Back to Search
Start Over
Unified Low-Rank Matrix Estimate via Penalized Matrix Least Squares Approximation.
- Source :
- IEEE Transactions on Neural Networks & Learning Systems; Feb2019, Vol. 30 Issue 2, p474-485, 12p
- Publication Year :
- 2019
-
Abstract
- Low-rank matrix estimation arises in a number of statistical and machine learning tasks. In particular, the coefficient matrix is considered to have a low-rank structure in multivariate linear regression and multivariate quantile regression. In this paper, we propose a method called penalized matrix least squares approximation (PMLSA) toward a unified yet simple low-rank matrix estimate. Specifically, PMLSA can transform many different types of low-rank matrix estimation problems into their asymptotically equivalent least-squares forms, which can be efficiently solved by a popular matrix fast iterative shrinkage-thresholding algorithm. Furthermore, we derive analytic degrees of freedom for PMLSA, with which a Bayesian information criterion (BIC)-type criterion is developed to select the tuning parameters. The estimated rank based on the BIC-type criterion is verified to be asymptotically consistent with the true rank under mild conditions. Extensive experimental studies are performed to confirm our assertion. [ABSTRACT FROM AUTHOR]
- Subjects :
- LOW-rank matrices
APPROXIMATION theory
MACHINE learning
Subjects
Details
- Language :
- English
- ISSN :
- 2162237X
- Volume :
- 30
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- IEEE Transactions on Neural Networks & Learning Systems
- Publication Type :
- Periodical
- Accession number :
- 134278832
- Full Text :
- https://doi.org/10.1109/TNNLS.2018.2844242