Scalable sparse covariance estimation via self-concordance
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We consider the class of convex minimization problems, composed of a self-concordant function, such as the metric, a convex data fidelity term h(·) and, a regularizing -- possibly non-smooth -- function g(·). This type of problems have recently attracted a great deal of interest, mainly due to their omnipresence in top-notch applications. Under this 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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