Scalable sparse covariance estimation via self-concordance
  We consider the class of convex minimization problems, composed of a self-concordant function, such as the $\log\det$ metric, a convex data fidelity term $h(\cdot)$ and, a regularizing -- possibly non-smooth -- function $g(\cdot)$. This type of problems have recently attracted a great deal of interest, mainly due to their omnipresence in top-notch applications. Under this \emph{locally} Lipschitz continuous gradient setting, we analyze the convergence behavior of proximal Newton schemes with the added twist of a probable presence of inexact evaluations. We prove attractive convergence rate guarantees and enhance state-of-the-art optimization schemes to accommodate such developments. Experimental results on sparse covariance estimation show the merits of our algorithm, both in terms of recovery efficiency and complexity. 
Anastasios Kyrillidis and Rabeeh Karimi Mahabadi and Quoc Tran-Dinh   and Volkan Cevher
stat.ML cs.IT math.IT math.OC