Towards Clarifying the Theory of the Deconfounder
It resolves theoretical ambiguities for researchers in causal inference, but is incremental as it builds on prior work.
This paper clarifies the theoretical requirements of the deconfounder algorithm for multiple causal inference, addressing refinements and counterexamples by showing that proposed counterexamples do not meet the necessary assumptions.
Wang and Blei (2019) studies multiple causal inference and proposes the deconfounder algorithm. The paper discusses theoretical requirements and presents empirical studies. Several refinements have been suggested around the theory of the deconfounder. Among these, Imai and Jiang clarified the assumption of "no unobserved single-cause confounders." Using their assumption, this paper clarifies the theory. Furthermore, Ogburn et al. (2020) proposes counterexamples to the theory. But the proposed counterexamples do not satisfy the required assumptions.