Low-rank latent matrix-factor prediction modeling for generalized high-dimensional matrix-variate regression

Area of Science:

• Biostatistics
• Medical Imaging Analysis
• Machine Learning for Healthcare

Background:

• Accurate diagnosis of COVID-19 is crucial, with computed tomography (CT) scans offering valuable 2D image biomarkers.
• Analyzing high-dimensional matrix-variate biomarkers from CT scans presents significant computational and statistical challenges.
• Existing methods often involve computationally intensive parameter tuning and may not fully preserve the structural information of matrix covariates.

Purpose of the Study:

• To develop a novel latent matrix-factor regression model for predicting COVID-19 responses using 2D CT scan biomarkers.
• To address the challenges of high-dimensionality and computational burden in analyzing matrix-variate data.
• To improve prediction accuracy and efficiency compared to existing penalized regression methods.

Main Methods:

• Formulation of a latent generalized matrix regression (LaGMaR) model.
• Extraction of low-dimensional matrix factor scores from high-dimensional matrix-variate biomarkers using a matrix factor model.
• Dimension reduction that respects the 2D structure of the matrix covariate, avoiding iterative procedures and parameter tuning.
• Estimation procedure derived by transforming a bilinear form matrix factor model to a high-dimensional vector factor model for applying principal components analysis.

Main Results:

• The LaGMaR model effectively reduces dimensionality while preserving the intrinsic 2D structural information of matrix covariates.
• Bilinear-form consistency of the estimated matrix coefficient and prediction consistency were established.
• Simulation experiments demonstrated that LaGMaR outperforms existing penalized methods in prediction capability across various generalized matrix regression scenarios.
• Application to a real COVID-19 dataset showed efficient prediction of the disease.

Conclusions:

• LaGMaR offers a computationally efficient and structurally informative approach for analyzing high-dimensional matrix-variate data in medical imaging.
• The model provides superior prediction performance for COVID-19 diagnosis compared to traditional penalized methods.
• LaGMaR is a convenient and effective tool for leveraging 2D image biomarkers from CT scans for disease prediction.