Machine learning systems have been extensively used as auxiliary tools in domains that require critical decision-making, such as healthcare and criminal justice. The explainability of decisions is crucial for users to develop trust on these systems. In recent years, the globally-consistent rule-based summary-explanation and its max-support (MS) problem have been proposed, which can provide explanations for particular decisions along with useful statistics of the dataset. However, globally-consistent summary-explanations with limited complexity typically have small supports, if there are any. In this paper, we propose a relaxed version of summary-explanation, i.e., the $q$-consistent summary-explanation, which aims to achieve greater support at the cost of slightly lower consistency. The challenge is that the max-support problem of $q$-consistent summary-explanation (MSqC) is much more complex than the original MS problem, resulting in over-extended solution time using standard branch-and-bound solvers. To improve the solution time efficiency, this paper proposes the weighted column sampling~(WCS) method based on solving smaller problems by sampling variables according to their simplified increase support (SIS) values. Experiments verify that solving MSqC with the proposed SIS-based WCS method is not only more scalable in efficiency, but also yields solutions with greater support and better global extrapolation effectiveness.

本研究提出了一种松弛版本的总结说明，即$q$-一致的总结说明，旨在以较小的一致性代价实现更大的支持。为了提高解决方案时间效率，本文基于按其简化的增加支持（SIS）值对变量进行抽样的WCS方法。实验证明，使用建议的SIS-based WCS方法解决MSqC不仅更具可伸缩性的效率，而且能产生更大的支持和更好的全局外推效果。

加强解释的支持性：基于加权列采样的q一致性摘要解释优化