You are all cordially invited to the AMLab colloquium coming Tuesday May 10 at 16:00 in C3.163, where Stephan Bongers will give a talk titled “Marginalization and Reduction of Structural Causal Models”. Afterwards there are drinks and snacks!
Abstract: Structural Causal Models (SCMs), also known as (Non-Parametric) Structural Equation Models (NP-SEMs), are widely used for causal modelling purposes. One of their advantages is that they allow for cycles, i.e., causal feedback loops. In this work, we give a rigorous treatment of Structural Causal Models. Two different types of variables play a role in SCMs: “endogenous” variables and “exogenous” variables (also known as “disturbance terms” or “noise” variables). We define a marginalization operation (“latent projection”) on SCMs that effectively removes a subset of the endogenous variables from the model. This operation can be seen as projecting the description of a full system to the description of a subsystem. We show
that this operation preserves the causal semantics. We also show that in the linear case, the number of exogenous variables can be reduced so that only a single one-dimensional disturbance term is needed for each endogenous variable. This “reduction” can reduce the model complexity significantly and offers parsimonious representations for the linear case. We show under some suitable conditions this reduction is not possible in general.