Inference in Gaussian Bayesian Network

Question

I am having some problem related to Partial Abductive Inference in Gaussian Bayesian Networks (Bayesian Networks which accommodates the continuous nature of the random variables and follow jointly a Gaussian distribution)...

My questions are:

1. Can the algorithms like junction tree propagation be applicable as it is for the discrete variable Bayesian Networks, in the case of the Gaussian Bayesian Networks?
2. If no then which algorithms are applicable in the case of the Gaussian Bayesian Networks?
3. Is there any complexity proof for the Partial Abductive Inference in case of Gaussian Bayesian Networks (As it is known that the task is NP-hard in case of discrete variable Bayesian Networks)?
4. Can the Evolutionary algorithms or MCMC sampling criteria be applied for approximate Partial Abductive Inference in Gaussian Bayesian Networks?

I will be highly grateful to you all if kindly help me in this regard. Thanks in advance...

Answer 1

Belief Propagation is a generic inference algorithm based on message passing that requires two operations, sum() and product(), which can be easily implemented for Gaussian variables.

Junction tree propagation is a special case of Belief Propagation running on trees, so it can be applied to Gaussian Bayesian networks too.

Those books explain inference in continuous Bayesian networks in some details:

• Christopher M. Bishop. Pattern Recognition and Machine Learning (Information Science and Statistics), 2009
• Daphne Koller, Nir Friedman. Probabilistic Graphical Models, Principles and Techniques, 2009