标题： 近似最优Lasso解的凸包方法 显示英文标题

标题： Convex Hull Approximation of Nearly Optimal Lasso Solutions

摘要： 在常规的特征选择过程中，通过求解如Lasso回归问题之类的优化问题获得一组重要特征，并期望所获得的特征能很好地解释数据。 在本研究中，我们考虑寻找一组多样但接近最优的解，而不是单一最优解。 为此，我们将问题表述为找到少量解，使得这些解的凸包近似表示接近最优解的集合。 所提出的算法包括两个步骤：首先，我们随机采样接近最优解集合的极值点。然后，使用贪心算法选择少量点。 实验结果表明，所提出的算法可以很好地近似解集。 结果还表明，我们可以获得具有较大多样性的Lasso解。 显示英文摘要

摘要： 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. In this study, instead of the single optimal solution, we consider finding a set of diverse yet nearly optimal solutions. To this end, we formulate the 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.