An automatic robust Bayesian approach to principal component regression.

Area of Science:

• Statistics
• Machine Learning

Background:

• Principal component regression (PCR) is valuable for high-dimensional data prediction.
• Bayesian approaches to PCR are less explored, especially robust methods.

Purpose of the Study:

• To develop a novel Bayesian principal component regression method robust to outliers.
• To enhance prediction accuracy and reliability in the presence of aberrant data points.

Main Methods:

• Introduced a Bayesian approach incorporating 'whole robustness' to penalize outliers in dependent variables and covariates.
• Utilized the geometry of principal components (PCs) for efficient identification of significant components.
• Employed model-averaging to consolidate predictions and address model uncertainty.

Main Results:

• The proposed method demonstrated robustness against outliers, yielding predictions consistent with the majority of the data.
• Effectively identified significant principal components, contributing to model interpretability.
• Outperformed non-robust Bayesian and frequentist counterparts in real-data evaluations.

Conclusions:

• The novel robust Bayesian PCR offers a reliable alternative for prediction with high-dimensional, potentially outlier-prone data.
• Provides a framework for automated statistical procedures with accessible code.
• Enhances the utility of Bayesian methods in robust statistical modeling.