Motivated by diagnosing the COVID-19 disease using 2D image biomarkers from computed tomography (CT) scans, we propose a novel latent matrix-factor regression model to predict responses that may come from an exponential distribution family, where covariates include high-dimensional matrix-variate biomarkers. A latent generalized matrix regression (LaGMaR) is formulated, where the latent predictor is a low-dimensional matrix factor score extracted from the low-rank signal of the matrix variate through a cutting-edge matrix factor model. Unlike the general spirit of penalizing vectorization plus the necessity of tuning parameters in the literature, instead, our prediction modeling in LaGMaR conducts dimension reduction that respects the geometry characteristic of intrinsic two-dimensional structure of the matrix covariate and thus avoids iteration. This greatly relieves the computation burden, and meanwhile maintains structural information so that the latent matrix factor feature can perfectly replace the intractable matrix-variate owing to high-dimensionality. The estimation procedure of LaGMaR is subtly derived by transforming the bilinear form matrix factor model onto a high-dimensional vector factor model, so that the method of principle components can be applied. We establish bilinear-form consistency of the estimated matrix coefficient of the latent predictor and consistency of prediction. The proposed approach can be implemented conveniently. Through simulation experiments, prediction capability of LaGMaR is shown to outperform existing penalized methods under diverse scenarios of generalized matrix regressions. Through the application to a real COVID-19 dataset, the proposed approach is shown to predict efficiently the COVID-19.
翻译:利用计算成的XM(CT)扫描的2D图像图像生物标记,对COVID-19疾病进行了分析,因此我们提出一个新的潜伏矩阵因素回归模型,以预测可能来自指数分布系的反应,其中共变体包括高维矩阵变异生物标记。 开发了潜伏通用矩阵回归(LaGamaR),其中潜伏预测器是一个低维矩阵系数分数,通过一个尖端的基质基质变异模型模型模型,从基质变异中提取了低维度矩阵系数。与惩罚矢量化的一般精神和调整文献中参数的必要性不同,相反,我们在LagmaR的预测模型进行规模的缩小,以尊重矩阵变异体结构结构结构结构结构特征,从而避免迭代。 潜伏矩阵系数系数因高度而完全可以取代难变的基质矩阵变异变异。 LaGMAR的估算程序通过将双线-19矩阵矩阵应用参数应用参数应用模型应用到高维度预测模型中,我们所展示的当前基质变量预测模型将显示为一种高维度的模型。