# Efficient Identification in Linear Structural Causal Models with Instrumental Cutsets

arXiv: https://arxiv.org/abs/1910.13493 · HTML: https://mlsanity.com/paper/1910.13493/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Oct 2019.

## Built on by (most cited first, 6 of 6)

- [SBI: A Simulation-Based Test of Identifiability for Bayesian Causal Inference](https://mlsanity.com/paper/2102.11761/) (2021)
- [Identification in Tree-shaped Linear Structural Causal Models](https://mlsanity.com/paper/2203.01852/) (2022)
- [Identification for Tree-shaped Structural Causal Models in Polynomial Time](https://mlsanity.com/paper/2311.14058/) (2023)
- [On the Complexity of Identification in Linear Structural Causal Models](https://mlsanity.com/paper/2407.12528/) (2024)
- [Estimating Causal Effects in Gaussian Linear SCMs with Finite Data](https://mlsanity.com/paper/2601.04673/) (2026)
- [Efficient Symbolic Computations for Identifying Causal Effects](https://mlsanity.com/paper/2604.20516/) (2026)

## Abstract (arXiv)

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.