Predictive Discretization During Model Selection

We present an approach to discretizing multivariate continuous data while learning the structure of a graphical model. We derive a joint scoring function from the principle of predictive accuracy, which inherently ensures the optimal trade-off between goodness of fit and model complexity including the number of discretization levels. Using the socalled finest grid implied by the data, our scoring function depends only on the number of data points in the various discretization levels (independent of the metric used in the continuous space). Our experiments with artificial data as well as with gene expression data show that discretization plays a crucial role regarding the resulting network structure.