Causal Network Inference Via Group Sparse Regularization.

Area of Science:

• Causal inference
• Network analysis
• Statistical modeling

Background:

• Inferring causal networks from observational data is challenging.
• Multivariate Autoregressive (MAR) processes are common models for time-series data.
• Existing methods struggle with limited observations relative to network complexity.

Purpose of the Study:

• To develop conditions for consistent sparse causal network structure estimation using Group Lasso (gLasso).
• To introduce and validate a
• false connection score
• (ψ) for assessing recovery accuracy.
• To propose a modified gLasso procedure for improved causal inference.

Main Methods:

• Derivation of theoretical conditions for consistent network recovery.
• Analysis of the
• false connection score
• (ψ) in asymptotic and non-asymptotic regimes.
• Development and testing of a modified Group Lasso (gLasso) algorithm.

Main Results:

• Consistent estimation of sparse causal networks is achievable with Group Lasso (gLasso) when ψ < 1.
• The
• false connection score
• (ψ) effectively predicts recovery performance, even with fewer observations than parameters.
• The modified gLasso procedure enhances the
• false connection score
• and reduces causal direction misidentification.

Conclusions:

• The proposed conditions and modified gLasso procedure enable robust causal network inference from limited data.
• The
• false connection score
• is a critical metric for evaluating the reliability of inferred causal structures.
• The approach demonstrates practical effectiveness through simulations and electrocorticogram (ECoG) data analysis.