Title: Communication-Avoiding Optimization Methods for Distributed Massive-Scale Sparse Inverse Covariance Estimation,
Abstract: Across a variety of scientific disciplines, sparse inverse covariance
estimation is a popular tool for capturing the underlying dependency
relationships in multivariate data. Unfortunately, most estimators are not
scalable enough to handle the sizes of modern high-dimensional data sets (often
on the order of terabytes), and assume Gaussian samples. To address these
deficiencies, we introduce HP-CONCORD, a highly scalable optimization method
for estimating a sparse inverse covariance matrix based on a regularized
pseudolikelihood framework, without assuming Gaussianity. Our parallel proximal
gradient method uses a novel communication-avoiding linear algebra algorithm
and runs across a multi-node cluster with up to 1k nodes (24k cores), achieving
parallel scalability on problems with up to ~819 billion parameters (1.28
million dimensions); even on a single node, HP-CONCORD demonstrates
scalability, outperforming a state-of-the-art method. We also use HP-CONCORD to
estimate the underlying dependency structure of the brain from fMRI data, and
use the result to identify functional regions automatically. The results show
good agreement with a clustering from the neuroscience literature.