We present SQUIC, a fast and scalable package for sparse precision matrix estimation. The algorithm employs a second-order method to solve the \(\ell_{1}\)-regularized maximum likelihood problem, utilizing highly optimized linear algebra subroutines. In comparative tests using synthetic datasets, we demonstrate that SQUIC not only scales to datasets of up to a million random variables but also consistently delivers run times that are significantly faster than other well-established sparse precision matrix estimation packages. Furthermore, we showcase the application of the introduced package in classifying microarray gene expressions. We demonstrate that by utilizing a matrix form of the tuning parameter (also known as the regularization parameter), SQUIC can effectively incorporate prior information into the estimation procedure, resulting in improved application results with minimal computational overhead.

我们提出斯奎克，一个用于稀疏精度矩阵估计的快速且可扩展的包。该算法采用二阶方法，利用高度优化的线性代数子例程来解决 \(\ell_{1}\) 正则化最大似然问题。在使用合成数据集的比较测试中，我们证明了斯奎克不仅可以扩展到多达一百万个随机变量的数据集，而且始终提供比其他成熟的稀疏精度矩阵估计包快得多的运行时间。此外，我们展示了引入的包在微阵列基因表达分类中的应用。我们证明，通过利用调整参数（也称为正则化参数）的矩阵形式，斯奎克可以有效地将先验信息纳入估计过程，从而以最小的计算开销改善应用结果。