Learning Causal Structures Based on Divide and Conquer

Area of Science:

• Causal inference
• Machine learning
• Statistics

Background:

• High-dimensional data presents challenges for causal inference.
• Existing constraint-based methods rely heavily on conditional independence (CI) tests, impacting efficiency and accuracy.
• Constructing true causal graphs from Markov equivalence classes is complex.

Purpose of the Study:

• To reduce redundant CI tests in high-dimensional causal inference.
• To improve the accuracy and efficiency of causal graph construction.
• To develop a method for distinguishing Markov equivalence classes.

Main Methods:

• A recursive decomposition approach is proposed to break down data into smaller subsets.
• Low-order CI tests are utilized within subsets, preserving d-separation properties.
• Regression-based CI tests are employed for linear non-Gaussian additive noise models to identify causal directions.

Main Results:

• The recursive decomposition significantly reduces redundant CI tests.
• The method effectively reconstructs complete causality by merging partial results.
• Regression-based tests enhance causal direction identification beyond V-structures and consistent propagation.

Conclusions:

• The proposed method offers a substantial reduction in redundant CI tests.
• It improves the ability to distinguish between Markov equivalence classes.
• This approach enhances the overall accuracy and efficiency of causal discovery in high-dimensional settings.