论文标题
从概括误差到运输成本不平等和背部
From Generalisation Error to Transportation-cost Inequalities and Back
论文作者
论文摘要
在这项工作中，我们将界限预期概括误差与运输成本不平等的问题联系起来。揭露两种方法背后的基本模式，我们能够概括它们，并超越Kullback-Leibler Diverences/互发信息和哥斯次级措施。特别是，我们能够提供一个结果，显示两个不等式家族之间的等效性：一个涉及功能和一个涉及措施的等效性。该结果概括了Bobkov和Götze提出的结果，将运输成本不平等与度量浓度联系起来。此外，它使我们能够恢复涉及共同信息的所有标准概括误差界限，并引入涉及任意发散度量的新的，更通用的界限。
In this work, we connect the problem of bounding the expected generalisation error with transportation-cost inequalities. Exposing the underlying pattern behind both approaches we are able to generalise them and go beyond Kullback-Leibler Divergences/Mutual Information and sub-Gaussian measures. In particular, we are able to provide a result showing the equivalence between two families of inequalities: one involving functionals and one involving measures. This result generalises the one proposed by Bobkov and Götze that connects transportation-cost inequalities with concentration of measure. Moreover, it allows us to recover all standard generalisation error bounds involving mutual information and to introduce new, more general bounds, that involve arbitrary divergence measures.
