Causal Abstraction with Soft Interventions
This work addresses a theoretical gap in causal modeling for researchers in causality and AI, but it is incremental as it builds directly on prior definitions.
The paper tackles the limitation of causal abstraction theory to hard interventions by extending it to soft interventions, which assign non-constant functions to variables without new causal connections, and proves that the intervention map has a specific explicit form.
Causal abstraction provides a theory describing how several causal models can represent the same system at different levels of detail. Existing theoretical proposals limit the analysis of abstract models to "hard" interventions fixing causal variables to be constant values. In this work, we extend causal abstraction to "soft" interventions, which assign possibly non-constant functions to variables without adding new causal connections. Specifically, (i) we generalize $τ$-abstraction from Beckers and Halpern (2019) to soft interventions, (ii) we propose a further definition of soft abstraction to ensure a unique map $ω$ between soft interventions, and (iii) we prove that our constructive definition of soft abstraction guarantees the intervention map $ω$ has a specific and necessary explicit form.