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King Abdullah University of Science and Technology
Parallel Selected Inversion and Gradient Estimation for Space-Time Gaussian Markov Random Fields
Performing a Bayesian inference on large spatio-temporal models requires computing the inverse elements and the log-determinant of large sparse precision matrices. Direct matrix factorizations such as Cholesky decomposition fail to scale well for large distributed problems. On the contrary, iterative approaches for the selected inversion and trace estimation have been gaining traction. We propose a parallel hybrid approach based on domain decomposition, which extends the Rao-Blackwellized Monte Carlo estimator for distributed precision matrices. Our approach exploits the strength of iterative Krylov methods as global solvers and efficiency of direct factorizations as local solvers to compute the selected inverse using a divide-and-conquer strategy. The gradient can then be computed from the approximated inverse. We demonstrate the scaling on a simulated dataset and apply the inversion algorithm on massive US daily temperature data.
|December 20, 2023 (Wed) 14:00 - 15:00