Efficient Identification in Linear Structural Causal Models with Instrumental Cutsets

TL;DR

This paper introduces efficient graphical criteria and algorithms for identifying causal effects in linear structural causal models, focusing on instrumental cutsets to improve computational efficiency and effectiveness over existing methods.

Contribution

It develops a new criterion called Instrumental Cutsets (IC) for efficient causal effect identification and analyzes the complexity of existing methods like TSID.

Findings

Efficient algorithms for unconditioned instrumental subsets.

Proved NP-Completeness of TSID-based identification.

Instrumental Cutsets outperform existing polynomial-time algorithms.

Abstract

One of the most common mistakes made when performing data analysis is attributing causal meaning to regression coefficients. Formally, a causal effect can only be computed if it is identifiable from a combination of observational data and structural knowledge about the domain under investigation (Pearl, 2000, Ch. 5). Building on the literature of instrumental variables (IVs), a plethora of methods has been developed to identify causal effects in linear systems. Almost invariably, however, the most powerful such methods rely on exponential-time procedures. In this paper, we investigate graphical conditions to allow efficient identification in arbitrary linear structural causal models (SCMs). In particular, we develop a method to efficiently find unconditioned instrumental subsets, which are generalizations of IVs that can be used to tame the complexity of many canonical algorithms found in the literature. Further, we prove that determining whether an effect can be identified with TSID (Weihs et al., 2017), a method more powerful than unconditioned instrumental sets and other efficient identification algorithms, is NP-Complete. Finally, building on the idea of flow constraints, we introduce a new and efficient criterion called Instrumental Cutsets (IC), which is able to solve for parameters missed by all other existing polynomial-time algorithms.