论文标题
通过缩放拉索的稀疏精度矩阵估计的有效的GPU平行坐标下降算法
An efficient GPU-Parallel Coordinate Descent Algorithm for Sparse Precision Matrix Estimation via Scaled Lasso
论文作者
论文摘要
稀疏精度矩阵在高斯图形模型中起着至关重要的作用，因为零离子分子元素表明给定的两个变量的相应两个变量的条件独立性。在高斯图形模型中，已经提出了许多方法，并给出了它们的理论特性。其中，通过缩放拉索（SPMESL）的稀疏精度矩阵估计具有一个吸引人的功能，在该特征中，自动设置了罚款水平以在稀疏性和可逆条件下实现最佳收敛率。相反，其他方法需要用于搜索最佳调整参数。尽管有这样的优势，但由于其昂贵的计算成本，SPMESL并未被广泛使用。在本文中，我们为SPMESL开发了一种GPU平行坐标下降（CD）算法，并在数值上表明，所提出的算法比针对SPMESL量身定制的最小角回归（LARS）快得多。进行了几项全面的数值研究，以研究拟议算法的可伸缩性和SPMESL的估计性能。结果表明，在所有情况下，SPMESL的虚假发现率最低，并且在列的稀疏度很高的情况下，最佳性能。
The sparse precision matrix plays an essential role in the Gaussian graphical model since a zero off-diagonal element indicates conditional independence of the corresponding two variables given others. In the Gaussian graphical model, many methods have been proposed, and their theoretical properties are given as well. Among these, the sparse precision matrix estimation via scaled lasso (SPMESL) has an attractive feature in which the penalty level is automatically set to achieve the optimal convergence rate under the sparsity and invertibility conditions. Conversely, other methods need to be used in searching for the optimal tuning parameter. Despite such an advantage, the SPMESL has not been widely used due to its expensive computational cost. In this paper, we develop a GPU-parallel coordinate descent (CD) algorithm for the SPMESL and numerically show that the proposed algorithm is much faster than the least angle regression (LARS) tailored to the SPMESL. Several comprehensive numerical studies are conducted to investigate the scalability of the proposed algorithm and the estimation performance of the SPMESL. The results show that the SPMESL has the lowest false discovery rate for all cases and the best performance in the case where the level of the sparsity of the columns is high.
