You are all cordially invited to the AMLab seminar on Tuesday **September 19** at 16:00 in C3.163, where **Stephan Bongers** will give a talk titled “**Marginalization of Structural Causal Models with feedback**”. Afterwards there are the usual drinks and snacks!

**Abstract**: Structural causal models (SCMs), also known as non-parametric structural equation models (NP-SEMs), are widely used for causal modeling purposes. This talk consists of two parts: part one gives a rigorous treatment of structural causal models, dealing with measure-theoretic complications that arise in the presence of feedback, and part two deals with the marginalizion of SCMs. In part one we deal with recursive models (those without feedback), models where the solutions to the structural equations are unique, and arbitrary non-recursive models, those where the solutions are non-existent or non-unique. We show how we can reason about causality in these models and show how this differs from the recursive causal perspective. In part two, we address the question how we can marginalize an SCM (possibly with feedback), consisting of endogenous and exogenous variables, to a subset of the endogenous variables? Marginalizing an SCM projects the SCM down to an SCM on a subset of the endogenous variables, leading to a more parsimonious but causally equivalent representation of the SCM. We give an abstract defintion of marginalization and propose two approaches how to marginalize SCMs in a constructive way. Those constructive approaches define both a marginalization operation that effectively removes a subset of the endogenous variables from the model and lead to an SCM that has the same causal semantics as the original SCM. We provide several conditions under which the existence of such marginalizations hold.