# Disentangling Mixtures of Unknown Causal Interventions

arXiv: https://arxiv.org/abs/2210.03242 · HTML: https://mlsanity.com/paper/2210.03242/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 21 references that are in the map.
- First posted on arXiv 1 Oct 2022.

## Builds on (most cited first, 5 of 5)

- [Permutation-Based Causal Structure Learning with Unknown Intervention Targets](https://mlsanity.com/paper/1910.09007/) (2019)
- [backShift: Learning causal cyclic graphs from unknown shift interventions](https://mlsanity.com/paper/1506.02494/) (2015)
- [Causal Structure Discovery from Distributions Arising from Mixtures of DAGs](https://mlsanity.com/paper/2001.11940/) (2020)
- [Learning Mixtures of DAG Models](https://mlsanity.com/paper/1301.7415/) (2013)
- [Causal Discovery with a Mixture of DAGs](https://mlsanity.com/paper/1901.09475/) (2019)

## Built on by (most cited first, 6 of 6)

- [BISCUIT: Causal Representation Learning from Binary Interactions](https://mlsanity.com/paper/2306.09643/) (2023)
- [Curious Causality-Seeking Agents Learn Meta Causal World](https://mlsanity.com/paper/2506.23068/) (2025)
- [Interventional Causal Discovery in a Mixture of DAGs](https://mlsanity.com/paper/2406.08666/) (2024)
- [Causal Discovery under Off-Target Interventions](https://mlsanity.com/paper/2402.08229/) (2024)
- [Unsupervised Representation Learning from Sparse Transformation Analysis](https://mlsanity.com/paper/2410.05564/) (2024)
- [Learning Mixtures of Unknown Causal Interventions](https://mlsanity.com/paper/2411.00213/) (2024)

## Abstract (arXiv)

In many real-world scenarios, such as gene knockout experiments, targeted interventions are often accompanied by unknown interventions at off-target sites. Moreover, different units can get randomly exposed to different unknown interventions, thereby creating a mixture of interventions. Identifying different components of this mixture can be very valuable in some applications. Motivated by such situations, in this work, we study the problem of identifying all components present in a mixture of interventions on a given causal Bayesian Network. We construct an example to show that, in general, the components are not identifiable from the mixture distribution. Next, assuming that the given network satisfies a positivity condition, we show that, if the set of mixture components satisfy a mild exclusion assumption, then they can be uniquely identified. Our proof gives an efficient algorithm to recover these targets from the exponentially large search space of possible targets. In the more realistic scenario, where distributions are given via finitely many samples, we conduct a simulation study to analyze the performance of an algorithm derived from our identifiability proof.