In this thesis, we considered two high-dimensional regression problems. In the first part, we considered a linear regression problem in high-dimensional setting, where the covariates can be ordered in some meaningful way. We proposed a so-called spline-lasso (with thresholding) to better capture the different effects within the influential grouped variables as well as to improve the feature selection ability. In the second part, a binary classification problem was considered. We proposed a new classification method to find a separating hyperplane. The method tried to assign a distance-based decaying weight to each training observations. Typically, a correctly classified point near the separating hyperplane would have higher weight than those far away from the boundary. Also mi...[ Read more ]

In this thesis, we considered two high-dimensional regression problems. In the first part, we considered a linear regression problem in high-dimensional setting, where the covariates can be ordered in some meaningful way. We proposed a so-called spline-lasso (with thresholding) to better capture the different effects within the influential grouped variables as well as to improve the feature selection ability. In the second part, a binary classification problem was considered. We proposed a new classification method to find a separating hyperplane. The method tried to assign a distance-based decaying weight to each training observations. Typically, a correctly classified point near the separating hyperplane would have higher weight than those far away from the boundary. Also misclassified points would be penalized so that our classification rule would enjoy good generalization performance. To solve for the optimal separating hyperplane, the majorization-minimization (MM) algorithm was applied.