# Learning Unknown Intervention Targets in Structural Causal Models from Heterogeneous Data

arXiv: https://arxiv.org/abs/2312.06091 · HTML: https://mlsanity.com/paper/2312.06091/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 52 references that are in the map.
- First posted on arXiv 11 Dec 2023.

## Builds on (most cited first, 15 of 15)

- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learning](https://mlsanity.com/paper/1805.08651/) (2018)
- [Unsupervised Feature Extraction by Time-Contrastive Learning and Nonlinear ICA](https://mlsanity.com/paper/1605.06336/) (2016)
- [Differentiable Causal Discovery from Interventional Data](https://mlsanity.com/paper/2007.01754/) (2020)
- [Disentanglement by Nonlinear ICA with General Incompressible-flow Networks (GIN)](https://mlsanity.com/paper/2001.04872/) (2020)
- [Identifiability of deep generative models without auxiliary information](https://mlsanity.com/paper/2206.10044/) (2022)
- [Permutation-Based Causal Structure Learning with Unknown Intervention Targets](https://mlsanity.com/paper/1910.09007/) (2019)
- [Causal structure based root cause analysis of outliers](https://mlsanity.com/paper/1912.02724/) (2019)
- [Causal Discovery in Heterogeneous Environments Under the Sparse Mechanism Shift Hypothesis](https://mlsanity.com/paper/2206.02013/) (2022)
- [Few-shot Domain Adaptation by Causal Mechanism Transfer](https://mlsanity.com/paper/2002.03497/) (2020)
- [Learning Causal Structures Using Regression Invariance](https://mlsanity.com/paper/1705.09644/) (2017)
- [On the Logic of Causal Models](https://mlsanity.com/paper/1304.2355/) (2013)
- [Scalable Intervention Target Estimation in Linear Models](https://mlsanity.com/paper/2111.07512/) (2021)
- [Causal Discovery in Linear Latent Variable Models Subject to Measurement Error](https://mlsanity.com/paper/2211.03984/) (2022)
- [Causal Discovery in Linear Structural Causal Models with Deterministic Relations](https://mlsanity.com/paper/2111.00341/) (2021)

## Built on by (most cited first, 7 of 7)

- [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)
- [Identifying biological perturbation targets through causal differential networks](https://mlsanity.com/paper/2410.03380/) (2024)
- [PRIM: Meta-Learned Bayesian Root Cause Analysis](https://mlsanity.com/paper/2605.08786/) (2026)
- [SCOUT: Cyclic Causal Discovery Under Soft Interventions with Unknown Targets](https://mlsanity.com/paper/2605.16620/) (2026)
- [Amortized Bayesian Causal Discovery of Extended Factor Graphs](https://mlsanity.com/paper/2607.22934/) (2026)
- [Beyond Conditional Independence: Root Cause Analysis with Deep Causal Models](https://mlsanity.com/paper/2609.36771/) (2026)

## Abstract (arXiv)

We study the problem of identifying the unknown intervention targets in structural causal models where we have access to heterogeneous data collected from multiple environments. The unknown intervention targets are the set of endogenous variables whose corresponding exogenous noises change across the environments. We propose a two-phase approach which in the first phase recovers the exogenous noises corresponding to unknown intervention targets whose distributions have changed across environments. In the second phase, the recovered noises are matched with the corresponding endogenous variables. For the recovery phase, we provide sufficient conditions for learning these exogenous noises up to some component-wise invertible transformation. For the matching phase, under the causal sufficiency assumption, we show that the proposed method uniquely identifies the intervention targets. In the presence of latent confounders, the intervention targets among the observed variables cannot be determined uniquely. We provide a candidate intervention target set which is a superset of the true intervention targets. Our approach improves upon the state of the art as the returned candidate set is always a subset of the target set returned by previous work. Moreover, we do not require restrictive assumptions such as linearity of the causal model or performing invariance tests to learn whether a distribution is changing across environments which could be highly sample inefficient. Our experimental results show the effectiveness of our proposed algorithm in practice.