an:06697897
Zbl 1407.62193
LeppĂ¤-aho, Janne; Pensar, Johan; Roos, Teemu; Corander, Jukka
Learning Gaussian graphical models with fractional marginal pseudo-likelihood
EN
Int. J. Approx. Reasoning 83, 21-42 (2017).
0888-613X
2017
j
62H12 62F15 68T05
approximate likelihood; fractional Bayes factors; model selection; structure learning; Gaussian graphical models
Summary: 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.