Binary Cumulant Varieties
Combinatorics
2011-09-06 v2 Algebraic Geometry
Statistics Theory
Statistics Theory
Abstract
Algebraic statistics for binary random variables is concerned with highly structured algebraic varieties in the space of 2x2x...x2-tensors. We demonstrate the advantages of representing such varieties in the coordinate system of binary cumulants. Our primary focus lies on hidden subset models. Parametrizations and implicit equations in cumulants are derived for hyperdeterminants, for secant and tangential varieties of Segre varieties, and for certain context-specific independence models. Extending work of Rota and collaborators, we explore the polynomial inequalities satisfied by cumulants.
Cite
@article{arxiv.1103.0153,
title = {Binary Cumulant Varieties},
author = {Bernd Sturmfels and Piotr Zwiernik},
journal= {arXiv preprint arXiv:1103.0153},
year = {2011}
}
Comments
Minor revisions. To appear in Annals of Combinatorics, BAD Math Day Special Issue