# When does the ID algorithm fail?

arXiv: https://arxiv.org/abs/2307.03750 · HTML: https://mlsanity.com/paper/2307.03750/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 13 references that are in the map.
- First posted on arXiv 7 Jul 2023.

## Builds on (most cited first, 5 of 5)

- [Nested Markov Properties for Acyclic Directed Mixed Graphs](https://mlsanity.com/paper/1701.06686/) (2017)
- [Margins of discrete Bayesian networks](https://mlsanity.com/paper/1501.02103/) (2015)
- [A Potential Outcomes Calculus for Identifying Conditional Path-Specific Effects](https://mlsanity.com/paper/1903.03662/) (2019)
- [The Proximal ID Algorithm](https://mlsanity.com/paper/2108.06818/) (2021)
- [Multivariate Counterfactual Systems And Causal Graphical Models](https://mlsanity.com/paper/2008.06017/) (2020)

## Built on by (most cited first, 7 of 7)

- [Identifying Macro Conditional Independencies and Macro Total Effects in Summary Causal Graphs with Latent Confounding](https://mlsanity.com/paper/2407.07934/) (2024)
- [Causal Effect Identification in LiNGAM Models with Latent Confounders](https://mlsanity.com/paper/2406.02049/) (2024)
- [Parameter identification in linear non-Gaussian causal models under general confounding](https://mlsanity.com/paper/2405.20856/) (2024)
- [Fast Proxy Experiment Design for Causal Effect Identification](https://mlsanity.com/paper/2407.05330/) (2024)
- [Complete Causal Identification from Ancestral Graphs under Selection Bias](https://mlsanity.com/paper/2603.26301/) (2026)
- [Symmetries and Causality: Causal Effect Identification Beyond IID Data](https://mlsanity.com/paper/2609.03697/) (2026)
- [Invariance of Clustering Operations in Causal Effect Identification](https://mlsanity.com/paper/2610.03101/) (2026)

## Abstract (arXiv)

The ID algorithm solves the problem of identification of interventional distributions of the form p(Y | do(a)) in graphical causal models, and has been formulated in a number of ways [12, 9, 6]. The ID algorithm is sound (outputs the correct functional of the observed data distribution whenever p(Y | do(a)) is identified in the causal model represented by the input graph), and complete (explicitly flags as a failure any input p(Y | do(a)) whenever this distribution is not identified in the causal model represented by the input graph). The reference [9] provides a result, the so called "hedge criterion" (Corollary 3), which aims to give a graphical characterization of situations when the ID algorithm fails to identify its input in terms of a structure in the input graph called the hedge. While the ID algorithm is, indeed, a sound and complete algorithm, and the hedge structure does arise whenever the input distribution is not identified, Corollary 3 presented in [9] is incorrect as stated. In this note, I outline the modern presentation of the ID algorithm, discuss a simple counterexample to Corollary 3, and provide a number of graphical characterizations of the ID algorithm failing to identify its input distribution.