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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

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Efficient Bayesian Regularization for Graphical Model Selection.

Suprateek Kundu¹, Bani K Mallick², Veera Baladandayuthapan³

¹Department of Biostatistics & Bioinformatics, Emory University, 1518 Clifton Road, Atlanta, Georgia 30322, U.S.A.

Bayesian Analysis

|October 30, 2020

Summary

This summary is machine-generated.

We developed a new Bayesian graphical model for high-dimensional data, improving precision matrix selection. This method is computationally efficient and accurate for large datasets, outperforming existing approaches.

Keywords:

Cholesky-based regularization covariance selection joint penalized credible regions selection consistency shrinkage priors

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Area of Science:

Statistics
Machine Learning
Computational Biology

Background:

Bayesian graphical models are crucial for analyzing complex data structures.
Existing methods struggle with high-dimensional data where the number of variables exceeds sample size.
Scalability remains a challenge in Bayesian graphical model selection.

Purpose of the Study:

To introduce a novel Bayesian graphical model selection approach for large-dimensional settings.
To decouple model fitting and covariance selection for computational efficiency.
To provide theoretical guarantees for selection consistency.

Main Methods:

A full model is fitted using a novel class of mixtures of inverse-Wishart priors.
Priors induce shrinkage on the precision matrix, equivalent to Cholesky-based regularization.
Post-fitting model selection employs penalized joint credible regions.
Gibbs samplers and efficient post-fitting inferences ensure computational feasibility.

Main Results:

The proposed method demonstrates computational feasibility for large dimensions.
Theoretical guarantees for selection consistency are established.
Simulations show favorable comparisons with competing methods in accuracy and speed.
The approach was successfully applied to cancer genomics data.

Conclusions:

The novel Bayesian graphical model offers an effective solution for high-dimensional data.
The decoupling strategy enhances computational efficiency and scalability.
The method provides reliable model selection with theoretical backing.