  Score based learning (SBL) is a promising approach for learning Bayesian
networks in the discrete domain. However, when employing SBL in the continuous
domain, one is either forced to move the problem to the discrete domain or use
metrics such as BIC/AIC, and these approaches are often lacking. Discretization
can have an undesired impact on the accuracy of the results, and BIC/AIC can
fall short of achieving the desired accuracy. In this paper, we introduce two
new scoring metrics for scoring Bayesian networks in the continuous domain: the
three-part minimum description length and the renormalized normalized maximum
likelihood metric. We rely on the minimum description length principle in
formulating these metrics. The metrics proposed are free of hyperparameters,
decomposable, and are asymptotically consistent. We evaluate our solution by
studying the convergence rate of the learned graph to the generating network
and, also, the structural hamming distance of the learned graph to the
generating network. Our evaluations show that the proposed metrics outperform
their competitors, the BIC/AIC metrics. Furthermore, using the proposed RNML
metric, SBL will have the fastest rate of convergence with the smallest
structural hamming distance to the generating network.
