SC18 - Distributed Memory Sparse Inverse Covariance Matrix Estimation on High-Performance Computing Architectures

The ?1-regularized Gaussian maximum likelihood estimator (MLE) has been shown to have strong statistical guarantees in recovering a sparse inverse covariance matrix, or alternatively the underlying graph structure of a Gaussian Markov Random Field, from very limited samples. In our SC18 paper 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. 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.