Estimating Joint Interventional Distributions from Marginal Interventional Data
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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.
Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 17 of its 54 references that are in the map. First posted on arXiv 3 Sep 2024.
Builds on
17 of 54 references.
References · 17
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5 more
- 2020Learning Joint Nonlinear Effects from Single-variable Interventions in the Presence of Hidden Confounderscited by 7
- 2021Causal versions of Maximum Entropy and Principle of Insufficient Reasoncited by 7
- 2023Bounding probabilities of causation through the causal marginal problemcited by 3
- 2024Identification of Average Causal Effects in Confounded Additive Noise Modelscited by 2
- 2021Causal aggregation: estimation and inference of causal effects by constraint-based data fusioncited by 1
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