Han Huang, Jiajia Yu, et al.
Journal of Computational Physics
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.
Han Huang, Jiajia Yu, et al.
Journal of Computational Physics
Yonggui Yan, Jie Chen, et al.
ICML 2023
Anming Gu, Edward Chien, et al.
ICLR 2025
Ioannis Georgakilas, Rafal Mirek, et al.
Condensates of Light 2024