够的未标记的数据学习。2)我们给出的算法，保证一个很好的预测，其近似也享有同样的泛化保证。3)我们突出了敏感性类中结构的自然例子，这减少了，甚至可能消除了额外的未标记数据的丰富需求，并从此揭示了什么使一个问题实例比另一个更容易学习。这些结果将现代模型压缩方法的范围嵌入到统计学习理论的总体目标中，从而通过最小化统一边界来建议适当的算法。
英文摘要：
Approximate learning machines have become popular in the era of small devices, including quantised, factorised, hashed, or otherwise compressed predictors, and the quest to explain and guarantee good generalisation abilities for such methods has just begun. In this paper we study the role of approximability in learning, both in the full precision and the approximated settings of the predictor that is learned from the data, through a notion of sensitivity of predictors to the action of the approximation operator at hand. We prove upper bounds on the generalisation of such predictors, yielding the following main findings, for any PAC-learnable class and any given approximation operator. 1) We show that under mild conditions, approximable target concepts are learnable from a smaller labelled sample, provided sufficient unlabelled data. 2) We give algorithms that guarantee a good predictor whose approximation also enjoys the same generalisation guarantees. 3) We highlight natural examples of structure in the class of sensitivities, which reduce, and possibly even eliminate the otherwise abundant requirement of additional unlabelled data, and henceforth shed new light onto what makes one problem instance easier to learn than another. These results embed the scope of modern model compression approaches into the general goal of statistical learning theory, which in return suggests appropriate algorithms through minimising uniform bounds.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
