Learning High-dimensional Directed Acyclic Graphs with Mixed Data-types

In recent years, great strides have been made for causal structure learning in the high-dimensional setting and in the mixed data-type setting when there are both discrete and continuous variables. However, due to the complications involved with modeling continuous-discrete variable interactions, the intersection of these two settings has been relatively understudied. The current paper explores the problem of efficiently extending causal structure learning algorithms to high-dimensional data with mixed data-types. First, we characterize a model over continuous and discrete variables. Second, we derive a degenerate Gaussian (DG) score for mixed data-types and discuss its asymptotic properties. Lastly, we demonstrate the practicality of the DG score on learning causal structures from simulated data sets.