OPTIMAL PARAMETER SETTING OF SINGLE AND MULTI-TASK LASSO

This thesis considers the problem of feature selection when the number of predictors is larger than the number of samples. The performance of supersaturated design (SSD) working with least absolute shrinkage and selection operator (LASSO) is studied in this setting. In order to achieve higher feature selection correctness, self-voting LASSO is implemented to select the tuning parameter while approximately optimize the probability of achieving Sign Correctness. Furthermore, we derive the probability of achieving Direction Correctness, and extend the self-voting LASSO to multi-task self-voting LASSO, which has a group screening effect for multiple tasks.