We impose rank one constraints on marginalizations of a tensor, given by a simplicial complex. Following work of Kirkup and Sullivant, such marginal independence models can be made toric by a linear change of coordinates. We study their toric ideals, with emphasis on random graph models and independent set polytopes of matroids. We develop the numerical algebra of parameter estimation, using both Euclidean distance and maximum likelihood, and we present a comprehensive database of small models.

翻译：我们根据一个简易综合体对强力的边缘化进行排位限制。 在Kirkup和Sullitt的工作之后,这种边际独立模型可以通过线性坐标的改变而形成。我们研究它们的尖性理想,重点是随机图形模型和独立的机器人多面体。我们利用Euclidean距离和最大可能性来开发参数估计的数值代数,我们提出了一个小型模型的综合数据库。