Abstract Structure learning methods for covariance and concentration graphs are often validated on synthetic models, usually obtained by randomly generating: (i) an undirected graph, and (ii) a compatible symmetric positive definite (SPD) matrix. In order to ensure positive definiteness in (ii), a dominant diagonal is usually imposed. In this work we investigate different methods to generate random symmetric positive definite matrices with undirected graphical constraints. We show that if the graph is chordal it is possible to sample uniformly from the set of correlation matrices compatible with the graph, while for general undirected graphs we rely on a partial orthogonalization method.

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关于生成随机高斯图模型

摘要 协方差和浓度图的结构学习方法通​​常在合成模型上得到验证，通常通过随机生成：(i) 无向图和 (ii) 兼容的对称正定 (SPD) 矩阵获得。为了确保 (ii) 中的正定性，通常会施加优势对角线。在这项工作中，我们研究了生成具有无向图形约束的随机对称正定矩阵的不同方法。我们表明，如果图是弦图，则可以从与图兼容的相关矩阵集中均匀采样，而对于一般无向图，我们依赖于部分正交化方法。