Relational Causal Models with Cycles:Representation and Reasoning
This work addresses a foundational gap in causal inference for social phenomena by enabling cycles in relational models, which is incremental as it builds on prior lifted representations but removes the no-cycles restriction.
The paper tackles the problem of causal reasoning in relational domains with feedback loops by introducing relational σ-separation and σ-abstract ground graphs, showing that these provide sound and complete conditions for handling cycles of arbitrary length.
Causal reasoning in relational domains is fundamental to studying real-world social phenomena in which individual units can influence each other's traits and behavior. Dynamics between interconnected units can be represented as an instantiation of a relational causal model; however, causal reasoning over such instantiation requires additional templating assumptions that capture feedback loops of influence. Previous research has developed lifted representations to address the relational nature of such dynamics but has strictly required that the representation has no cycles. To facilitate cycles in relational representation and learning, we introduce relational $σ$-separation, a new criterion for understanding relational systems with feedback loops. We also introduce a new lifted representation, $σ$-abstract ground graph which helps with abstracting statistical independence relations in all possible instantiations of the cyclic relational model. We show the necessary and sufficient conditions for the completeness of $σ$-AGG and that relational $σ$-separation is sound and complete in the presence of one or more cycles with arbitrary length. To the best of our knowledge, this is the first work on representation of and reasoning with cyclic relational causal models.