Bertsimas, D, Lamperski, J and Pauphilet, J (2020) Certifiably optimal sparse inverse covariance estimation. Mathematical Programming, 184 (1-2). pp. 491-530. ISSN 0025-5610
Abstract
We consider the maximum likelihood estimation of sparse inverse covariance matrices. We demonstrate that current heuristic approaches primarily encourage robustness, instead of the desired sparsity. We give a novel approach that solves the cardinality constrained likelihood problem to certifiable optimality. The approach uses techniques from mixed-integer optimization and convex optimization, and provides a high-quality solution with a guarantee on its suboptimality, even if the algorithm is terminated early. Using a variety of synthetic and real datasets, we demonstrate that our approach can solve problems where the dimension of the inverse covariance matrix is up to 1000 s. We also demonstrate that our approach produces significantly sparser solutions than Glasso and other popular learning procedures, makes less false discoveries, while still maintaining state-of-the-art accuracy.
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Item Type: | Article |
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Subject Areas: | Management Science and Operations |
Additional Information: |
© 2020 Springer Nature |
Date Deposited: | 23 Nov 2020 09:40 |
Subjects: | Mathematical programming |
Last Modified: | 21 Nov 2024 02:24 |
URI: | https://lbsresearch.london.edu/id/eprint/1561 |