Learning Continuous Decomposable Models Using Mutual Information and Statistical Copulas

Area of Science:

• Statistics
• Machine Learning
• Computational Biology

Background:

• Learning dependence graphs from multivariate continuous data is difficult due to heterogeneous marginal distributions.
• Existing methods can be sensitive to smoothing and confound marginal issues with dependence.

Purpose of the Study:

• To develop a novel information-theoretic objective for structure learning in decomposable (chordal) Markov random fields.
• To address challenges posed by heterogeneous marginal distributions in dependence graph learning.

Main Methods:

• Derived a theoretical result expressing mutual information as a difference of clique/separator copula entropies under decomposability.
• Defined a copula information score with an additive complexity penalty and derived closed-form local scores for edge updates.
• Implemented a nonparametric pipeline using pseudo-observations and kernel density estimation for copula entropy computation.

Main Results:

• The proposed nonparametric greedy procedure demonstrated improved edge recovery accuracy on synthetic chordal benchmarks.
• Outperformed a likelihood-driven nonparametric baseline in structure learning tasks.
• Generated interpretable dependence summaries on a real-world airway epithelial gene expression dataset.

Conclusions:

• The developed copula information score offers a robust and accurate method for learning dependence structures in decomposable graphs.
• The approach effectively handles heterogeneous data and provides interpretable results.
• This work advances structure learning by providing a theoretically grounded and practically applicable information-theoretic score.