SEMdag: Fast learning of Directed Acyclic Graphs via node or layer ordering

by Mario Grassi, Barbara Tarantino

A Directed Acyclic Graph (DAG) offers an easy approach to define causal structures among gathered nodes: causal linkages are represented by arrows between the variables, leading from cause to effect. Recently, industry and academics have paid close attention to DAG structure learning from observable data, and many techniques have been put out to address the problem. We provide a two-step approach, named SEMdag(), that can be used to quickly learn high-dimensional linear SEMs. It is included in the R package SEMgraph and employs a two-stage order-based search using previous knowledge (Knowledge-based, KB) or data-driven method (Bottom-up, BU), under the premise that a linear SEM with equal variance error terms is assumed. We evaluated our framework’s for finding plausible DAGs against six well-known causal discovery techniques (ARGES, GES, PC, LiNGAM, CAM, NOTEARS). We conducted a series of experiments using observed expression (or RNA-seq) data, taking into account a pair of training and testing datasets for four distinct diseases: Amyotrophic Lateral Sclerosis (ALS), Breast cancer (BRCA), Coronavirus disease (COVID-19) and ST-elevation myocardial infarction (STEMI). The results show that the SEMdag() procedure can recover a graph structure with good disease prediction performance evaluated by a conventional supervised learning algorithm (RF): in the scenario where the initial graph is sparse, the BU approach may be a better choice than the KB one; in the case where the graph is denser, both BU an KB report high performance, with highest score for KB approach based on topological layers. Besides its superior disease predictive performance compared to previous research, SEMdag() offers the user the flexibility to define distinct structure learning algorithms and can handle high dimensional issues with less computing load. SEMdag() function is implemented in the R package SEMgraph, easily available at https://CRAN.R-project.org/package=SEMgraph.