# Ancestral Instrument Method for Causal Inference without Complete Knowledge

arXiv: https://arxiv.org/abs/2201.03810 · HTML: https://mlsanity.com/paper/2201.03810/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 41 references that are in the map.
- First posted on arXiv 11 Jan 2022.

## Builds on (most cited first, 6 of 6)

- [Generalized Random Forests](https://mlsanity.com/paper/1610.01271/) (2016)
- [On the Testability of Causal Models with Latent and Instrumental Variables](https://mlsanity.com/paper/1302.4976/) (2013)
- [Instrumental Variables Estimation with Some Invalid Instruments and its Application to Mendelian Randomization](https://mlsanity.com/paper/1401.5755/) (2014)
- [Valid Causal Inference with (Some) Invalid Instruments](https://mlsanity.com/paper/2006.11386/) (2020)
- [Instrumental Variables: An Econometrician's Perspective](https://mlsanity.com/paper/1410.0163/) (2014)
- [Semi-Instrumental Variables: A Test for Instrument Admissibility](https://mlsanity.com/paper/1301.2261/) (2013)

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

- [Data-Driven Causal Effect Estimation Based on Graphical Causal Modelling: A Survey](https://mlsanity.com/paper/2208.09590/) (2022)
- [Instrumental Variables in Causal Inference and Machine Learning: A Survey](https://mlsanity.com/paper/2212.05778/) (2022)
- [Conditional Instrumental Variable Regression with Representation Learning for Causal Inference](https://mlsanity.com/paper/2310.01865/) (2023)
- [Discovering Ancestral Instrumental Variables for Causal Inference from Observational Data](https://mlsanity.com/paper/2206.01931/) (2022)
- [Disentangled Representation Learning for Causal Inference with Instruments](https://mlsanity.com/paper/2412.04641/) (2024)
- [Interaction-Data-guided Conditional Instrumental Variables for Debiasing Recommender Systems](https://mlsanity.com/paper/2408.09651/) (2024)

## Abstract (arXiv)

Unobserved confounding is the main obstacle to causal effect estimation from observational data. Instrumental variables (IVs) are widely used for causal effect estimation when there exist latent confounders. With the standard IV method, when a given IV is valid, unbiased estimation can be obtained, but the validity requirement on a standard IV is strict and untestable. Conditional IVs have been proposed to relax the requirement of standard IVs by conditioning on a set of observed variables (known as a conditioning set for a conditional IV). However, the criterion for finding a conditioning set for a conditional IV needs a directed acyclic graph (DAG) representing the causal relationships of both observed and unobserved variables. This makes it challenging to discover a conditioning set directly from data. In this paper, by leveraging maximal ancestral graphs (MAGs) for causal inference with latent variables, we study the graphical properties of ancestral IVs, a type of conditional IVs using MAGs, and develop the theory to support data-driven discovery of the conditioning set for a given ancestral IV in data under the pretreatment variable assumption. Based on the theory, we develop an algorithm for unbiased causal effect estimation with a given ancestral IV and observational data. Extensive experiments on synthetic and real-world datasets demonstrate the performance of the algorithm in comparison with existing IV methods.