Some recent developments on the geometry of causation

A fundamental task in modern artificial intelligence is to identify transparent ways to represent cause-effect relations and then design efficient and reliable methods for learning such representations from data. These tasks can, respectively, be termed the problem of representation and the problem of causal discovery, and each problem has close connections to the world of nonlinear algebra. Classically, the problem of representation is solved using directed acyclic graphical (DAG) models, which are then learned from data using a variety of techniques - among which the most popular is greedy search. After taking a geometric view of this classical story, we will dive into the newest trends in causal discovery algorithms, which rely on a combination of observational and interventional data to learn a causal DAG. To understand the geometry and algebra of such causal models, we will broaden our perspective beyond DAGs to the family of staged trees. This new perspective will not only allow us to generalize and unify some previous results on the algebraic geometry of DAG models and staged trees, but it will also motivate a new family of context-specific causal models, called CStrees, that admit nice representation theorems analogous to those of DAGs. Time permitting, we will discuss the statistical theory of these new models, and see some applications to real data.