Bayesian Pliable Lasso With Horseshoe Prior for Interaction Effects in GLMs With Missing Responses

Area of Science:

• Statistics
• Machine Learning
• Computational Biology

Background:

• Sparse regression identifies key predictors but often struggles with interaction modeling and uncertainty quantification.
• The frequentist pliable lasso models interactions under heredity constraints but lacks Bayesian inference capabilities.
• Incorporating prior knowledge and quantifying uncertainty are crucial for robust statistical modeling.

Purpose of the Study:

• To develop a Bayesian pliable lasso for enhanced sparse regression, particularly for modeling interactions.
• To provide a framework for uncertainty quantification and prior knowledge integration in interaction selection.
• To extend the Bayesian pliable lasso to generalized linear models and handle missing responses.

Main Methods:

• Proposed a Bayesian pliable lasso using sparsity-inducing priors (e.g., horseshoe) on main and interaction effects.
• Implemented a hierarchical prior structure to enforce heredity constraints and adaptively shrink coefficients.
• Developed an efficient Gibbs sampling algorithm for posterior inference, including a tailored approach for missing responses.

Main Results:

• The Bayesian pliable lasso yields sparse and interpretable interaction structures.
• Principled measures of uncertainty are provided, enhancing model interpretability.
• Demonstrated superior performance in recovering complex interaction patterns compared to existing methods, using simulations and real-data.

Conclusions:

• The proposed Bayesian pliable lasso offers a powerful and flexible approach for sparse regression with interaction modeling.
• The framework effectively handles missing data and provides robust uncertainty quantification.
• The method is publicly available as the R package hspliable.