On optimal regression trees to detect critical intervals for multivariate functional data
本文针对多元函数型数据设计了最优随机回归树，通过LASSO正则化在预测精度与稀疏性间取得平衡，能自动检测对预测关键且长度可控的区间，数值实验表明该方法优于基准程序。
In this paper, we tailor optimal randomized regression trees to handle multivariate functional data. A compromise between prediction accuracy and sparsity is sought. Whilst fitting the tree model, the detection of a reduced number of intervals that are critical for prediction, as well as the control of their length, is performed. Local and global sparsities can be modeled through the inclusion of LASSO-type regularization terms over the coefficients associated to functional predictor variables. The resulting optimization problem is formulated as a nonlinear continuous and smooth model with linear constraints. The numerical experience reported shows that our approach is competitive against benchmark procedures, being also able to trade off prediction accuracy and sparsity.