# Linear Causal Discovery with Interventional Constraints

arXiv: https://arxiv.org/abs/2510.26342 · HTML: https://mlsanity.com/paper/2510.26342/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 32 of its 85 references that are in the map.
- First posted on arXiv 30 Oct 2025.

## Builds on (most cited first, 30 of 32)

- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [DAG-GNN: DAG Structure Learning with Graph Neural Networks](https://mlsanity.com/paper/1904.10098/) (2019)
- [Direct and Indirect Effects](https://mlsanity.com/paper/1301.2300/) (2013)
- [Gradient-Based Neural DAG Learning](https://mlsanity.com/paper/1906.02226/) (2019)
- [Differentiable Causal Discovery from Interventional Data](https://mlsanity.com/paper/2007.01754/) (2020)
- [D'ya like DAGs? A Survey on Structure Learning and Causal Discovery](https://mlsanity.com/paper/2103.02582/) (2021)
- [CAM: Causal additive models, high-dimensional order search and penalized regression](https://mlsanity.com/paper/1310.1533/) (2013)
- [Causal Inference and Causal Explanation with Background Knowledge](https://mlsanity.com/paper/1302.4972/) (2013)
- [Foundations of Structural Causal Models with Cycles and Latent Variables](https://mlsanity.com/paper/1611.06221/) (2016)
- [Score matching enables causal discovery of nonlinear additive noise models](https://mlsanity.com/paper/2203.04413/) (2022)
- [The Causal-Neural Connection: Expressiveness, Learnability, and Inference](https://mlsanity.com/paper/2107.00793/) (2021)
- [Deep End-to-end Causal Inference](https://mlsanity.com/paper/2202.02195/) (2022)
- [A survey of Bayesian Network structure learning](https://mlsanity.com/paper/2109.11415/) (2021)
- [Efficient Neural Causal Discovery without Acyclicity Constraints](https://mlsanity.com/paper/2107.10483/) (2021)
- [Causal machine learning for predicting treatment outcomes](https://mlsanity.com/paper/2410.08770/) (2024)
- [Causal Machine Learning for Healthcare and Precision Medicine](https://mlsanity.com/paper/2205.11402/) (2022)
- [Theoretical Impediments to Machine Learning With Seven Sparks from the Causal Revolution](https://mlsanity.com/paper/1801.04016/) (2018)
- [Diffusion Models for Causal Discovery via Topological Ordering](https://mlsanity.com/paper/2210.06201/) (2022)
- [Causal Discovery with Language Models as Imperfect Experts](https://mlsanity.com/paper/2307.02390/) (2023)
- [Differentiable Causal Discovery Under Unmeasured Confounding](https://mlsanity.com/paper/2010.06978/) (2020)
- [Scale-free networks are rare](https://mlsanity.com/paper/1801.03400/) (2018)
- [The impact of prior knowledge on causal structure learning](https://mlsanity.com/paper/2102.00473/) (2021)
- [NTS-NOTEARS: Learning Nonparametric DBNs With Prior Knowledge](https://mlsanity.com/paper/2109.04286/) (2021)
- [Integrating Large Language Models in Causal Discovery: A Statistical Causal Approach](https://mlsanity.com/paper/2402.01454/) (2024)
- [Cyclic Causal Discovery from Continuous Equilibrium Data](https://mlsanity.com/paper/1309.6849/) (2013)
- [The Landscape of Causal Discovery Data: Grounding Causal Discovery in Real-World Applications](https://mlsanity.com/paper/2412.01953/) (2024)
- [Sample Complexity Bounds for Score-Matching: Causal Discovery and Generative Modeling](https://mlsanity.com/paper/2310.18123/) (2023)
- [Active causal structure learning with advice](https://mlsanity.com/paper/2305.19588/) (2023)
- [Local Causal Discovery with Linear non-Gaussian Cyclic Models](https://mlsanity.com/paper/2403.14843/) (2024)
- [Efficient least squares for estimating total effects under linearity and causal sufficiency](https://mlsanity.com/paper/2008.03481/) (2020)

## Abstract (arXiv)

Incorporating causal knowledge and mechanisms is essential for refining causal models and improving downstream tasks such as designing new treatments. In this paper, we introduce a novel concept in causal discovery, termed interventional constraints, which differs fundamentally from interventional data. While interventional data require direct perturbations of variables, interventional constraints encode high-level causal knowledge in the form of inequality constraints on causal effects. For instance, in the Sachs dataset (Sachs et al. 2005), Akt has been shown to be activated by PIP3, meaning PIP3 exerts a positive causal effect on Akt. Existing causal discovery methods allow enforcing structural constraints (for example, requiring a causal path from PIP3 to Akt), but they may still produce incorrect causal conclusions such as learning that "PIP3 inhibits Akt". Interventional constraints bridge this gap by explicitly constraining the total causal effect between variable pairs, ensuring learned models respect known causal influences. To formalize interventional constraints, we propose a metric to quantify total causal effects for linear causal models and formulate the problem as a constrained optimization task, solved using a two-stage constrained optimization method. We evaluate our approach on real-world datasets and demonstrate that integrating interventional constraints not only improves model accuracy and ensures consistency with established findings, making models more explainable, but also facilitates the discovery of new causal relationships that would otherwise be costly to identify.