Scalable sparse covariance estimation via self-concordance

Anastasios Kyrillidis; Rabeeh Karimi Mahabadi; Quoc Tran-Dinh; Volkan Cevher

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arXiv · 1405.3263

Scalable sparse covariance estimation via self-concordance

Anastasios Kyrillidis·Rabeeh Karimi Mahabadi·Quoc Tran-Dinh·Volkan Cevher

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Abstract

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.

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BibTeX RIS

Anastasios Kyrillidis, Rabeeh Karimi Mahabadi, Quoc Tran-Dinh, Volkan Cevher. 2014-05-13. Scalable sparse covariance estimation via self-concordance. https://arxiv.org/abs/1405.3263

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