Selecting massive variables using an iterated conditional modes/medians algorithm

Area of Science:

• Statistics
• Machine Learning
• Computational Biology

Background:

• Massive variable selection is crucial in high-dimensional data analysis.
• Existing Empirical Bayes methods offer advantages like incorporating prior information and data-driven hyperparameters.
• Hierarchical structures in variable interconnections pose challenges for traditional methods.

Purpose of the Study:

• To propose a novel algorithm for empirical Bayes selection of massive variables.
• To incorporate sparsity and complex prior information into the variable selection process.
• To develop a computationally efficient method for high-dimensional data.

Main Methods:

• Development of an Iterated Conditional Modes/Medians (ICM/M) algorithm.
• Utilizing iterative conditional modes for data-driven hyperparameter estimation.
• Employing iterative conditional medians for model coefficient estimation and variable selection.

Main Results:

• The ICM/M algorithm is computationally fast and extends existing empirical Bayes thresholding.
• The method effectively incorporates sparsity and complex prior information.
• Empirical studies demonstrate competitive performance, even for massive regression predictors.

Conclusions:

• The proposed ICM/M algorithm provides an efficient and adaptive approach for empirical Bayes variable selection.
• It offers a flexible framework for handling complex data structures and prior information.
• The method shows promise for applications involving massive datasets and high-dimensional inference.