Root cause discovery via permutations and Cholesky decomposition.

Area of Science:

• Causal inference
• Genetics
• Machine learning

Background:

• Monogenic disorders are caused by a single gene.
• Identifying the specific disease-causing gene is challenging, especially with unknown causal relationships.
• Current methods for root cause discovery in linear structural equation models have limitations.

Purpose of the Study:

• To develop a method for identifying the root cause (disease-causing gene) in monogenic disorders.
• To determine if the root cause is identifiable without knowing the causal ordering.
• To adapt root cause discovery methods for high-dimensional genetic data.

Main Methods:

• Utilized linear structural equation models with unknown causal ordering.
• Analyzed a simple method based on squared z-scores, identifying its limitations.
• Developed a novel approach leveraging permutations and Cholesky decomposition for root cause identifiability.
• Proposed a method for root cause discovery based on permutation properties.
• Adapted the method for high-dimensional settings.

Main Results:

• Proved that the root cause is identifiable even when the causal ordering is unknown.
• Characterized the conditions under which a simple z-score method fails.
• Identified specific permutations that correctly identify the root cause.
• Demonstrated the effectiveness of the proposed methods through simulations.
• Successfully applied the high-dimensional method to a gene expression dataset.

Conclusions:

• The root cause of a monogenic disorder is identifiable without prior knowledge of the causal ordering.
• The proposed method using permutations and Cholesky decomposition offers a robust approach to root cause discovery.
• The developed high-dimensional method is effective for identifying disease-causing genes in complex genetic datasets.