Abstract

n these lectures I propose and explore novel statistical modeling approaches, focusing on the Accelerated Failure Time (AFT) model combined with a penalized likelihood method for variable selection and estimation. Lecture 1. By using a log-linear representation, the inference problem is transformed into a structured sparse regression problem. Specifically, we incorporate a double penalty in the model that promotes both sparsity and a grouping effect. We establish the theoretical consistency of the estimator and present an efficient iterative computational algorithm based on the proximal gradient descent method. Lecture 2. An extension of this approach is the cooperative version, which introduces an “agreement” penalty to encourage alignment of predictions from different data views. This can be particularly powerful when the data views share an underlying relationship in their signals which can be leveraged to enhance the overall signal quality. We establish the theoretical consistency of the estimator and present an efficient iterative computational algorithm based on the proximal gradient descent method. Lecture 3. We evaluate the model’s performance using both synthetic data and real-world data from cancer survival analysis to identify potential new biomarkers. 1