Abstract
Analytic shrinkage is a statistical technique that offers a fast alternative to crossvalidation for the regularization of covariance matrices and has appealing consistency properties. We show that the proof of consistency requires bounds on the growth rates of eigenvalues and their dispersion, which are often violated in data. We prove consistency under assumptions which do not restrict the covariance structure and therefore better match real world data. In addition, we propose an extension of analytic shrinkage-orthogonal complement shrinkage-which adapts to the covariance structure. Finally we demonstrate the superior performance of our novel approach on data from the domains of finance, spoken letter and optical character recognition, and neuroscience.
| Original language | English |
|---|---|
| Title of host publication | Advances in Neural Information Processing Systems |
| Publisher | Neural information processing systems foundation |
| Publication status | Published - 2013 |
| Event | 27th Annual Conference on Neural Information Processing Systems, NIPS 2013 - Lake Tahoe, NV, United States Duration: 2013 Dec 5 → 2013 Dec 10 |
Other
| Other | 27th Annual Conference on Neural Information Processing Systems, NIPS 2013 |
|---|---|
| Country | United States |
| City | Lake Tahoe, NV |
| Period | 13/12/5 → 13/12/10 |
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ASJC Scopus subject areas
- Computer Networks and Communications
- Information Systems
- Signal Processing
Cite this
Generalizing analytic shrinkage for arbitrary covariance structures. / Bartz, Daniel; Muller, Klaus.
Advances in Neural Information Processing Systems. Neural information processing systems foundation, 2013.Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
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TY - GEN
T1 - Generalizing analytic shrinkage for arbitrary covariance structures
AU - Bartz, Daniel
AU - Muller, Klaus
PY - 2013
Y1 - 2013
N2 - Analytic shrinkage is a statistical technique that offers a fast alternative to crossvalidation for the regularization of covariance matrices and has appealing consistency properties. We show that the proof of consistency requires bounds on the growth rates of eigenvalues and their dispersion, which are often violated in data. We prove consistency under assumptions which do not restrict the covariance structure and therefore better match real world data. In addition, we propose an extension of analytic shrinkage-orthogonal complement shrinkage-which adapts to the covariance structure. Finally we demonstrate the superior performance of our novel approach on data from the domains of finance, spoken letter and optical character recognition, and neuroscience.
AB - Analytic shrinkage is a statistical technique that offers a fast alternative to crossvalidation for the regularization of covariance matrices and has appealing consistency properties. We show that the proof of consistency requires bounds on the growth rates of eigenvalues and their dispersion, which are often violated in data. We prove consistency under assumptions which do not restrict the covariance structure and therefore better match real world data. In addition, we propose an extension of analytic shrinkage-orthogonal complement shrinkage-which adapts to the covariance structure. Finally we demonstrate the superior performance of our novel approach on data from the domains of finance, spoken letter and optical character recognition, and neuroscience.
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M3 - Conference contribution
AN - SCOPUS:84898987337
BT - Advances in Neural Information Processing Systems
PB - Neural information processing systems foundation
ER -