Improving Discretization Exploiting Dependence Structure

Bayesian networks are multivariate statistical models using a directed acyclic graph to represent statistical dependencies among variables. When dealing with Bayesian Networks it is common to assume that all the variables are discrete. This is not often the case in many real contexts where also continuous variables are observed. A common solution consists in discretizing the continuous variables. In this paper we propose a discretization algorithm based on the Kullback-Leibler divergence measure. Formally, we deal with the problem of discretizing a continuous variable Y conditionally on its parents. We show that such a problem is polynomially solvable. A simulation study is finally performed.