A multivariate symmetric Bernoulli distribution has marginals that are uniform over the pair {0,1}. Consider the problem of sampling from this distribution given a prescribed correlation between each pair of variables. Not all correlation structures can be attained. Here we completely characterize the admissible correlation vectors as those given by convex combinations of simpler distributions. This allows us to bijectively relate the correlations to the well-known CUTn polytope, as well as determine if the correlation is possible through a linear programming formulation.

中文翻译：

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容许的伯努利相关

多元对称伯努利分布具有在{0,1}对上均匀的边际。给定每对变量之间的规定相关性，考虑从这种分布采样的问题。并非所有相关结构都可以实现。在这里，我们将可允许的相关向量完全表征为由更简单分布的凸组合给出的相关向量。这使我们能够将相关性与众所周知的CUTn多表位进行双射相关，并通过线性编程公式确定相关性是否可能。