# Efficient Identification of Direct Causal Parents via Invariance and Minimum Error Testing

arXiv: https://arxiv.org/abs/2409.12797 · HTML: https://mlsanity.com/paper/2409.12797/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 67 references that are in the map.
- First posted on arXiv 19 Sep 2024.

## Builds on (most cited first, 27 of 27)

- [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)
- [The Risks of Invariant Risk Minimization](https://mlsanity.com/paper/2010.05761/) (2020)
- [Causal Discovery with Continuous Additive Noise Models](https://mlsanity.com/paper/1309.6779/) (2013)
- [Differentiable Causal Discovery from Interventional Data](https://mlsanity.com/paper/2007.01754/) (2020)
- [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)
- [Domain Adaptation by Using Causal Inference to Predict Invariant Conditional Distributions](https://mlsanity.com/paper/1707.06422/) (2017)
- [Score matching enables causal discovery of nonlinear additive noise models](https://mlsanity.com/paper/2203.04413/) (2022)
- [Deep End-to-end Causal Inference](https://mlsanity.com/paper/2202.02195/) (2022)
- [Efficient Neural Causal Discovery without Acyclicity Constraints](https://mlsanity.com/paper/2107.10483/) (2021)
- [Permutation-based Causal Inference Algorithms with Interventions](https://mlsanity.com/paper/1705.10220/) (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)
- [Causal Discovery from Changes](https://mlsanity.com/paper/1301.2312/) (2013)
- [Active Invariant Causal Prediction: Experiment Selection through Stability](https://mlsanity.com/paper/2006.05690/) (2020)
- [Jointly interventional and observational data: estimation of interventional Markov equivalence classes of directed acyclic graphs](https://mlsanity.com/paper/1303.3216/) (2013)
- [Causal Feature Selection via Orthogonal Search](https://mlsanity.com/paper/2007.02938/) (2020)
- [Towards Efficient Local Causal Structure Learning](https://mlsanity.com/paper/2103.00378/) (2021)
- [Variance Minimization in the Wasserstein Space for Invariant Causal Prediction](https://mlsanity.com/paper/2110.07064/) (2021)
- [Invariant Ancestry Search](https://mlsanity.com/paper/2202.00913/) (2022)
- [Knockout: A simple way to handle missing inputs](https://mlsanity.com/paper/2405.20448/) (2024)
- [Robust Learning via Conditional Prevalence Adjustment](https://mlsanity.com/paper/2310.15766/) (2023)
- [Adapting to Shifting Correlations with Unlabeled Data Calibration](https://mlsanity.com/paper/2409.05996/) (2024)

## Abstract (arXiv)

Invariant causal prediction (ICP) is a popular technique for finding causal parents (direct causes) of a target via exploiting distribution shifts and invariance testing (Peters et al., 2016). However, since ICP needs to run an exponential number of tests and fails to identify parents when distribution shifts only affect a few variables, applying ICP to practical large scale problems is challenging. We propose MMSE-ICP and fastICP, two approaches which employ an error inequality to address the identifiability problem of ICP. The inequality states that the minimum prediction error of the predictor using causal parents is the smallest among all predictors which do not use descendants. fastICP is an efficient approximation tailored for large problems as it exploits the inequality and a heuristic to run fewer tests. MMSE-ICP and fastICP not only outperform competitive baselines in many simulations but also achieve state-of-the-art result on a large scale real data benchmark.