Generalized Scalar-on-Image Regression Models via Total Variation
提出一种广义标量对图像回归模型（GSIRM-TV），假设斜率函数属于有界总变分空间以刻画图像的分片光滑性，通过惩罚总变分优化估计参数，并给出非渐近误差界，在ADNI海马体数据上表现优于现有方法。
The use of imaging markers to predict clinical outcomes can have a great impact in public health. The aim of this paper is to develop a class of generalized scalar-on-image regression models via total variation (GSIRM-TV), in the sense of generalized linear models, for scalar response and imaging predictor with the presence of scalar covariates. A key novelty of GSIRM-TV is that it is assumed that the slope function (or image) of GSIRM-TV belongs to the space of bounded total variation in order to explicitly account for the piecewise smooth nature of most imaging data. We develop an efficient penalized total variation optimization to estimate the unknown slope function and other parameters. We also establish nonasymptotic error bounds on the excess risk. These bounds are explicitly specified in terms of sample size, image size, and image smoothness. Our simulations demonstrate a superior performance of GSIRM-TV against many existing approaches. We apply GSIRM-TV to the analysis of hippocampus data obtained from the Alzheimers Disease Neuroimaging Initiative (ADNI) dataset.