Graphical Gaussian models with edge and vertex symmetries
Graphical Gaussian models with edge and vertex symmetries
复制标题
具有边和顶点对称性的图形高斯模型
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
S. Lauritzen
中科院分区：
文献类型：
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作者：
Søren Højsgaard;S. Lauritzen
总结：我们通过对浓度或相关矩阵施加对称性限制来引入新类型的图形高斯模型。 模型可以用彩色图表示，其中与相同颜色的边或顶点相关联的参数被限制为相同。我们研究了这些模型的性质，并推导出计算最大似然估计的必要算法。我们确定的浓度和相关矩阵是等价的限制条件。这是例如当对称性由变量标签的置换生成时的情况。对于这样的模型，一个特别简单的似然函数的最大化是可用的。
Summary. We introduce new types of graphical Gaussian models by placing symmetry restrictions on the concentration or correlation matrix. The models can be represented by coloured graphs, where parameters that are associated with edges or vertices of the same colour are restricted to being identical. We study the properties of such models and derive the necessary algorithms for calculating maximum likelihood estimates. We identify conditions for restrictions on the concentration and correlation matrices being equivalent. This is for example the case when symmetries are generated by permutation of variable labels. For such models a particularly simple maximization of the likelihood function is available.