Computation of the mutual information in a Bayesian network
Usage
mutual_info(bnfit, node)
Value
A dataframe with the following columns: Nodes - the vertices of the BN; MutualInfo - the mutual information of the corresponding node.
Arguments
bnfit
object of class bn.fit.
node
a node of bnfit.
Details
The mutual information between two variables \(X_j\) and \(X_i\) with sample spaces \(\mathcal{X}_i\) and \(\mathcal{X}_j\), respectively, is equal to $$\sum_{x_j\in\mathcal{X}_j}\sum_{x_i\in\mathcal{X}_i}p(x_i,x_j)\log\frac{p(x_i,x_j)}{p(x_i)p(x_j)}.$$
References
Albrecht, D., Nicholson, A. E., & Whittle, C. (2014). Structural sensitivity for the knowledge engineering of Bayesian networks. In Probabilistic Graphical Models (pp. 1-16). Springer International Publishing.