ICML 2017poster27 citations
How Close Are the Eigenvectors of the Sample and Actual Covariance Matrices?
Abstract
How many samples are sufficient to guarantee that the eigenvectors of the sample covariance matrix are close to those of the actual covariance matrix? For a wide family of distributions, including distributions with finite second moment and sub-gaussian distributions supported in a centered Euclidean ball, we prove that the inner product between eigenvectors of the sample and actual covariance matrices decreases proportionally to the respective eigenvalue distance and the number of samples. Our findings imply
BibTeX
@InProceedings{pmlr-v70-loukas17a,
title = {How Close Are the Eigenvectors of the Sample and Actual Covariance Matrices?},
author = {Andreas Loukas},
booktitle = {Proceedings of the 34th International Conference on Machine Learning},
pages = {2228--2237},
year = {2017},
editor = {Precup, Doina and Teh, Yee Whye},
volume = {70},
series = {Proceedings of Machine Learning Research},
month = {06--11 Aug},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v70/loukas17a/loukas17a.pdf},
url = {https://proceedings.mlr.press/v70/loukas17a.html},
abstract = {How many samples are sufficient to guarantee that the eigenvectors of the sample covariance matrix are close to those of the actual covariance matrix? For a wide family of distributions, including distributions with finite second moment and sub-gaussian distributions supported in a centered Euclidean ball, we prove that the inner product between eigenvectors of the sample and actual covariance matrices decreases proportionally to the respective eigenvalue distance and the number of samples. Our findings imply