Binary cumulant varieties
Piotr Zwiernik
Algebraic statistics for binary random variables is concerned with
highly structured algebraic varieties in the space of
2x2x...x2-tensors. Some of these varieties are classic in algebraic
geometry. We demonstrate the advantages of representing these
varieties in the coordinate system of binary cumulants. The key idea
is that certain invariant properties of cumulants can be translated
into geometry. A similar idea was used in the development of umbral
calculus. I will present parametrizations and implicit equations in
cumulants for hyperdeterminants, and for secant and tangential
varieties of Segre varieties. (This is a joint work with Bernd
Sturmfels)