We propose a Bayesian approximate inference method for learning the
dependence structure of a Gaussian graphical model. Using pseudo-likelihood, we
derive an analytical expression to approximate the marginal likelihood for an
arbitrary graph structure without invoking any assumptions about
decomposability. The majority of the existing methods for learning Gaussian
graphical models are either restricted to decomposable graphs or require
specification of a tuning parameter that may have a substantial impact on
learned structures. By combining a simple sparsity inducing prior for the graph
structures with a default reference prior for the model parameters, we obtain a
fast and easily applicable scoring function that works well for even
high-dimensional data. We demonstrate the favourable performance of our
approach by large-scale comparisons against the leading methods for learning
non-decomposable Gaussian graphical models. A theoretical justification for our
method is provided by showing that it yields a consistent estimator of the
graph structure.

本文提出了一种新的基于贝叶斯近似推断的方法，用于学习高斯图模型的依赖结构，通过伪似然方法，无需引入有关可分解性的任何假设即可得到近似边缘似然值，结合简单的稀疏性先验和默认的参考 prior，得到了一个快速适用于高维数据的评估函数，本方法与其他方法的比较表明其性能良好并且能够一致地估计图结构。