# Scalable Intervention Target Estimation in Linear Models

arXiv: https://arxiv.org/abs/2111.07512 · HTML: https://mlsanity.com/paper/2111.07512/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 28 references that are in the map.
- First posted on arXiv 15 Nov 2021.

## Builds on (most cited first, 9 of 9)

- [Differentiable Causal Discovery from Interventional Data](https://mlsanity.com/paper/2007.01754/) (2020)
- [Learning Neural Causal Models from Unknown Interventions](https://mlsanity.com/paper/1910.01075/) (2019)
- [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)
- [Learning linear structural equation models in polynomial time and sample complexity](https://mlsanity.com/paper/1707.04673/) (2017)
- [An Algorithm for Deciding if a Set of Observed Independencies Has a Causal Explanation](https://mlsanity.com/paper/1303.5435/) (2013)
- [Direct Estimation of Differences in Causal Graphs](https://mlsanity.com/paper/1802.05631/) (2018)
- [Differential Network Analysis via the Lasso Penalized D-Trace Loss](https://mlsanity.com/paper/1511.09188/) (2015)
- [A Direct Approach for Sparse Quadratic Discriminant Analysis](https://mlsanity.com/paper/1510.00084/) (2015)

## Built on by (most cited first, 10 of 10)

- [Learning Linear Causal Representations from Interventions under General Nonlinear Mixing](https://mlsanity.com/paper/2306.02235/) (2023)
- [Linear Causal Disentanglement via Interventions](https://mlsanity.com/paper/2211.16467/) (2022)
- [Causal Bandits for Linear Structural Equation Models](https://mlsanity.com/paper/2208.12764/) (2022)
- [The Landscape of Causal Discovery Data: Grounding Causal Discovery in Real-World Applications](https://mlsanity.com/paper/2412.01953/) (2024)
- [Learning Unknown Intervention Targets in Structural Causal Models from Heterogeneous Data](https://mlsanity.com/paper/2312.06091/) (2023)
- [iSCAN: Identifying Causal Mechanism Shifts among Nonlinear Additive Noise Models](https://mlsanity.com/paper/2306.17361/) (2023)
- [Root Cause Analysis of Outliers in Unknown Cyclic Graphs](https://mlsanity.com/paper/2510.06995/) (2025)
- [Test-Time Learning of Causal Structure from Interventional Data](https://mlsanity.com/paper/2602.19131/) (2026)
- [Privacy Amplification by Iteration for ADMM with (Strongly) Convex Objective Functions](https://mlsanity.com/paper/2312.08685/) (2023)
- [PRIM: Meta-Learned Bayesian Root Cause Analysis](https://mlsanity.com/paper/2605.08786/) (2026)

## Abstract (arXiv)

This paper considers the problem of estimating the unknown intervention targets in a causal directed acyclic graph from observational and interventional data. The focus is on soft interventions in linear structural equation models (SEMs). Current approaches to causal structure learning either work with known intervention targets or use hypothesis testing to discover the unknown intervention targets even for linear SEMs. This severely limits their scalability and sample complexity. This paper proposes a scalable and efficient algorithm that consistently identifies all intervention targets. The pivotal idea is to estimate the intervention sites from the difference between the precision matrices associated with the observational and interventional datasets. It involves repeatedly estimating such sites in different subsets of variables. The proposed algorithm can be used to also update a given observational Markov equivalence class into the interventional Markov equivalence class. Consistency, Markov equivalency, and sample complexity are established analytically. Finally, simulation results on both real and synthetic data demonstrate the gains of the proposed approach for scalable causal structure recovery. Implementation of the algorithm and the code to reproduce the simulation results are available at urlhttps://github.com/bvarici/intervention-estimation.