论文标题
Pista：图形套索的预处理迭代软阈值算法
pISTA: preconditioned Iterative Soft Thresholding Algorithm for Graphical Lasso
论文作者
论文摘要
我们提出了一种新型的准Newton方法，用于解决稀疏的逆协方差估计问题，也称为图形最小的绝对收缩和选择算子（Glasso）。通常使用二阶二次近似解决此问题。但是，在这样的算法中，Hessian术语很复杂且计算昂贵。因此，我们的方法将Hessian的倒数用作预处理，以更复杂的\（\ ell_1 \）元素的成本简化和近似二次元素。仅由\（\ ell_1 \）彼此的子衍生物耦合到所得的预处理问题的变量，可以使用梯度本身以最低的成本来猜测，算法可以在GPU硬件加速器上有效地平行和实现算法。关于合成和实际数据的数值结果表明，我们的方法与其他最先进的方法具有竞争力。
We propose a novel quasi-Newton method for solving the sparse inverse covariance estimation problem also known as the graphical least absolute shrinkage and selection operator (GLASSO). This problem is often solved using a second-order quadratic approximation. However, in such algorithms the Hessian term is complex and computationally expensive to handle. Therefore, our method uses the inverse of the Hessian as a preconditioner to simplify and approximate the quadratic element at the cost of a more complex \(\ell_1\) element. The variables of the resulting preconditioned problem are coupled only by the \(\ell_1\) sub-derivative of each other, which can be guessed with minimal cost using the gradient itself, allowing the algorithm to be parallelized and implemented efficiently on GPU hardware accelerators. Numerical results on synthetic and real data demonstrate that our method is competitive with other state-of-the-art approaches.
