2017/06/19 by Mark Huber, Huber, Mark, Nevena Marić +1 · 1 citation
Computer Science · Mathematics · #Advanced Statistical Methods and Models #Blind Source Separation Techniques #Combinatorics (math.CO) #FOS: Mathematics #Metric Geometry (math.MG) #Optimization and Control (math.OC) #Probability (math.PR) #Statistical Methods and Bayesian Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1706.06182
openalex publication_date 2017/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 \rm 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~\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.