Penalized Estimation of Sparse Directed Acyclic Graphs From Categorical Data Under Intervention

We develop in this article a penalized likelihood method to estimate sparse causal Bayesian networks from categorical data under experimental intervention. The structure of a Bayesian network is represented by a directed acyclic graph (DAG). We model causal interactions in a discrete network by the multi-logit regression and achieve structure estimation of a DAG via maximizing a regularized likelihood. The adaptive group lasso penalty is employed to encourage sparsity by selecting grouped dummy variables encoding the level of a factor together. We develop a blockwise coordinate descent algorithm to solve the penalized likelihood problem subject to the acyclicity constraint of a DAG. We apply our method to three simulated networks and a real biological network, and demonstrate that our method shows very competitive performance compared to existing methods.