Context

• In BayesiaLab, the Kullback-Leibler Divergence (or KL Divergence) is used to measure the strength of the relationship between two nodes that are directly connected by an arc.
• We commonly refer to the KL Divergence also as Arc Force.
• Formally, ​the Kullback-Leibler Divergence $D_{KL}$ measures the difference between two distributions $P$ and $Q$. $$D_{KL}(P({\cal X})\|Q({\cal X}))=\sum_{\cal X}P({\cal X})log_2\frac{P({\cal X})}{Q({\cal X})}$$
• For our purposes, we consider $P$ the Bayesian network that does include the arc for which we wish to compute the Arc Force, and $Q$ the Bayesian network that does not contain that arc but is otherwise identical.
• We interpret this difference $D_{KL}$ as the "force of the arc" or Arc Force.
• Note that Filtered Values are taken into account for computing the Arc Force.
• In this Used Guide, we use Kullback-Leibler Divergence, KL Divergence, and Arc Force interchangeably.

Usage

• Select Menu > Analysis > Visual > Overall > Arc > Kullback-Leibler or press the F key as a shortcut.

• The width of each arc in the network is now proportional to the Kullback-Leibler Divergence or Arc Force.

• An additional control panel is available in the Toolbar, which allows you to define Arc Force thresholds for the arcs.

• By moving the slider or typing in a specific value, BayesiaLab grays out all arcs that don't meet that threshold.

• Alternatively, you can use the previous and next buttons to step through the specific thresholds at which arcs are added and disappear respectively.

• Click the Arc Comment icon on the Toolbar to display the Arc Force values as comments on each arc.

  

• The top value in the Arc Comment label shows the absolute value of the Arc Force.

• The bottom value, highlighted in blue, shows the arc's share of the sum of all Arc Forces in the network, i.e., the blue percentages of all arcs add up to 100%.

• By clicking the checkmark icon for validation, you can save all computed Arc Force values as Arc Comments that will be retained even after this analysis concludes. This validation saves the thickness of each arc as a graphical property.

• Clicking the cancel icon concludes the analysis without saving any information from the analysis.

Workflow