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On the Solution of ℓ0-Constrained Sparse Inverse Covariance Estimation Problems.
- Source :
-
INFORMS Journal on Computing . Spring2021, Vol. 33 Issue 2, p531-550. 20p. - Publication Year :
- 2021
-
Abstract
- The sparse inverse covariance matrix is used to model conditional dependencies between variables in a graphical model to fit a multivariate Gaussian distribution. Estimating the matrix from data are well known to be computationally expensive for large-scale problems. Sparsity is employed to handle noise in the data and to promote interpretability of a learning model. Although the use of a convex ℓ1 regularizer to encourage sparsity is common practice, the combinatorial ℓ0 penalty often has more favorable statistical properties. In this paper, we directly constrain sparsity by specifying a maximally allowable number of nonzeros, in other words, by imposing an ℓ0 constraint. We introduce an efficient approximate Newton algorithm using warm starts for solving the nonconvex ℓ0-constrained inverse covariance learning problem. Numerical experiments on standard data sets show that the performance of the proposed algorithm is competitive with state-of-the-art methods. Summary of Contribution: The inverse covariance estimation problem underpins many domains, including statistics, operations research, and machine learning. We propose a scalable optimization algorithm for solving the nonconvex ℓ0-constrained problem. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10919856
- Volume :
- 33
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- INFORMS Journal on Computing
- Publication Type :
- Academic Journal
- Accession number :
- 150564777
- Full Text :
- https://doi.org/10.1287/ijoc.2020.0991