Pairwise Likelihood Ratios for Estimation of Non-Gaussian Structural Equation Models.

Area of Science:

• Causal inference
• Statistical modeling
• Machine learning

Background:

• Determining causal direction between variables is crucial in many scientific fields.
• Existing methods for causal discovery often struggle with non-Gaussian data or limited sample sizes.
• The linear non-Gaussian acyclic model (LiNGAM) provides a framework for causal discovery.

Purpose of the Study:

• To develop new measures for estimating causal direction between non-Gaussian random variables.
• To extend these measures for estimating the linear non-Gaussian acyclic model (LiNGAM) in complex scenarios.
• To evaluate the proposed framework's performance against existing methods, particularly in data-scarce or noisy conditions.

Main Methods:

• Development of likelihood ratio-based measures for causal direction.
• Introduction of simple first-order approximations of the likelihood ratio.
• Analysis of measures using cumulant-based statistics for validation.
• Extension of the method to estimate LiNGAM for multivariate, cyclic, and nonlinear models.

Main Results:

• The proposed measures accurately determine causal directions.
• The framework effectively estimates LiNGAM for more variables than observations.
• The method demonstrates robustness in scenarios with few data points or noisy data.
• Simulated fMRI data analysis suggests utility in neuroimaging.

Conclusions:

• The novel likelihood ratio-based framework offers a computationally simple and effective approach to causal discovery.
• The method performs comparably or better than existing techniques, especially in challenging data conditions.
• The framework's applicability extends to complex causal structures and is particularly relevant for neuroimaging research with limited time-series data.