Two-step sparse boosting for high-dimensional longitudinal data with varying coefficients

Varying-coefficient models are widely used to model nonparametric interaction and recently adopted to analyze longitudinal data measured repeatedly over time. We focus on high-dimensional longitudinal observations in this article. A novel two-step sparse boosting approach is proposed to carry out the variable selection and the model-based prediction. As a new machine learning tool, boosting provides seamless integration of model estimation and variable selection for complicated regression functions. Specifically, in the first step the sparse boosting technique assuming independence is applied to facilitate an initial estimate of the correlation structure while in the second step the estimated correlation structure is incorporated in the loss function of the sparse boosting algorithm. Extensive numerical examples illustrate the advantage of the two-step sparse boosting method. An application of yeast cell cycle gene expression data is further provided to demonstrate the proposed methodology.