|タイトル||Convex Hull Approximation of Nearly Optimal Lasso Solutions|
In an ordinary feature selection procedure, a set of important features is obtained by solving an optimization problem such as the Lasso regression problem, and we expect that the obtained features explain the data well. However, if there are some highly correlated features, it can incur the risk of overlooking the actually important features. In this study, instead of the single optimal solution, we consider the set of nearly optimal solutions, which consists of continually many points. We formulate a feature selection problem as finding a small number of solutions such that the convex hull of these solutions approximates the set of nearly optimal solutions. The proposed algorithm consists of two steps: First, we randomly sample the extreme points of the set of nearly optimal solutions. Then, we select a small number of points using a greedy algorithm. The experimental results indicate that the proposed algorithm can approximate the solution set well. The results also indicate that we can obtain Lasso solutions with a large diversity.