Niels Richard Hansen: Cyclic graphical models and causal learning

- Speaker: Niels Richard Hansen (University of Copenhagen) - Title: Cyclic graphical models and causal learning - Discussant: Patrick Forré (University of Amsterdam) - Abstract: Directed Graphs (DGs) can be used both formally and informally to represent and communicate causal relations. The formal mathematical theory is particularly well developed for Directed Acyclic Graphs (DAGs) to support structural causal models, do-calculus, identification theory and causal learning. It is natural to interpret DGs with cycles as allowing for feedback mechanisms, but this can be formalized by different incompatible mathematical theories. In the first part of the talk I will survey two competing theories: equilibrium models and dynamic models. In the second part of the talk I will focus on so-called local independence models induced by dynamic models, and their graphical representation via DGs and Directed Mixed Graphs (DMGs). I will show how equivalence classes of DMGs can be represented in terms of maximal elements, which, in turn, can be learned from data via conditional local independence testing. The theory will be illustrated by an application to neuron spike data for multiple neurons.