Cognitive Impairment Prediction in Alzheimer’s Disease with Regularized Modal Regression

Accurate and automatic predictions of cognitive assessment via neuroimaging markers are critical for early detection of Alzheimer's disease. Linear regression models have been successfully used in the association study between neuroimaging features and cognitive performance for Alzheimer's disease study. However, most existing methods are built on least squares under the mean square error (MSE) criterion, which are sensitive to outliers and their performance may be degraded for heavy-tailed noise (such as for complex brain disorder data). In this paper, we go beyond this criterion by investigating regularized modal regression from a statistical learning viewpoint. A new regularized scheme based on modal regression is proposed for estimation and variable selection, which is robust to outliers, heavy-tailed noise, and skewed noise. We conduct theoretical analysis and establish the approximation bound for learning the conditional mode function, the sparsity analysis for variable selection, and the robustness characterization. The experimental evaluations on simulated data and ADNI cohort data are provided to support the promising performance of the proposed algorithm.