TABLE 1.

Notation

xi	a random variable
x	a sample of m variables: x = [x1, x2, · · ·, xm]⊤
X	the data matrix of n samples, X ∈ ℝn×m
xi,:	the i-th row of X, representing a sample
x:,i	the i-th column of X, representing the realization of the random variable xi on n samples
Θ	the parameters of a Gaussian Bayesian Network θ = [θ1, · · ·, θm], Θ ∈ ℝm×m
Pai	a vector containing the parents of xi
PAi	a matrix whose j-th column represents a realization of Pai on the j-th sample.
G	an m× m matrix for BN: if there is a directed edge from xi to xj, Gij = 1, otherwise Gij = 0
P	an m× m matrix for BN: if there is a directed path from xi to xj, Pij = 1, otherwise Pij = 0