The ℓ₁-regularized Gaussian maximum likelihood method is a common approach for sparse precision matrix estimation, but one that poses a computational challenge for high-dimensional datasets. We present a novel ℓ₁-regularized maximum likelihood method for performant large-scale sparse precision matrix estimation utilizing the block structures in the underlying computations. We identify the computational bottlenecks and contribute a block coordinate descent update as well as a block approximate matrix inversion routine, which is then parallelized using a shared-memory scheme. We demonstrate the effectiveness, accuracy, and performance of these algorithms. Our numerical examples and comparative results with various modern open-source packages reveal that these precision matrix estimation methods can accelerate the computation of covariance matrices by two to three orders of magnitude, while keeping memory requirements modest. Furthermore, we conduct large-scale case studies for applications from finance and medicine with several thousand random variables to demonstrate applicability for real-world datasets.

的ℓ ₁ -regularized高斯最大似然法是用于稀疏精度矩阵估计的常用方法，而是一个用于构成高维数据集的计算的挑战。我们提出了一个新颖的ℓ ₁底层计算中使用块结构进行高性能大规模稀疏精度矩阵估计的正则化最大似然方法。我们确定了计算瓶颈，并贡献了一个块坐标下降更新以及一个块近似矩阵求逆例程，然后使用共享内存方案对其进行并行化。我们演示了这些算法的有效性，准确性和性能。我们的数值示例和使用各种现代开源软件包的比较结果表明，这些精确矩阵估计方法可以将协方差矩阵的计算速度提高2到3个数量级，同时保持对内存的需求适度。此外，