标题： 距离协方差的组合学：多样变量选择中准凹集函数的包含最小最大化者 显示英文标题

标题： Combinatorics of Distance Covariance: Inclusion-Minimal Maximizers of Quasi-Concave Set Functions for Diverse Variable Selection

摘要： 在本文中，我们证明了负样本距离协方差函数是随机变量样本的准凹集函数，这些随机变量在统计上不是独立的。 我们利用这些性质，提出贪心算法来组合优化一些促进多样性的（低统计依赖性）距离协方差函数。 我们的贪心算法获得了这种促进多样性的目标函数的所有包含最小最大化值。 包含最小最大化值是全局最优最大化值的多个解集，它们不是解集中任何其他最大化集的真子集。 我们展示了将这种方法应用于特征选择设置中以获得多样化特征（协变量/变量/预测因子）的结果，用于回归（或分类）问题。 我们还将我们的多样化特征选择算法与[7]中的基于距离协方差的相关特征选择算法结合，以生成既相关又按非递增多样性水平排序的协变量子集。 显示英文摘要

摘要： In this paper we show that the negative sample distance covariance function is a quasi-concave set function of samples of random variables that are not statistically independent. We use these properties to propose greedy algorithms to combinatorially optimize some diversity (low statistical dependence) promoting functions of distance covariance. Our greedy algorithm obtains all the inclusion-minimal maximizers of this diversity promoting objective. Inclusion-minimal maximizers are multiple solution sets of globally optimal maximizers that are not a proper subset of any other maximizing set in the solution set. We present results upon applying this approach to obtain diverse features (covariates/variables/predictors) in a feature selection setting for regression (or classification) problems. We also combine our diverse feature selection algorithm with a distance covariance based relevant feature selection algorithm of [7] to produce subsets of covariates that are both relevant yet ordered in non-increasing levels of diversity of these subsets.