Stanisław Woźniak, Hlynur Jónsson, et al.
Nature Communications
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 ℝ𝑛. We conclude with experiments and open problems motivated by this new way to summarize distributional shape.
Stanisław Woźniak, Hlynur Jónsson, et al.
Nature Communications
Tal Shnitzer, Mikhail Yurochkin, et al.
ICML 2022
Shrivani Pandiya, Serge Ecoffey, et al.
ECTC 2023
Laura Gardiner, Ritesh Krishna
Nat. Food.