Convex Modeling of Interactions with Strong Heredity

Area of Science:

• Statistics
• Machine Learning
• Bioinformatics

Background:

• Regression models with interactions are crucial for understanding complex relationships.
• Enforcing strong heredity is essential for interpretability and biological relevance in high-dimensional data.
• Existing methods like VANISH and hierNet offer partial solutions but lack generality.

Purpose of the Study:

• To propose FAMILY, a generalized framework for fitting regression models with interactions under strong heredity.
• To provide an efficient and convergent optimization algorithm for the proposed framework.
• To extend the framework to generalized linear models and evaluate its performance.

Main Methods:

• Formulation as a convex optimization problem.
• Solution using an efficient alternating directions method of multipliers (ADMM) algorithm.
• Derivation of an unbiased estimator for the degrees of freedom.

Main Results:

• The ADMM algorithm guarantees convergence to the global optimum.
• The framework is adaptable to various convex penalty functions and generalized linear models.
• Demonstrated performance through simulation studies and analysis of HIV sequence data.

Conclusions:

• FAMILY offers a versatile and efficient approach to regression modeling with interactions and strong heredity.
• The method generalizes and improves upon existing techniques.
• The framework shows promise for applications in bioinformatics and other fields requiring interpretable models.