Causal discovery by continuous optimization with weighted superstructure

Area of Science:

• Machine Learning
• Causal Inference
• Computational Statistics

Background:

• Score-based causal discovery methods excel but struggle with high dimensionality, limited samples, and heterogeneous noise.
• Constraint-based methods show promise in noisy, low-sample scenarios, suggesting the value of conditional independence (CI) information.

Purpose of the Study:

• To improve continuous optimization-based causal discovery by incorporating reliable conditional independence (CI) information.
• To enhance robustness in high-dimensional, low-sample, and heterogeneous noise settings.

Main Methods:

• Utilized low-order (0-order, 1-order) conditional independence (CI) tests to build a weighted superstructure from observed data.
• Integrated weighted CI constraints derived from the superstructure into a continuous optimization framework.
• Provided theoretical convergence guarantees for the proposed constrained optimization framework.

Main Results:

• Demonstrated significant performance improvements for continuous optimization methods in causal discovery.
• Showcased particular effectiveness in low-sample regimes and under heterogeneous noise conditions.
• Validated the approach through extensive experiments on both synthetic and real-world datasets.

Conclusions:

• The proposed method effectively enhances continuous optimization-based causal discovery by leveraging weighted CI constraints.
• The integration of CI information offers a robust solution for complex causal discovery problems, particularly with limited data.
• The findings suggest a promising direction for improving the reliability and applicability of causal discovery algorithms.