Gregory Czap, Kyungju Noh, et al.
APS Global Physics Summit 2025
We introduce π-variance, a generalization of variance built on the machinery of random bipartite matchings. π-variance measures the expected cost of matching two sets of π samples from a distribution to each other, capturing local rather than global information about a measure as π increases; it is easily approximated stochastically using sampling and linear programming. In addition to defining π-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 βπ. We conclude with experiments and open problems motivated by this new way to summarize distributional shape.
Gregory Czap, Kyungju Noh, et al.
APS Global Physics Summit 2025
Masaya Kubota, Masaki Kuribayashi, et al.
MobileHCI 2024
Vagner Figueredo De Santana, Sara Berger, et al.
IUI 2025
En-de Chu, Jason Tran, et al.
APS Global Physics Summit 2025