Deep tobit model: an integrated framework for high-dimensional censored regression with variable selection

This article introduces the Deep Tobit model, a deep learning framework designed for high-dimensional censored regression with variable selection. The model leverages the negative Tobit log-likelihood as the loss function of a deep neural network (DNN) to account for data censoring, making it particularly suitable for analyzing left-censored data such as aero-engine casing vibration and HIV viral load. The two-stage feature selection (TSFS) algorithm is proposed to jointly estimate the sparse parameter and other neural network parameters, ensuring both accurate prediction and interpretability. The article also provides theoretical guarantees for the convergence and selection consistency of the TSFS algorithm, along with extensive numerical studies and case studies that demonstrate the model's superior performance compared to other benchmarks. The case studies include the aero-engine casing vibration data and HIV viral load data, showcasing the model's ability to identify key factors affecting vibration and drug resistance mutations. The article concludes with a discussion on future research directions, such as exploring alternative regularization techniques and extending the model to accommodate right-censored and interval-censored data.