# Cross-validating causal discovery via Leave-One-Variable-Out

arXiv: https://arxiv.org/abs/2411.05625 · HTML: https://mlsanity.com/paper/2411.05625/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 50 references that are in the map.
- First posted on arXiv 8 Nov 2024.

## Builds on (most cited first, 19 of 19)

- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [Gradient-Based Neural DAG Learning](https://mlsanity.com/paper/1906.02226/) (2019)
- [Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Game](https://mlsanity.com/paper/2102.13647/) (2021)
- [Anchor regression: heterogeneous data meets causality](https://mlsanity.com/paper/1801.06229/) (2018)
- [Score matching enables causal discovery of nonlinear additive noise models](https://mlsanity.com/paper/2203.04413/) (2022)
- [Identifiability Guarantees for Causal Disentanglement from Soft Interventions](https://mlsanity.com/paper/2307.06250/) (2023)
- [Graphical Models for Processing Missing Data](https://mlsanity.com/paper/1801.03583/) (2018)
- [Causal Discovery from Changes](https://mlsanity.com/paper/1301.2312/) (2013)
- [Scalable Causal Discovery with Score Matching](https://mlsanity.com/paper/2304.03382/) (2023)
- [Learning Linear Non-Gaussian Causal Models in the Presence of Latent Variables](https://mlsanity.com/paper/1908.03932/) (2019)
- [Entropic Causal Inference](https://mlsanity.com/paper/1611.04035/) (2016)
- [Causal Inference Through the Structural Causal Marginal Problem](https://mlsanity.com/paper/2202.01300/) (2022)
- [Self-Compatibility: Evaluating Causal Discovery without Ground Truth](https://mlsanity.com/paper/2307.09552/) (2023)
- [Causal discovery in heavy-tailed models](https://mlsanity.com/paper/1908.05097/) (2019)
- [Deep Learning of Causal Structures in High Dimensions](https://mlsanity.com/paper/2212.04866/) (2022)
- [Integrating overlapping datasets using bivariate causal discovery](https://mlsanity.com/paper/1910.11356/) (2019)
- [Obtaining Causal Information by Merging Datasets with MAXENT](https://mlsanity.com/paper/2107.07640/) (2021)
- [Causal Discovery of Linear Non-Gaussian Causal Models with Unobserved Confounding](https://mlsanity.com/paper/2408.04907/) (2024)
- [Out-of-Variable Generalization for Discriminative Models](https://mlsanity.com/paper/2304.07896/) (2023)

## Built on by (most cited first, 3 of 3)

- [On Different Notions of Redundancy in Conditional-Independence-Based Discovery of Graphical Models](https://mlsanity.com/paper/2502.08531/) (2025)
- [TCD-Arena: Assessing Robustness of Time Series Causal Discovery Methods Against Assumption Violations](https://mlsanity.com/paper/2605.03045/) (2026)
- [Falsifying Causal Graphs With Outlier Events](https://mlsanity.com/paper/2607.12145/) (2026)

## Abstract (arXiv)

We propose a new approach to falsify causal discovery algorithms without ground truth, which is based on testing the causal model on a variable pair excluded during learning the causal model. Specifically, given data on X, Y, boldsymbolZ=X, Y, Z1,dots,Zk, we apply the causal discovery algorithm separately to the 'leave-one-out' data sets X, boldsymbolZ and Y, boldsymbolZ. We demonstrate that the two resulting causal models, in the form DAGs, ADMGs, CPDAGs or PAGs, often entail conclusions on the dependencies between X and Y and allow to estimate mathbbE(Ymid X=x) without any joint observations of X and Y, given only the leave-one-out datasets. This estimation is called "Leave-One-Variable-Out (LOVO)" prediction. Its error can be estimated since the joint distribution P(X, Y) is available, and X and Y have only been omitted for the purpose of falsification. We present two variants of LOVO prediction: One graphical method, which is applicable to general causal discovery algorithms, and one version tailored towards algorithms relying on specific a priori assumptions, such as linear additive noise models. Simulations indicate that the LOVO prediction error is indeed correlated with the accuracy of the causal outputs, affirming the method's effectiveness.