Testing Conditional Independence Between Latent Variables by Independence Residuals.

Area of Science:

• Causal inference and machine learning
• Statistical modeling and analysis

Background:

• Conditional independence (CI) testing is crucial for causal discovery but often assumes fully observable variables.
• Existing latent CI tests face robustness and efficiency issues, limiting their applicability in fields like psychology and medicine.

Purpose of the Study:

• To develop a robust and efficient method for testing conditional independence between latent variables.
• To address the limitations of current CI testing methods in scenarios with unobserved variables.

Main Methods:

• Proposes an auxiliary regression-based CI (AReCI) test using measured variables as surrogates for latent variables.
• The AReCI test performs regression over latent variables within linear causal models.
• The method is theoretically shown to be effective for both Gaussian and non-Gaussian data.

Main Results:

• The AReCI test successfully addresses conditional independence testing between latent variables.
• The partial correlation test is identified as a special case of the AReCI test.
• A new causal discovery method utilizing the AReCI test demonstrates effectiveness on synthetic and real-world data.

Conclusions:

• The AReCI test provides a significant advancement for causal discovery in the presence of latent variables.
• The proposed method offers a more robust and efficient approach compared to existing latent CI tests.
• The effectiveness of the AReCI test is validated through empirical studies.