论文标题
$ k $ - 变化：差异概念
$k$-Variance: A Clustered Notion of Variance
论文作者
论文摘要
我们介绍了$ k $ - 变化，这是在随机双方匹配机械上构建的差异的概括。 $ k $ - 变化量衡量的是，将两组$ k $样本从分布相匹配的预期成本，从而捕获有关$ k $增加的本地而不是全球信息；使用采样和线性编程很容易随机近似。除了定义$ k $变化并证明其基本属性外，我们还提供了几种关键情况下对此数量的深入分析，包括一维措施，群集措施以及集中于$ \ Mathbb r^n $的低维基集。我们以这种总结分布形状的新方法激励的实验和开放问题得出结论。
We introduce $k$-variance, a generalization of variance built on the machinery of random bipartite matchings. $K$-variance measures the expected cost of matching two sets of $k$ samples from a distribution to each other, capturing local rather than global information about a measure as $k$ increases; it is easily approximated stochastically using sampling and linear programming. In addition to defining $k$-variance and proving its basic properties, we provide in-depth analysis of this quantity in several key cases, including one-dimensional measures, clustered measures, and measures concentrated on low-dimensional subsets of $\mathbb R^n$. We conclude with experiments and open problems motivated by this new way to summarize distributional shape.
