We propose a novel algorithm for the support estimation of partially known Gaussian graphical models that incorporates prior information about the underlying graph. In contrast to classical approaches that provide a point estimate based on a maximum likelihood or a maximum a posteriori criterion using (simple) priors on the precision matrix, we consider a prior on the graph and rely on annealed Langevin diffusion to generate samples from the posterior distribution. Since the Langevin sampler requires access to the score function of the underlying graph prior, we use graph neural networks to effectively estimate the score from a graph dataset (either available beforehand or generated from a known distribution). Numerical experiments demonstrate the benefits of our approach.

翻译：我们提出了一种新颖的算法，用于估计部分已知高斯图模型的支持集，该算法整合了关于底层图结构的先验信息。与基于最大似然或最大后验准则（使用简单先验作用于精度矩阵）提供点估计的经典方法不同，我们考虑对图结构的先验，并采用退火朗之万扩散从后验分布中生成样本。由于朗之万采样器需要访问底层图先验的分数函数，我们使用图神经网络从图数据集（预先可用或从已知分布生成）中有效估计该分数。数值实验证明了我们方法的优势。