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Archive / INF Seminars / INF_2025_06_02_VeronicaVinciotti

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	Penalized covariance estimation in high dimensions

Host: Wit Ernst-Jan Camiel

Monday

02.06

USI Campus EST, Room D5.01

12:30 - 13:30


	Prof. Veronica Vinciotti University of Trento

Abstract: This talk considers the problem of estimation of a covariance matrix for multivariate Gaussian data in a high dimensional setting. Existing approaches include maximum likelihood estimation under a prespecified sparsity pattern, l_1-penalized loglikelihood optimization and ridge regularization of the sample covariance. These three approaches can be addressed in a unified way by considering the constrained optimization of an objective function that involves two suitably defined penalty terms. This unified procedure exploits the advantages of each individual approach, while bringing novelty in the combination of the three. We provide an efficient algorithm for the optimization of the regularized objective function and describe the relationship between the two penalty terms, thereby highlighting the importance of the joint application of the three methods. In particular, the sparse estimates of covariance matrices returned by the procedure are stable and accurate, both in low and high dimensional settings, and their calculation is more efficient than existing approaches under a partially known sparsity pattern. An illustration on sonar data is presented for the identification of the covariance structure among signals bounced off a certain material. The method is implemented in the publicly available R package gicf.

Biography: In 2003, Veronica Vinciotti received a PhD in statistics from Imperial College London. She then worked as a postgraduate researcher at the department of computer science at Brunel University London until 2007, when she joined the department of mathematics as a permanent member of staff and progressed to reader in 2017. Since 2020, she has been an associate professor in statistics at the department of mathematics at the University of Trento.