Efficient Identification in Linear Structural Causal Models with Instrumental Cutsets

Daniel Kumor, Bryant Chen, Elias Bareinboim

Abstract: One of the most common mistakes made by the current generation of data scientists is attributing causal meaning to regression coefficients. Formally, a causal interpretation can only be attached to a coefficient if the corresponding effect is identifiable from the observational data. Building on the literature of instrumental variables (IVs), a plethora of methods were developed to identify causal effects in the context of linear causality (Pearl, 2000, Ch. 5). However, almost invariably, the most powerful such methods suffer from computational deficiencies (requiring exponential time). In this paper, we investigate graphical conditions to allow efficient identification in arbitrary structural causal models (SCMs). Specifically, we develop a new method to efficiently find instrumental subsets, which are generalizations of IVs, and we then show how this method can be applied to tame the computational complexity of many algorithms in the field. Further, we prove that determining whether an effect can be identified with TSID (Weihs et. al. 2017), a method more powerful than instrumental sets and other efficient identification methods, is NP-Complete, making it impractical to use in any setting of reasonable size. Finally, building on flow constraints, we introduce a new procedure called Instrumental Cutsets (IC), which is able to solve for parameters missed by all other polynomial procedures available in the literature.

Code Link: https://github.com/dkumor/instrumental-cutsets

CMT Num: 6781