In this paper, we study sparse inverse covariance matrix estimation incorporating partly smooth nonconvex regularizers. To solve the resulting regularized log-determinant problem, we develop DIIR-QUIC—a novel Damped Inexact Iteratively Reweighted algorithm based on QUadratic approximate Inverse Covariance (QUIC) method. Our approach generalizes the classic iteratively reweighted \(\ell_1\) scheme through damped fixed-point updates. A key novelty of DIIR-QUIC is an inexact termination criterion for the subproblems that permits controlled inexactness in solutions to accelerate each iteration while still guaranteeing identification of the active manifold in finitely many steps. We establish the global convergence of DIIR-QUIC and, under the Kurdyka-\L{}ojasiewicz property, prove Q-linear convergence of the perturbed objective values and R-linear convergence of the iterates. Extensive numerical experiments on synthetic and real-world datasets demonstrate that DIIR-QUIC outperforms existing approaches in computational efficiency and estimation accuracy.
Efficient QUIC-Based Damped Inexact Iterative Reweighting for Sparse Inverse Covariance Estimation with Nonconvex Partly Smooth Regularization
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