Learning causal or directional relationships for large-scale multivariate data is an extremely challenging problem. The directed acyclic graphical (DAG) model methodology provides one framework for addressing this problem. However there are a number of statistical and computational challenges associated with learning DAG models from observational data. In this talk, I present three of my recent pieces of work that investigates and addresses these challenges. Firstly, I discuss one of the fundamental assumptions in many algorithms for learning DAG models, the so-called faithfulness assumption. I show that this faithfulness assumption is extremely restrictive and unlikely to be satisfied in most practical scenarios. Secondly, I present a strictly weaker assumption than the faithfulness assumption that is guaranteed to recover the DAG model by considering a new approach based on searching over causal orderings. Finally, I present a computationally tractable algorithm for learning count-data DAG models based on a computationally feasible approach to learning the causal orderings.

This is based on joint work with Caroline Uhler (MIT EECS) and Gunwoong Park (UW Madison).