Causal Abstraction with Soft InterventionsDownload PDF

Published: 17 Mar 2023, Last Modified: 19 May 2023CLeaR 2023 OralReaders: Everyone
Keywords: Causal Abstraction, Soft Interventions, Structural Causal Models
Abstract: 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 $\tau$-abstraction from Beckers and Halpern (2019) to soft interventions, (ii) we propose a further definition of soft abstraction to ensure a unique map $\omega$ between soft interventions, and (iii) we prove that our constructive definition of soft abstraction guarantees the intervention map $\omega$ has a specific and necessary explicit form.
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