Tuesday, 22 September, 11:15
Liam Solus
Combinatorics, Algebra, and Intervention
 The modern theory of causality is founded in our ability to encode both probabilistic and causal information about a data-generating distribution within the structure of a graph. Doing so in the proper way allows us to derive theorems which can be applied when developing data-driven causal structure learning algorithms, as well as probabilistic and causal inference. Such algorithms work best in the cases where the corresponding theorems point to nice combinatorial structure in the graph. Going deeper, if we also consider a parameterization of the joint distribution, we find that nice properties of the model can be attributed to nice properties of its defining algebraic variety in the ambient parameter space. Classic results of this nature are known for probabilistic graphical models. In this talk, we will see how such results generalize to interventional graphical models, which are now being used to learn causal structure from a mixture of observational and interventional data. Time permitting, we will explore how the proofs of these algebraic results give rise to new methods for modeling causation in context-specific settings.