Linear Deconfounded Score Method: Scoring DAGs With Dense Unobserved Confounding.

Area of Science:

• Causal Inference
• Machine Learning
• Statistical Modeling

Background:

• Unmeasured confounding poses a significant challenge to causal discovery from observational data.
• Constraint-based methods struggle when unobserved variables widely affect observed ones, leading to unidentifiable causal effects.
• Existing methods often fail in high-dimensional settings with widespread unobserved confounding.

Purpose of the Study:

• To develop a method for discovering causal relationships in the presence of unmeasured confounding.
• To leverage the principle of independent mechanisms to disentangle spurious and causal effects.
• To propose a scalable algorithm for causal discovery in complex systems.

Main Methods:

• Utilizing the principle of independent mechanisms to identify statistical footprints of unobserved confounding.
• Applying a sparse linear Gaussian directed acyclic graph (DAG) model for causal structure recovery.
• Developing an adjusted score-based causal discovery algorithm compatible with general-purpose solvers.

Main Results:

• Demonstrated that unobserved confounding leaves a detectable statistical footprint under the principle of independent mechanisms.
• Showed that a sparse linear Gaussian DAG can be approximately recovered from observational data.
• The proposed algorithm scales to high-dimensional problems and is robust to deviations from model assumptions.

Conclusions:

• Causal discovery is feasible even with widespread unmeasured confounding by exploiting the principle of independent mechanisms.
• The developed algorithm offers a scalable and robust solution for identifying causal structures in complex observational datasets.
• The methodology shows potential for extension to nonlinear structural models, broadening its applicability.