Random Matrix Improved Covariance Estimation for a Large Class of Metrics

Malik Tiomoko, Romain Couillet, Florent Bouchard, Guillaume Ginolhac
Proceedings of the 36th International Conference on Machine Learning, PMLR 97:6254-6263, 2019.

Abstract

Relying on recent advances in statistical estimation of covariance distances based on random matrix theory, this article proposes an improved covariance and precision matrix estimation for a wide family of metrics. The method is shown to largely outperform the sample covariance matrix estimate and to compete with state-of-the-art methods, while at the same time being computationally simpler and faster. Applications to linear and quadratic discriminant analyses also show significant gains, therefore suggesting practical interest to statistical machine learning.

Cite this Paper

BibTeX
@InProceedings{pmlr-v97-tiomoko19a, title = {Random Matrix Improved Covariance Estimation for a Large Class of Metrics}, author = {Tiomoko, Malik and Couillet, Romain and Bouchard, Florent and Ginolhac, Guillaume}, booktitle = {Proceedings of the 36th International Conference on Machine Learning}, pages = {6254--6263}, year = {2019}, editor = {Chaudhuri, Kamalika and Salakhutdinov, Ruslan}, volume = {97}, series = {Proceedings of Machine Learning Research}, month = {09--15 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v97/tiomoko19a/tiomoko19a.pdf}, url = {https://proceedings.mlr.press/v97/tiomoko19a.html}, abstract = {Relying on recent advances in statistical estimation of covariance distances based on random matrix theory, this article proposes an improved covariance and precision matrix estimation for a wide family of metrics. The method is shown to largely outperform the sample covariance matrix estimate and to compete with state-of-the-art methods, while at the same time being computationally simpler and faster. Applications to linear and quadratic discriminant analyses also show significant gains, therefore suggesting practical interest to statistical machine learning.} }
Endnote
%0 Conference Paper %T Random Matrix Improved Covariance Estimation for a Large Class of Metrics %A Malik Tiomoko %A Romain Couillet %A Florent Bouchard %A Guillaume Ginolhac %B Proceedings of the 36th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Ruslan Salakhutdinov %F pmlr-v97-tiomoko19a %I PMLR %P 6254--6263 %U https://proceedings.mlr.press/v97/tiomoko19a.html %V 97 %X Relying on recent advances in statistical estimation of covariance distances based on random matrix theory, this article proposes an improved covariance and precision matrix estimation for a wide family of metrics. The method is shown to largely outperform the sample covariance matrix estimate and to compete with state-of-the-art methods, while at the same time being computationally simpler and faster. Applications to linear and quadratic discriminant analyses also show significant gains, therefore suggesting practical interest to statistical machine learning.
APA
Tiomoko, M., Couillet, R., Bouchard, F. & Ginolhac, G.. (2019). Random Matrix Improved Covariance Estimation for a Large Class of Metrics. Proceedings of the 36th International Conference on Machine Learning, in Proceedings of Machine Learning Research 97:6254-6263 Available from https://proceedings.mlr.press/v97/tiomoko19a.html.

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