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pISTA: preconditioned Iterative Soft Thresholding Algorithm for Graphical Lasso
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Gal Shalom
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Wednesday, 26.01.2022, 10:30
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Zoom Lecture: 91228689582

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. To this end,our algorithm uses the inverse of the Hessian as a preconditioner to simplify and approximate the quadratic element at the cost of a more complex l1 element. The variables of the resulting preconditioned problem are coupled only by the l1 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.