# Association analysis

Association analysis (Since version 7.16) measures the strengths of associations between sets of nodes or variables X and Y.

For example, it can be used to measure the strength of links in a network.

Supported for discrete, continuous, hybrid (discrete - continuous) and multi-variate nodes.

## Mutual information

Mutual information quantifies the amount of information that can be gained from one variable through the other. Often denoted $I\left(X;Y\right)$.

## Entropy

The Entropy for X and Y, denoted $H\left(X\right)$ and $H\left(Y\right)$ respectively, are reported for convenience, as the normalized forms of the mutual information require them.

## Symmetric mutual information

The symmetric mutual information (symmetric uncertainty) is a normalized version of the mutual information. It tells us the strength of the association given the level of uncertainty present in X and Y.

It equals $2 * I\left(X;Y\right) / \left(H\left(X\right) + H\left(Y\right)\right)$

## Proficiency

The proficiency (uncertainty coefficient) normalizes the mutual information for either X or Y. For example, the proficiency of X given Y tells us how strong the relationship is given that we know Y.

The proficiency of X given Y, denoted $U\left(X|Y\right)$ equals $I\left(X;Y\right)/H\left(X\right)$, and $U\left(Y|X\right)$ equals $I\left(X;Y\right)/H\left(Y\right)$.