Article
Bernoulli Correlations and Cut Polytopes
arXiv.org
(2017)
Abstract
Given n symmetric Bernoulli variables, what can be said about their correlation matrix viewed as a vector? We show that the set of those vectors R(Bn) is a polytope and identify its vertices. Those extreme points correspond to correlation vectors associated to the discrete uniform distributions on diagonals of the cube [0,1]n. We also show that the polytope is affinely isomorphic to a well-known cut polytope CUT(n) which is defined as a convex hull of the cut vectors in a complete graph with vertex set {1,…,n}. The isomorphism is obtained explicitly as R(Bn)=1−2 CUT(n). As a corollary of this work, it is straightforward using linear programming to determine if a particular correlation matrix is realizable or not. Furthermore, a sampling method for multivariate symmetric Bernoullis with given correlation is obtained. In some cases the method can also be used for general, not exclusively Bernoulli, marginals.
Disciplines
Publication Date
2017
Citation Information
Nevena Maric and Mark Huber. "Bernoulli Correlations and Cut Polytopes" arXiv.org (2017) Available at: http://works.bepress.com/nevena-maric/3/