Spike-and-slab least absolute shrinkage and selection operator generalized additive models and scalable algorithms...

Area of Science:

• Statistics
• Machine Learning
• Biostatistics

Background:

• Generalized Additive Models (GAMs) struggle with high-dimensional data and functional selection.
• Existing methods face challenges like excess shrinkage and scalability issues with Bayesian approaches.

Purpose of the Study:

• To propose Bayesian hierarchical generalized additive models (GHAMs) for improved high-dimensional data analysis.
• To develop a flexible functional selection mechanism addressing linear vs. nonlinear effects.
• To provide a scalable computational algorithm for model fitting.

Main Methods:

• Reparameterization of smoothing penalties for effective shrinkage.
• A novel two-part spike-and-slab LASSO prior for sparse and flexible function estimation.
• Implementation of a scalable EM-Coordinate Descent algorithm in the R package BHAM.

Main Results:

• GHAMs demonstrate superior predictive and computational performance compared to state-of-the-art models.
• Simulation studies and metabolomics data analyses validate the proposed methodology.
• The functional selection approach shows trade-offs related to effect hierarchy assumptions.

Conclusions:

• Bayesian hierarchical generalized additive models offer a robust solution for high-dimensional data analysis.
• The developed methods improve predictive accuracy and computational efficiency.
• The flexible functional selection provides valuable insights into model interpretability.