Annals of Combinatorics

, Volume 17, Issue 1, pp 229–250 | Cite as

Binary Cumulant Varieties

  • Bernd Sturmfels
  • Piotr ZwiernikEmail author


Algebraic statistics for binary random variables is concerned with highly structured algebraic varieties in the space of 2×2×···×2-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.

Mathematics Subject Classification

13P25 05A40 14Q15 60C05 


algebraic statistics cumulants moments binary data context-specific independence hyperdeterminant Segre variety secant variety 


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Copyright information

© Springer Basel 2012

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA
  2. 2.Department of StatisticsUniversity of CaliforniaBerkeleyUSA

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