Deep Transformation Model

The increasing data complexity leads to the demand for more general and flexible modeling approaches. We consider a nonparametric transformation model with weak assumptions, which encompasses many popular models as special cases. A rank-based deep neural network (DNN) estimation approach is developed, with a loss function significantly different from the existing ones. It can accommodate outliers in response, which is a robustness property not broadly shared. For computational feasibility, we propose a double rectified linear unit (DReLU)-based estimator. To accommodate a diverging number of input variables and/or noises, we propose variable selection based on group penalization. We further expand the scope to accommodate censored survival data. We establish a new deep ReLU network approximation result as well as the estimation and variable selection properties. Numerical studies, including simulations and data analyses, establish practical utility of the proposed methods.