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C O D E: GGMGwishart v1.0

Description: The GGMGwishart v1.0 MATLAB code package implements several marginal likelihood approximation methods for non-decomposable Gaussian Graphical Models (GGMs) under a G-Wishart prior. The methods are described in our NIPS 2009 paper. The approximations include BIC score, Laplace approximation, diagonal Hessian Laplace approximation, and the Monte Carlo estimator of Atay-Kayis and Massam.

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Package Contents: The main files in included in this package are: System Requirements: Example: This example computes the marginal likelihood approximation given by each of the included methods for all four-node GGMs using the Iris virginica data. The results can be compared to Figure 3 of Atay-Kayis and Massam [p. 333] shown below.

Figure 1: Graphs and posterior probabilities for the top 16 graphs as computed by Atay-Kayis and Massam.

Figure 2: Graphs and posterior probabilities for the four methods included in this code package. MC is the Monte Carlo method of Atay-Kayis and Massam. The MC results are very close to those given in Atay-Kayis and Massam.

Figure 3: KL divergence from the Monte Carlo posterior over graphs to the posteriors compute from BIC, diagonal Hessian Laplace, and Laplace marginal likelihood approximations. We see that Laplace is more accurate than diagonal Laplace, which is more accurate than BIC.
This site last updated March 3, 2014. © Benjamin M. Marlin