Estimating Joint Interventional Distributions from Marginal Interventional Data

2026-04-20 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics · Depth: Expert, extended

Summary

Researchers from the Max Planck Institute for Intelligent Systems and Amazon Research have developed i-CMAXENT, an extension of the Causal Maximum Entropy (CMAXENT) method. This new approach allows for the estimation of joint conditional distributions of variables by exploiting interventional data, in addition to observational data, using the Maximum Entropy principle. The method proves that the solution lies within the exponential family, similar to traditional Maximum Entropy. i-CMAXENT addresses two key tasks: performing causal feature selection from mixed observational and single-variable interventional data, and inferring joint interventional distributions. On synthetic data, i-CMAXENT outperforms existing methods for merging datasets in causal feature selection and achieves comparable results to the Kernel Conditional Independence (KCI) test, even when KCI has access to full joint observations.

Key takeaway

For AI scientists and research scientists working with incomplete or disparate causal datasets, i-CMAXENT offers a robust method to infer joint interventional distributions and perform causal feature selection. You should consider integrating i-CMAXENT when traditional methods like KCI are impractical due to the lack of full joint observational data, especially in scenarios where single-variable interventions are available. This approach can significantly improve the accuracy of identifying true causal parents and estimating complex causal effects from fragmented experimental evidence.

Key insights

i-CMAXENT infers joint causal distributions from mixed observational and interventional data using Maximum Entropy.

Principles

• Interventional data enhances causal feature selection.
• Maximum Entropy solutions reside in the exponential family.
• Combining data types improves causal inference accuracy.

Method

i-CMAXENT extends CMAXENT by incorporating interventional data as constraints into a Maximum Conditional Entropy optimization problem, yielding an exponential family distribution. Lagrange multipliers are minimized to fit empirical averages.

In practice

• Use i-CMAXENT for causal feature selection with partial interventional data.
• Apply i-CMAXENT to estimate joint interventional effects from single-variable interventions.
• Combine observational and interventional data for robust causal modeling.

Topics

• Interventional Causal Maximum Entropy
• Causal Feature Selection
• Joint Interventional Distributions
• Maximum Entropy Principle
• Causal Marginal Problem

Code references

• google/jax

Best for: AI Scientist, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.