# Differentiable Causal Discovery Under Latent Interventions

arXiv: https://arxiv.org/abs/2203.02336 · HTML: https://mlsanity.com/paper/2203.02336/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 49 references that are in the map.
- First posted on arXiv 4 Mar 2022.

## Builds on (most cited first, 25 of 25)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Semi-Supervised Learning with Deep Generative Models](https://mlsanity.com/paper/1406.5298/) (2014)
- [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)
- [Neural Autoregressive Flows](https://mlsanity.com/paper/1804.00779/) (2018)
- [Learning Sparse Nonparametric DAGs](https://mlsanity.com/paper/1909.13189/) (2019)
- [Learning Bayesian Networks: The Combination of Knowledge and Statistical Data](https://mlsanity.com/paper/1302.6815/) (2013)
- [CAM: Causal additive models, high-dimensional order search and penalized regression](https://mlsanity.com/paper/1310.1533/) (2013)
- [Causal Inference in the Presence of Latent Variables and Selection Bias](https://mlsanity.com/paper/1302.4983/) (2013)
- [Learning Neural Causal Models from Unknown Interventions](https://mlsanity.com/paper/1910.01075/) (2019)
- [Masked Gradient-Based Causal Structure Learning](https://mlsanity.com/paper/1910.08527/) (2019)
- [Permutation-based Causal Inference Algorithms with Interventions](https://mlsanity.com/paper/1705.10220/) (2017)
- [Learning Sparse Causal Models is not NP-hard](https://mlsanity.com/paper/1309.6824/) (2013)
- [Structural Agnostic Modeling: Adversarial Learning of Causal Graphs](https://mlsanity.com/paper/1803.04929/) (2018)
- [Stick-Breaking Variational Autoencoders](https://mlsanity.com/paper/1605.06197/) (2016)
- [Addendum on the scoring of Gaussian directed acyclic graphical models](https://mlsanity.com/paper/1402.6863/) (2014)
- [On the Equivalence of Causal Models](https://mlsanity.com/paper/1304.1108/) (2013)

## Built on by (most cited first, 21 of 21)

- [BISCUIT: Causal Representation Learning from Binary Interactions](https://mlsanity.com/paper/2306.09643/) (2023)
- [Structure Learning with Continuous Optimization: A Sober Look and Beyond](https://mlsanity.com/paper/2304.02146/) (2023)
- [Learning nonparametric latent causal graphs with unknown interventions](https://mlsanity.com/paper/2306.02899/) (2023)
- [BaCaDI: Bayesian Causal Discovery with Unknown Interventions](https://mlsanity.com/paper/2206.01665/) (2022)
- [Passive learning of active causal strategies in agents and language models](https://mlsanity.com/paper/2305.16183/) (2023)
- [Causal Entropy Optimization](https://mlsanity.com/paper/2208.10981/) (2022)
- [Towards Interpretable Deep Generative Models via Causal Representation Learning](https://mlsanity.com/paper/2504.11609/) (2025)
- [Characterization and Greedy Learning of Gaussian Structural Causal Models under Unknown Interventions](https://mlsanity.com/paper/2211.14897/) (2022)
- [ProDAG: Projected Variational Inference for Directed Acyclic Graphs](https://mlsanity.com/paper/2405.15167/) (2024)
- [psiDAG: Projected Stochastic Approximation Iteration for DAG Structure Learning](https://mlsanity.com/paper/2410.23862/) (2024)
- [Curious Causality-Seeking Agents Learn Meta Causal World](https://mlsanity.com/paper/2506.23068/) (2025)
- [CAnDOIT: Causal Discovery with Observational and Interventional Data from Time-Series](https://mlsanity.com/paper/2410.02844/) (2024)
- [OCDB: Revisiting Causal Discovery with a Comprehensive Benchmark and Evaluation Framework](https://mlsanity.com/paper/2406.04598/) (2024)
- [Score-based Greedy Search for Structure Identification of Partially Observed Linear Causal Models](https://mlsanity.com/paper/2510.04378/) (2025)
- [Incorporating Expert Knowledge into Bayesian Causal Discovery of Mixtures of Directed Acyclic Graphs](https://mlsanity.com/paper/2510.06735/) (2025)
- [Distinguishing Cause from Effect on Categorical Data: The Uniform Channel Model](https://mlsanity.com/paper/2303.08572/) (2023)
- [Revisiting Differentiable Structure Learning: Inconsistency of ℓ1 Penalty and Beyond](https://mlsanity.com/paper/2410.18396/) (2024)
- [Graph Agnostic Causal Bayesian Optimisation](https://mlsanity.com/paper/2411.03028/) (2024)
- [Disentangled Representations for Causal Cognition](https://mlsanity.com/paper/2407.00744/) (2024)
- [Theoretical Guarantees for Causal Discovery on Large Random Graphs](https://mlsanity.com/paper/2511.02536/) (2025)
- [Efficient Differentiable Causal Discovery via Reliable Super-Structure Learning](https://mlsanity.com/paper/2601.05474/) (2026)

## Abstract (arXiv)

Recent work has shown promising results in causal discovery by leveraging interventional data with gradient-based methods, even when the intervened variables are unknown. However, previous work assumes that the correspondence between samples and interventions is known, which is often unrealistic. We envision a scenario with an extensive dataset sampled from multiple intervention distributions and one observation distribution, but where we do not know which distribution originated each sample and how the intervention affected the system, textiti.e., interventions are entirely latent. We propose a method based on neural networks and variational inference that addresses this scenario by framing it as learning a shared causal graph among an infinite mixture (under a Dirichlet process prior) of intervention structural causal models. Experiments with synthetic and real data show that our approach and its semi-supervised variant are able to discover causal relations in this challenging scenario.