# Invariant Ancestry Search

arXiv: https://arxiv.org/abs/2202.00913 · HTML: https://mlsanity.com/paper/2202.00913/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 52 references that are in the map.
- First posted on arXiv 2 Feb 2022.

## Builds on (most cited first, 18 of 18)

- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [Causal Discovery with Continuous Additive Noise Models](https://mlsanity.com/paper/1309.6779/) (2013)
- [Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Game](https://mlsanity.com/paper/2102.13647/) (2021)
- [Invariant Causal Prediction for Nonlinear Models](https://mlsanity.com/paper/1706.08576/) (2017)
- [Foundations of Structural Causal Models with Cycles and Latent Variables](https://mlsanity.com/paper/1611.06221/) (2016)
- [Domain Adaptation by Using Causal Inference to Predict Invariant Conditional Distributions](https://mlsanity.com/paper/1707.06422/) (2017)
- [Permutation-Based Causal Structure Learning with Unknown Intervention Targets](https://mlsanity.com/paper/1910.09007/) (2019)
- [A causal framework for distribution generalization](https://mlsanity.com/paper/2006.07433/) (2020)
- [Theoretical Impediments to Machine Learning With Seven Sparks from the Causal Revolution](https://mlsanity.com/paper/1801.04016/) (2018)
- [Invariant Causal Prediction for Sequential Data](https://mlsanity.com/paper/1706.08058/) (2017)
- [Active Invariant Causal Prediction: Experiment Selection through Stability](https://mlsanity.com/paper/2006.05690/) (2020)
- [Separators and Adjustment Sets in Causal Graphs: Complete Criteria and an Algorithmic Framework](https://mlsanity.com/paper/1803.00116/) (2018)
- [Statistical Testing under Distributional Shifts](https://mlsanity.com/paper/2105.10821/) (2021)
- [An Algorithm for Finding Minimum d-Separating Sets in Belief Networks](https://mlsanity.com/paper/1302.3549/) (2013)
- [Variance Minimization in the Wasserstein Space for Invariant Causal Prediction](https://mlsanity.com/paper/2110.07064/) (2021)
- [On the Number of Minimal Separators in Graphs](https://mlsanity.com/paper/1503.01203/) (2015)

## Built on by (most cited first, 5 of 5)

- [A Scale-Invariant Sorting Criterion to Find a Causal Order in Additive Noise Models](https://mlsanity.com/paper/2303.18211/) (2023)
- [Causal Discovery using Model Invariance through Knockoff Interventions](https://mlsanity.com/paper/2207.04055/) (2022)
- [Model-based causal feature selection for general response types](https://mlsanity.com/paper/2309.12833/) (2023)
- [Maximum Risk Minimization with Random Forests](https://mlsanity.com/paper/2512.10445/) (2025)
- [Efficient Identification of Direct Causal Parents via Invariance and Minimum Error Testing](https://mlsanity.com/paper/2409.12797/) (2024)

## Abstract (arXiv)

Recently, methods have been proposed that exploit the invariance of prediction models with respect to changing environments to infer subsets of the causal parents of a response variable. If the environments influence only few of the underlying mechanisms, the subset identified by invariant causal prediction (ICP), for example, may be small, or even empty. We introduce the concept of minimal invariance and propose invariant ancestry search (IAS). In its population version, IAS outputs a set which contains only ancestors of the response and is a superset of the output of ICP. When applied to data, corresponding guarantees hold asymptotically if the underlying test for invariance has asymptotic level and power. We develop scalable algorithms and perform experiments on simulated and real data.