Estimation of the covariance structure of heavy-tailed distributions

Xiaohan Wei; Stanislav Minsker

NeurIPS 2017poster47 citations

Estimation of the covariance structure of heavy-tailed distributions

Abstract

We propose and analyze a new estimator of the covariance matrix that admits strong theoretical guarantees under weak assumptions on the underlying distribution, such as existence of moments of only low order. While estimation of covariance matrices corresponding to sub-Gaussian distributions is well-understood, much less in known in the case of heavy-tailed data. As K. Balasubramanian and M. Yuan write,

BibTeX

@inproceedings{NIPS2017_10c272d0,
 author = {Wei, Xiaohan and Minsker, Stanislav},
 booktitle = {Advances in Neural Information Processing Systems},
 editor = {I. Guyon and U. Von Luxburg and S. Bengio and H. Wallach and R. Fergus and S. Vishwanathan and R. Garnett},
 pages = {},
 publisher = {Curran Associates, Inc.},
 title = {Estimation of the covariance structure of heavy-tailed distributions},
 url = {https://proceedings.neurips.cc/paper_files/paper/2017/file/10c272d06794d3e5785d5e7c5356e9ff-Paper.pdf},
 volume = {30},
 year = {2017}
}