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, DAG (directed acyclic graph) is useful for expressing causal relationship between random variables. By estimating the DAG structure for the observed data, we can analyze the data more efficiently. In this paper, we propose the new method to estimate the corresponding DAG structure for given continuous type data when the structure is sparse, and we check the proposed method works well and fast to find the near-optimum model in many situation. To do this, we find sufficiently many possible candidate undirected edges, and then we give the direction for each edge. We update the structure with no directed cycle by choosing the locally best action for each candidate edge. If the structure is sparse, random forest is good to determine whether two random variables are dependent or not, and $L_1$ penalized log-likelihood can be reflected the sparsity of the graph. We could take possible candidate edges by using these techniques. To decide the locally best action, we use a score function based on MLE. But we can use another score functions and apply the same procedure as described in this paper.