# The Proximal ID Algorithm

arXiv: https://arxiv.org/abs/2108.06818 · HTML: https://mlsanity.com/paper/2108.06818/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 49 references that are in the map.
- First posted on arXiv 15 Aug 2021.

## Builds on (most cited first, 10 of 10)

- [Identifying Causal Effects With Proxy Variables of an Unmeasured Confounder](https://mlsanity.com/paper/1609.08816/) (2016)
- [An Introduction to Proximal Causal Learning](https://mlsanity.com/paper/2009.10982/) (2020)
- [Semiparametric proximal causal inference](https://mlsanity.com/paper/2011.08411/) (2020)
- [Causal Inference Under Unmeasured Confounding With Negative Controls: A Minimax Learning Approach](https://mlsanity.com/paper/2103.14029/) (2021)
- [Nested Markov Properties for Acyclic Directed Mixed Graphs](https://mlsanity.com/paper/1701.06686/) (2017)
- [A confounding bridge approach for double negative control inference on causal effects](https://mlsanity.com/paper/1808.04945/) (2018)
- [The Case for Evaluating Causal Models Using Interventional Measures and Empirical Data](https://mlsanity.com/paper/1910.05387/) (2019)
- [Kernel Methods for Unobserved Confounding: Negative Controls, Proxies, and Instruments](https://mlsanity.com/paper/2012.10315/) (2020)
- [A Potential Outcomes Calculus for Identifying Conditional Path-Specific Effects](https://mlsanity.com/paper/1903.03662/) (2019)
- [Multivariate Counterfactual Systems And Causal Graphical Models](https://mlsanity.com/paper/2008.06017/) (2020)

## Built on by (most cited first, 11 of 11)

- [Causal Structure Learning: a Combinatorial Perspective](https://mlsanity.com/paper/2206.01152/) (2022)
- [Partial Identification with Noisy Covariates: A Robust Optimization Approach](https://mlsanity.com/paper/2202.10665/) (2022)
- [Proximal Causal Learning of Conditional Average Treatment Effects](https://mlsanity.com/paper/2301.10913/) (2023)
- [Partial Identification of Causal Effects Using Proxy Variables](https://mlsanity.com/paper/2304.04374/) (2023)
- [When does the ID algorithm fail?](https://mlsanity.com/paper/2307.03750/) (2023)
- [Causal Inference with Hidden Mediators](https://mlsanity.com/paper/2111.02927/) (2021)
- [Optimal Treatment Regimes for Proximal Causal Learning](https://mlsanity.com/paper/2212.09494/) (2022)
- [Non-parametric identifiability and sensitivity analysis of synthetic control models](https://mlsanity.com/paper/2301.07656/) (2023)
- [Spillover Detection for Donor Selection in Synthetic Control Models](https://mlsanity.com/paper/2406.11399/) (2024)
- [Assumption-lean falsification tests of rate double-robustness of double-machine-learning estimators](https://mlsanity.com/paper/2306.10590/) (2023)
- [Automating the Selection of Proxy Variables of Unmeasured Confounders](https://mlsanity.com/paper/2405.16130/) (2024)

## Abstract (arXiv)

Unobserved confounding is a fundamental obstacle to establishing valid causal conclusions from observational data. Two complementary types of approaches have been developed to address this obstacle: obtaining identification using fortuitous external aids, such as instrumental variables or proxies, or by means of the ID algorithm, using Markov restrictions on the full data distribution encoded in graphical causal models. In this paper we aim to develop a synthesis of the former and latter approaches to identification in causal inference to yield the most general identification algorithm in multivariate systems currently known -- the proximal ID algorithm. In addition to being able to obtain nonparametric identification in all cases where the ID algorithm succeeds, our approach allows us to systematically exploit proxies to adjust for the presence of unobserved confounders that would have otherwise prevented identification. In addition, we outline a class of estimation strategies for causal parameters identified by our method in an important special case. We illustrate our approach by simulation studies and a data application.