# Kullback-Leibler Divergence (Arc Force)

- 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 DKL**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
**DKL**as the "force of the arc" or**Arc Force**. - Note that Filtered Values are taken into account for computing the
**Arc Force**.

Throughout this website, we use

**Kullback-Leibler Divergence**,**KL Divergence**, and**Arc Force**interchangeably.Last modified 7mo ago