论文标题
零和约束的套索问题的分解方法
A decomposition method for lasso problems with zero-sum constraint
论文作者
论文摘要
在本文中，我们考虑了零和限制的拉索问题，这通常是在高维空间中分析组成数据所需的。提出了一种新型算法来解决这些问题，结合了量身定制的活性集技术，以使用2坐标下降方案识别最佳溶液中的零变量。在每次迭代中，该算法都在两种不同的策略之间进行选择：第一个策略需要计算目标函数平滑项的整个梯度，并且在主动设定估算中更准确，而第二种仅使用部分导数，并且在计算上更有效。证明了全局融合到最佳解决方案，并在合成和真实数据集上提供了数值结果，显示了所提出方法的有效性。该软件可公开可用。
In this paper, we consider lasso problems with zero-sum constraint, commonly required for the analysis of compositional data in high-dimensional spaces. A novel algorithm is proposed to solve these problems, combining a tailored active-set technique, to identify the zero variables in the optimal solution, with a 2-coordinate descent scheme. At every iteration, the algorithm chooses between two different strategies: the first one requires to compute the whole gradient of the smooth term of the objective function and is more accurate in the active-set estimate, while the second one only uses partial derivatives and is computationally more efficient. Global convergence to optimal solutions is proved and numerical results are provided on synthetic and real datasets, showing the effectiveness of the proposed method. The software is publicly available.
