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Certifiably optimal sparse inverse covariance estimation
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10107_2019_1419_ReferencePDF.pdf
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1007.14 KB
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Adobe PDF
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b7835217c86fbffab1a7f990faafb8c5
Author(s)
Bertsimas, Dimitris
Lamperski, Jourdain
Pauphilet, Jean
Date Issued
August 17, 2019
Publisher
Springer Berlin Heidelberg
Version
Author's final manuscript
Abstract
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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Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s10107-019-01419-7
