Networks Between Categorical or Discretized Numeric Variables

Abstract

Categorical variables take on non-numeric values, e.g., a discretized numeric variable can be interpreted as a categorical variable. Many association measures exist for measuring the statistical dependence between categorical variables (e.g., Pearson chi-square statistic, likelihood ratio test statistic, Fisher’s exact test, mutual information). Association measures between two discretized numeric vectors have been used to measure nonlinear dependencies between them. We describe several approaches for defining weighted networks among categorical variables. In particular, mutual information networks are often used for constructing gene networks. The close relationship between mutual information and a likelihood ratio test statistic allows us to define a conditional measure of mutual information, which accounts for additional covariates. Estimating the mutual information between numeric variables is rather challenging and involves parameter choices. We argue that in many applications the mutual information measure can be approximated by a correlation-based measure. We review the ARACNE approach for constructing an unweighted mutual information network and generalize it to correlation networks and other association networks.