Everything that can be learned about a causal structure with latent variables by observational and interventional probing schemes
Keywords: Marginalized DAGs (mDAGs), Interventions, Latent Variables
TL;DR: Two causal structures with latent variables can be distinguished from data obtained by performing observations and interventions if and only if they are associated with the same mDAG structure.
Abstract: When is it impossible to distinguish between two causal structures with latent variables from statistical data obtained by probing each visible variable? If we simply passively observe each visible variable, then it is well-known that many different causal structures can realize the same joint probability distributions. Even for the simplest case of two visible variables, for instance, one cannot distinguish between one variable being a causal parent of the other and the two variables being confounded by a latent common cause. However, it is possible to distinguish between these two causal structures if we have recourse to more powerful probing schemes, such as the possibility of intervening on one of the variables and observing the other.
Herein, we address the question of which causal structures remain indistinguishable even given the most informative types of probing schemes on the visible variables. We find that two causal structures remain indistinguishable if and only if they are both associated with the same mDAG structure (as defined in [Evans, 2016]). We also investigate to what extent one can weaken the probing schemes implemented on the visible variables, such as allowing only for do-interventions that can fix a variable to one of its possible values affects, and still have the same discrimination power as a maximally informative probing scheme.
Submission Number: 7
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