# Estimating Joint Interventional Distributions from Marginal Interventional Data

arXiv: https://arxiv.org/abs/2409.01794 · HTML: https://mlsanity.com/paper/2409.01794/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 54 references that are in the map.
- First posted on arXiv 3 Sep 2024.

## Builds on (most cited first, 17 of 17)

- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [Invariant Causal Prediction for Nonlinear Models](https://mlsanity.com/paper/1706.08576/) (2017)
- [Causal Discovery from Changes](https://mlsanity.com/paper/1301.2312/) (2013)
- [Causal inference methods for combining randomized trials and observational studies: a review](https://mlsanity.com/paper/2011.08047/) (2020)
- [Constraint-based Causal Discovery from Multiple Interventions over Overlapping Variable Sets](https://mlsanity.com/paper/1403.2150/) (2014)
- [A Minimax Approach to Supervised Learning](https://mlsanity.com/paper/1606.02206/) (2016)
- [Causal Inference Through the Structural Causal Marginal Problem](https://mlsanity.com/paper/2202.01300/) (2022)
- [Causal Effect Identification from Multiple Incomplete Data Sources: A General Search-based Approach](https://mlsanity.com/paper/1902.01073/) (2019)
- [Integrating overlapping datasets using bivariate causal discovery](https://mlsanity.com/paper/1910.11356/) (2019)
- [Data Integration in Causal Inference](https://mlsanity.com/paper/2110.01106/) (2021)
- [Disentangling Causal Effects from Sets of Interventions in the Presence of Unobserved Confounders](https://mlsanity.com/paper/2210.05446/) (2022)
- [Obtaining Causal Information by Merging Datasets with MAXENT](https://mlsanity.com/paper/2107.07640/) (2021)
- [Learning Joint Nonlinear Effects from Single-variable Interventions in the Presence of Hidden Confounders](https://mlsanity.com/paper/2005.11528/) (2020)
- [Causal versions of Maximum Entropy and Principle of Insufficient Reason](https://mlsanity.com/paper/2102.03906/) (2021)
- [Bounding probabilities of causation through the causal marginal problem](https://mlsanity.com/paper/2304.02023/) (2023)
- [Identification of Average Causal Effects in Confounded Additive Noise Models](https://mlsanity.com/paper/2407.10014/) (2024)
- [Causal aggregation: estimation and inference of causal effects by constraint-based data fusion](https://mlsanity.com/paper/2106.03024/) (2021)

## Built on by (most cited first, 2 of 2)

- [ACTIVA: Amortized Causal Effect Estimation via Transformer-based Variational Autoencoder](https://mlsanity.com/paper/2503.01290/) (2025)
- [Learning Joint Interventional Effects from Single-Variable Interventions in Additive Models](https://mlsanity.com/paper/2506.04945/) (2025)

## Abstract (arXiv)

In this paper we show how to exploit interventional data to acquire the joint conditional distribution of all the variables using the Maximum Entropy principle. To this end, we extend the Causal Maximum Entropy method to make use of interventional data in addition to observational data. Using Lagrange duality, we prove that the solution to the Causal Maximum Entropy problem with interventional constraints lies in the exponential family, as in the Maximum Entropy solution. Our method allows us to perform two tasks of interest when marginal interventional distributions are provided for any subset of the variables. First, we show how to perform causal feature selection from a mixture of observational and single-variable interventional data, and, second, how to infer joint interventional distributions. For the former task, we show on synthetically generated data, that our proposed method outperforms the state-of-the-art method on merging datasets, and yields comparable results to the KCI-test which requires access to joint observations of all variables.