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

Area of Science:

• Statistics
• Machine Learning
• Data Science

Background:

• High-dimensional data with left-censored responses present analytical challenges.
• Existing methods like classical Tobit models and deep learning have limitations in handling nonlinearity, variable selection, and interpretability.

Purpose of the Study:

• To propose an integrated deep learning framework, the Deep Tobit model, for analyzing high-dimensional left-censored data.
• To develop a robust two-stage feature selection algorithm with theoretical guarantees.
• To improve both variable selection and prediction accuracy in censored data analysis.

Main Methods:

• Developed the Deep Tobit model using the negative Tobit log-likelihood as its loss function to address data censoring.
• Implemented a two-stage feature selection algorithm with proven convergence rate and selection consistency.
• Validated the model through extensive simulation studies and real-world applications.

Main Results:

• The Deep Tobit model demonstrated superior performance compared to state-of-the-art baselines.
• The framework achieved high accuracy in both variable selection and prediction.
• Successful application to aero-engine vibration and HIV viral load datasets.

Conclusions:

• The Deep Tobit model offers a powerful and effective solution for analyzing complex censored data.
• The integrated approach balances prediction performance with essential variable selection and interpretability.
• This framework advances the analysis of high-dimensional left-censored data in various scientific fields.