当前位置:
X-MOL 学术
›
arXiv.cs.DM
›
论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Concave Aspects of Submodular Functions
arXiv - CS - Discrete Mathematics Pub Date : 2020-06-27 , DOI: arxiv-2006.16784 Rishabh Iyer and Jeff Bilmes
arXiv - CS - Discrete Mathematics Pub Date : 2020-06-27 , DOI: arxiv-2006.16784 Rishabh Iyer and Jeff Bilmes
Submodular Functions are a special class of set functions, which generalize
several information-theoretic quantities such as entropy and mutual information
[1]. Submodular functions have subgradients and subdifferentials [2] and admit
polynomial-time algorithms for minimization, both of which are fundamental
characteristics of convex functions. Submodular functions also show signs
similar to concavity. Submodular function maximization, though NP-hard, admits
constant-factor approximation guarantees, and concave functions composed with
modular functions are submodular. In this paper, we try to provide a more
complete picture of the relationship between submodularity with concavity. We
characterize the super-differentials and polyhedra associated with upper bounds
and provide optimality conditions for submodular maximization using the-super
differentials. This paper is a concise and shorter version of our longer
preprint [3].
中文翻译:
子模函数的凹面
子模函数是一类特殊的集合函数,它概括了若干信息论量,例如熵和互信息 [1]。次模函数具有次梯度和次微分 [2] 并允许多项式时间算法进行最小化,这两者都是凸函数的基本特征。子模块函数也显示出类似于凹度的迹象。子模函数最大化虽然是 NP 难的,但允许常数因子逼近保证,并且由模函数组成的凹函数是子模的。在本文中,我们试图更完整地描述次模量与凹度之间的关系。我们描述了与上限相关的超微分和多面体,并使用超微分为子模最大化提供了最优条件。这篇论文是我们较长的预印本 [3] 的简洁和简短版本。
更新日期:2020-07-01
中文翻译:
子模函数的凹面
子模函数是一类特殊的集合函数,它概括了若干信息论量,例如熵和互信息 [1]。次模函数具有次梯度和次微分 [2] 并允许多项式时间算法进行最小化,这两者都是凸函数的基本特征。子模块函数也显示出类似于凹度的迹象。子模函数最大化虽然是 NP 难的,但允许常数因子逼近保证,并且由模函数组成的凹函数是子模的。在本文中,我们试图更完整地描述次模量与凹度之间的关系。我们描述了与上限相关的超微分和多面体,并使用超微分为子模最大化提供了最优条件。这篇论文是我们较长的预印本 [3] 的简洁和简短版本。