Relative Mutual Information

Definition

Based on Mutual Information, Relative Mutual Information is defined as:

$${I_R}\left( {X,Y} \right){\rm{ }} = {\rm{ }}{{I\left( {X,Y} \right)} \over {H\left( X \right)}}$$

Relative Mutual Information expresses in percent how much the entropy (or uncertainty) of $X$ is reduced by observing $Y$.

In older versions of BayesiaLab, Relative Mutual Information was also called Normalized Mutual Information.

Please see the up-to-date definition of Normalized Mutual Information.

Usage

• BayesiaLab reports the Relative Mutual Information in the Target Analysis Report: Main Menu > Analysis > Report > Target > Relationship with Target Node.

• Note that this table shows the Relative Mutual Information of each node, e.g., XRay, Dyspnea, etc., only with regard to the Target Node, Cancer.

• The Relative Mutual Information can also be shown by selecting Main Menu > Analysis > Visual > Overall > Arc > Mutual Information and then clicking the Show Arc Comments icon or selecting Main Menu > View > Show Arc Comments.

• Note that the corresponding options under Preferences > Analysis > Visual Analysis > Arc's Mutual Information Analysis have to be selected first:

• In Preferences, Child refers to the Relative Mutual Information from the Parent onto the Child node, i.e., in the direction of the arc.

• Conversely, Parent refers to the Relative Mutual Information from the Child onto the Parent node, i.e., in the opposite direction of the arc.