Maximum Likelihood Estimation Over Directed Acyclic Gaussian Graphs.

Area of Science:

• Statistics
• Machine Learning
• Causal Inference

Background:

• Estimating multiple directed graphs is complex with inhomogeneous data.
• Directed acyclic graphs (DAGs) represent causal relationships among variables.
• Gaussian graphical models are often used for causal inference.

Purpose of the Study:

• To develop a method for estimating multiple DAGs with known variable ordering.
• To identify sparse structures and detect changes in adjacency matrices.
• To infer causal relations from complex datasets.

Main Methods:

• A constrained maximum likelihood method with non-convex constraints was proposed.
• The method incorporates constraints on adjacency matrix elements and their differences.
• An efficient algorithm using augmented Lagrange multipliers and difference convex methods was developed.

Main Results:

• The proposed method effectively identifies sparse structures in graphs.
• It successfully detects structural changes across adjacency matrices.
• Numerical results demonstrate strong performance compared to existing methods.

Conclusions:

• The developed constrained maximum likelihood method accurately estimates multiple DAGs.
• The efficient algorithm facilitates practical application in causal inference.
• The approach shows promise for analyzing both simulated and real-world data.