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- W2679343643 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 $R(mathcal{B}_n)$ 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 ${rm CUT}(n)$ which is defined as a convex hull of the cut vectors in a complete graph with vertex set ${1,ldots,n}$. The isomorphism is obtained explicitly as $R(mathcal{B}_n)= {mathbf{1}}-2~{rm CUT}(n)$. 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." @default.
- W2679343643 created "2017-06-30" @default.
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- W2679343643 date "2017-06-19" @default.
- W2679343643 modified "2023-09-27" @default.
- W2679343643 title "Bernoulli Correlations and Cut Polytopes" @default.
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