Regularized Modal Regression with Applications in Cognitive Impairment Prediction
Linear regression models have been successfully used to function estimation and model selection in high-dimensional data analysis. However, most existing methods are built on least squares with the mean square error (MSE) criterion, which are sensitive to outliers and their performance may be degraded for heavy-tailed noise. In this paper, we go beyond this criterion by investigating the regularized modal regression from a statistical learning viewpoint. A new regularized modal regression model is proposed for estimation and variable selection, which is robust to outliers, heavy-tailed noise, and skewed noise. On the theoretical side, we establish the approximation estimate for learning the conditional mode function, the sparsity analysis for variable selection, and the robustness characterization. On the application side, we applied our model to successfully improve the cognitive impairment prediction using the Alzheimer's Disease Neuroimaging Initiative (ADNI) cohort data.
The authors present a regularized modal regression method. The statistical learning view of this proposed method is studied and the resulting model is applied to Alzheimer's disease studies. There are several presentation and evaluation issues for this work in its current form. 
Firstly, the authors motivate the paper using Alzheimer's disease studies and argue that modal regression is the way to analyze correlations between several disease markers of the disease. This seems very artificial. The necessity of use conditional mode for regression has nothing specific for the Alzheimer's application. The motivation for RMR makes sense without any AD related context. The authors then argue that the main contribution for the work is designing modal regression for AD (line 52). However, for the rest of the methods the discussion is about statistical learning -- no AD at all. This presentation is dubious. The authors need to decide if the work is statistical learning theory for modal regression OR an application of modal regression for AD (for the latter more applied journals are relevant and not this venue).
Moving beyond this overall presentation issue, if we assume that modal regression for AD is the focus of the paper, then the results should show precisely this performance improvement compared to the rest mean-based regression. However, as shown in section 4 this does not seem to be the case. In several cases the performance of LSR is very close to RMR. It should be pointed out that when reporting such sets of error measures, one should perform statistical tests to check if the performance difference is significant i.e., p-value differences between all the entries of Tables. Beyond, the tables the message is not clear in the Figures -- the visualizations need to be improved (or quantified in some sense). This non-appealing improvements of AD data evaluations is all the more reason that the authors should choose 'standard' regression datasets and show the performance gains of RMR explicitly (once this is done, the results of AD can be trusted and any small improvement can be deemed OK).