With increasing volume of data being used across machine learning tasks, the capability to target specific subsets of data becomes more important. To aid in this capability, the recently proposed Submodular Mutual Information (SMI) has been effectively applied across numerous tasks in literature to perform targeted subset selection with the aid of a exemplar query set. However, all such works are deficient in providing theoretical guarantees for SMI in terms of its sensitivity to a subset's relevance and coverage of the targeted data. For the first time, we provide such guarantees by deriving similarity-based bounds on quantities related to relevance and coverage of the targeted data. With these bounds, we show that the SMI functions, which have empirically shown success in multiple applications, are theoretically sound in achieving good query relevance and query coverage.

翻译：随着机器学习任务中数据量的不断增加，针对特定数据子集进行选择的能力变得愈发重要。为增强这一能力，近期提出的子模互信息（SMI）已在文献中众多任务中得到有效应用，通过借助示例查询集实现目标子集选择。然而，已有工作在SMI对子集相关性及目标数据覆盖度的敏感性方面缺乏理论保证。本文首次通过推导基于相似度的目标数据相关性与覆盖度相关量的界限，提供了此类保证。基于这些界限，我们证明了在多个应用中已取得实证成功的SMI函数在理论上能够实现良好的查询相关性与查询覆盖度。