Learning sparse DAG models based on continuous type data

Abstract

The graphical models are used to represent the conditional independence relationship of the random variables. Especially, the graphical model whose model structure is given in the form of a DAG(directed acyclic graph) is useful for expressing causal relationships between random variables. We can read data more easily and efficiently by learning the model structure provided that the data are from a DAG model. In this paper, we propose a new method of learning a DAG structure for given continuous type data under condition that the structure is sparse. We checked that the proposed method works well and fast in finding a nearly optimal model in many situations. To carry out this, we begin with an undirected graph which is constructed by applying a nonparametric regression method such as the random forest method. We then assign directions to the edges in such a way that the likelihood of the model may increase at each assignment of edge-direction. It is imperative that directed cycles are to be avoided in the DAG. In case of sparse DAG models, $L_1$ penalized log-likelihood would also be instrumental for the DAG learning.