Large-scale l0 sparse inverse covariance estimation

Abstract

There has been significant interest in sparse inverse covariance estimation in areas such as statistics, machine learning, and signal processing. In this problem, the sparse inverse of a covariance matrix of a multivariate normal distribution is estimated. A Penalised Log-Likelihood (PLL) optimisation problem is solved to obtain the matrix estimator, where the penalty is responsible for inducing sparsity. The most natural sparsity promoting penalty is the non-convex l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> function. Due to speed and memory limitations, the existing algorithms for dealing with the non-convex l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> PLL problem are unable to be used in high dimensional settings. Here we address this issue by presenting a new block iterative approach for this problem, which can handle large-scale data sizes. Simulations demonstrate that our approach outperforms existing methods for this problem.