边际独立模型

Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation Pub Date : 2021-12-19 DOI:10.1145/3476446.3536193

T. Boege, Sonja Petrovi'c, B. Sturmfels

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引用次数: 4

摘要

我们对张量的边际施加秩一约束，由一个简单复合体给出。根据Kirkup和Sullivant的工作，这种边际独立模型可以通过坐标的线性变化来实现。研究了它们的环理想，重点研究了拟阵的随机图模型和独立集多面体。我们发展了参数估计的数值代数，同时使用欧几里得距离和极大似然，我们提出了一个综合的小模型数据库。

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Marginal Independence Models

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.

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Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation

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