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We propose a novel quasi-Newton method for solving the sparse inversecovariance estimation problem also known as the graphical least absoluteshrinkage and selection operator (GLASSO). This problem is often solved using asecond-order quadratic approximation. However, in such algorithms the Hessianterm is complex and computationally expensive to handle. Therefore, our methoduses the inverse of the Hessian as a preconditioner to simplify and approximatethe quadratic element at the cost of a more complex \(\ell_1\) element. Thevariables of the resulting preconditioned problem are coupled only by the\(\ell_1\) sub-derivative of each other, which can be guessed with minimal costusing the gradient itself, allowing the algorithm to be parallelized andimplemented efficiently on GPU hardware accelerators. Numerical results onsynthetic and real data demonstrate that our method is competitive with otherstate-of-the-art approaches.

pISTA: preconditioned Iterative Soft Thresholding Algorithm for Graphical Lasso