We consider the problem of inferring the conditional independence graph (CIG) of Gaussian vectors from multi-attribute data. Most existing methods for graph estimation are based on single-attribute models where one associates a scalar random variable with each node. In multi-attribute graphical models, each node represents a random vector. For single-attribute graphical models, considerable body of work exists where one first tests for exclusion of each edge from the saturated model, and then infers the CIG. In this paper, we propose and analyze a deviance test based on generalized likelihood ratio, for edge exclusion in multi-attribute Gaussian graphical models. The null distribution of the test statistic is derived to allow analytical calculation of the test threshold. An alternative computationally fast version of the deviance test statistic is also derived. Numerical results based on synthetic as well as real data are presented.

中文翻译：

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从多属性高斯数据进行图估计的偏差检验

我们考虑从多属性数据推断高斯向量的条件独立图（CIG）的问题。大多数现有的图估计方法都基于单属性模型，其中将一个标量随机变量与每个节点相关联。在多属性图形模型中，每个节点代表一个随机向量。对于单属性图形模型，存在大量工作，其中首先测试从饱和模型中排除每条边，然后推断 CIG。在本文中，我们提出并分析了基于广义似然比的偏差检验，用于多属性高斯图形模型中的边缘排除。导出测试统计量的零分布以允许对测试阈值进行分析计算。还导出了偏差测试统计量的替代计算快速版本。给出了基于合成数据和真实数据的数值结果。