Feature screening rules and algorithms for efficient optimization of sparse regression models

Ultra high-dimensional data (data that collect a large number, i.e. millions, of features about subjects) has become a popular topic in many fields such as genetic studies, image recognition, and natural language processing, as these data sets are more and more easily available. Sparse penalized regression models are powerful ways to analyze this type of data because they can identify important features in the data. Efficient algorithms for these models, thus, have become valuable. Screening methods can identify features that will not be in the model and eliminate those features before solving the model and greatly reduce time and memory costs. This thesis focuses on developing more efficient screening methods and extending screening methods to more models.

First, we propose an adaptive hybrid screening algorithm framework that does screening adaptively along the path of tuning parameter values to reduce the computation costs of screening with little impact on its ability to eliminate features. Second, we derive a screening rule for lasso penalized Cox regression models, a powerful technique for identifying important features in predicting patient survival. Third, we derive a screening rule for the elastic net, which has good performance when features are correlated. Last, all the proposed methods are implemented and tested in the publicly available biglasso R package. They show significant improvement in efficiency compared to other existing methods.