mutual information and edge weights in a bayesian network The mutual information between two random variables X and Y can be stated formally as follows:
I(X ; Y) = H(X) – H(X | Y)
Where I(X ; Y) is the mutual information for X and Y, H(X) is the entropy for X and H(X | Y) is the conditional entropy for X given Y. The result has the units of bits.
Is the above a realistic representation of the weights along the edge of a bayesian network? Or is a probabilistic representation more suitable? If so, what is the best representation?
How should the edge weights be view from probabilistic perspective in a bayesian network context for directed edges; The probability of the nodes I understand to be posterior or marginal probability, but the edges are slightly more ambiguous.
Update 2021/12/08:


If you could provide the community with literature resources or a graphic/sketch of your problem formulation and thoughts, then you will receive more specific answers.
And to answer your questions as it stands:

Is the above a realistic representation of the weights along the edge of a bayesian network?

No.

Or is a probabilistic representation more suitable? If so, what is the best representation?

Yes.
Bayesian networks do not have weights associated with their edges.
An edge in a Bayesian network represents the conditional probability for a corresponding random variable, which is represented as a node/vertex in the graph.
Finally, the edges refer to conditional probability distributions, whereas the components of mutual information are based on joint probability distribution and marginal probability distribution.
