In this manuscript, we offer a gentle review of submodularity and supermodularity and their properties. We offer a plethora of submodular definitions; a full description of a number of example submodular functions and their generalizations; example discrete constraints; a discussion of basic algorithms for maximization, minimization, and other operations; a brief overview of continuous submodular extensions; and some historical applications. We then turn to how submodularity is useful in machine learning and artificial intelligence. This includes summarization, and we offer a complete account of the differences between and commonalities amongst sketching, coresets, extractive and abstractive summarization in NLP, data distillation and condensation, and data subset selection and feature selection. We discuss a variety of ways to produce a submodular function useful for machine learning, including heuristic hand-crafting, learning or approximately learning a submodular function or aspects thereof, and some advantages of the use of a submodular function as a coreset producer. We discuss submodular combinatorial information functions, and how submodularity is useful for clustering, data partitioning, parallel machine learning, active and semi-supervised learning, probabilistic modeling, and structured norms and loss functions.

本研究回顾了子模及超模的定义与基本特性，介绍了多种子模函数及其泛化，离散限制的例子，最大化、最小化的算法，以及连续子模扩展。然后，着重探讨了子模函数在机器学习和人工智能领域中的应用，包括总结、聚类、数据子集选择和特征选择等方面。

机器学习和人工智能中的次模性