We consider the problem of estimating sparse inverse covariance matrices for high-dimensional datasets using the L1-regularized Gaussian maximum likelihood method. This task is particularly challenging as the required computational resources increase superlinearly with the dimensionality of the dataset. We introduce a performant and scalable algorithm which builds on the current advancements of second-order, maximum likelihood methods. The routine leverages the intrinsic parallelism in the linear algebra operations and exploits the underlying sparsity of the problem. The computational bottlenecks are identified and the respective subroutines are parallelized using an MPI-OpenMP approach. Numerical examples conducted on a 5,320 node Cray XC50 system at the Swiss National Supercomputing Center show that, in comparison to the state-of-the-art algorithms, the proposed routine provides significant strong-scaling speedup with ideal scalability up to 128 nodes. The developed framework is used to approximate the sparse inverse covariance matrix of both synthetic and real-world datasets with up to 10 million dimensions.
Proceedings of the ACM/IEEE International Conference on High Performance Computing, Networking, Storage and Analysis