# Structural restrictions in local causal discovery: identifying direct causes of a target variable

arXiv: https://arxiv.org/abs/2307.16048 · HTML: https://mlsanity.com/paper/2307.16048/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 79 references that are in the map.
- First posted on arXiv 29 Jul 2023.

## Builds on (most cited first, 22 of 22)

- [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)
- [Detecting causal associations in large nonlinear time series datasets](https://mlsanity.com/paper/1702.07007/) (2017)
- [Causal Inference and Causal Explanation with Background Knowledge](https://mlsanity.com/paper/1302.4972/) (2013)
- [Invariant Causal Prediction for Nonlinear Models](https://mlsanity.com/paper/1706.08576/) (2017)
- [Anchor regression: heterogeneous data meets causality](https://mlsanity.com/paper/1801.06229/) (2018)
- [Causal Autoregressive Flows](https://mlsanity.com/paper/2011.02268/) (2020)
- [Invariant Causal Prediction for Sequential Data](https://mlsanity.com/paper/1706.08058/) (2017)
- [On Causal Discovery with Equal Variance Assumption](https://mlsanity.com/paper/1807.03419/) (2018)
- [On the Identifiability and Estimation of Causal Location-Scale Noise Models](https://mlsanity.com/paper/2210.09054/) (2022)
- [Kernel-based Tests for Joint Independence](https://mlsanity.com/paper/1603.00285/) (2016)
- [Identifying Patient-Specific Root Causes with the Heteroscedastic Noise Model](https://mlsanity.com/paper/2205.13085/) (2022)
- [Telling Cause from Effect using MDL-based Local and Global Regression](https://mlsanity.com/paper/1709.08915/) (2017)
- [Learning Quadratic Variance Function (QVF) DAG models via OverDispersion Scoring (ODS)](https://mlsanity.com/paper/1704.08783/) (2017)
- [Instrumental Variables: An Econometrician's Perspective](https://mlsanity.com/paper/1410.0163/) (2014)
- [On the Equivalence of Causal Models](https://mlsanity.com/paper/1304.1108/) (2013)
- [Efficient Bayesian network structure learning via local Markov boundary search](https://mlsanity.com/paper/2110.06082/) (2021)
- [Nonlinear Causal Discovery with Confounders](https://mlsanity.com/paper/2302.03178/) (2023)
- [Score-based Causal Learning in Additive Noise Models](https://mlsanity.com/paper/1311.6359/) (2013)
- [Cause-Effect Inference in Location-Scale Noise Models: Maximum Likelihood vs. Independence Testing](https://mlsanity.com/paper/2301.12930/) (2023)
- [A Critical View of the Structural Causal Model](https://mlsanity.com/paper/2002.10007/) (2020)
- [Identifiability of causal graphs under nonadditive conditionally parametric causal models](https://mlsanity.com/paper/2303.15376/) (2023)

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

- [CLEAR: Calibrated Learning for Epistemic and Aleatoric Risk](https://mlsanity.com/paper/2507.08150/) (2025)
- [Local Causal Discovery with Background Knowledge](https://mlsanity.com/paper/2408.07890/) (2024)
- [Cross-World Assumption and Refining Prediction Intervals for Individual Treatment Effects](https://mlsanity.com/paper/2507.12581/) (2025)
- [Retrospective Counterfactual Prediction by Conditioning on the Factual Outcome: A Cross-World Approach](https://mlsanity.com/paper/2603.27320/) (2026)
- [On the Identifiability of Mixed Ordinal and Exponential Family Causal DAGs under Linear Parametric Models](https://mlsanity.com/paper/2609.17942/) (2026)

## Abstract (arXiv)

We consider the problem of learning a set of direct causes of a target variable from an observational joint distribution. Learning directed acyclic graphs (DAGs) that represent the causal structure is a fundamental problem in science. Several results are known when the full DAG is identifiable from the distribution, such as assuming a nonlinear Gaussian data-generating process. Here, we are only interested in identifying the direct causes of one target variable (local causal structure), not the full DAG. This allows us to relax the identifiability assumptions and develop possibly faster and more robust algorithms. In contrast to the Invariance Causal Prediction framework, we only assume that we observe one environment without any interventions. We discuss different assumptions for the data-generating process of the target variable under which the set of direct causes is identifiable from the distribution. While doing so, we put essentially no assumptions on the variables other than the target variable. In addition to the novel identifiability results, we provide two practical algorithms for estimating the direct causes from a finite random sample and demonstrate their effectiveness on several benchmark and real datasets.