Interplay of minimax estimation and minimax support recovery under sparsity

Mohamed Ndaoud
; Proceedings of the 30th International Conference on Algorithmic Learning Theory, PMLR 98:647-668, 2019.

Abstract

In this paper, we study a new notion of scaled minimaxity for sparse estimation in high-dimensional linear regression model. We present more optimistic lower bounds than the one given by the classical minimax theory and hence improve on existing results. We recover sharp results for the global minimaxity as a consequence of our study. Fixing the scale of the signal-to-noise ratio, we prove that the estimation error can be much smaller than the global minimax error. We construct a new optimal estimator for the scaled minimax sparse estimation. An optimal adaptive procedure is also described.

Cite this Paper


BibTeX
@InProceedings{pmlr-v98-ndaoud19a, title = {Interplay of minimax estimation and minimax support recovery under sparsity}, author = {Ndaoud, Mohamed}, booktitle = {Proceedings of the 30th International Conference on Algorithmic Learning Theory}, pages = {647--668}, year = {2019}, editor = {Aurélien Garivier and Satyen Kale}, volume = {98}, series = {Proceedings of Machine Learning Research}, address = {Chicago, Illinois}, month = {22--24 Mar}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v98/ndaoud19a/ndaoud19a.pdf}, url = {http://proceedings.mlr.press/v98/ndaoud19a.html}, abstract = {In this paper, we study a new notion of scaled minimaxity for sparse estimation in high-dimensional linear regression model. We present more optimistic lower bounds than the one given by the classical minimax theory and hence improve on existing results. We recover sharp results for the global minimaxity as a consequence of our study. Fixing the scale of the signal-to-noise ratio, we prove that the estimation error can be much smaller than the global minimax error. We construct a new optimal estimator for the scaled minimax sparse estimation. An optimal adaptive procedure is also described. } }
Endnote
%0 Conference Paper %T Interplay of minimax estimation and minimax support recovery under sparsity %A Mohamed Ndaoud %B Proceedings of the 30th International Conference on Algorithmic Learning Theory %C Proceedings of Machine Learning Research %D 2019 %E Aurélien Garivier %E Satyen Kale %F pmlr-v98-ndaoud19a %I PMLR %J Proceedings of Machine Learning Research %P 647--668 %U http://proceedings.mlr.press %V 98 %W PMLR %X In this paper, we study a new notion of scaled minimaxity for sparse estimation in high-dimensional linear regression model. We present more optimistic lower bounds than the one given by the classical minimax theory and hence improve on existing results. We recover sharp results for the global minimaxity as a consequence of our study. Fixing the scale of the signal-to-noise ratio, we prove that the estimation error can be much smaller than the global minimax error. We construct a new optimal estimator for the scaled minimax sparse estimation. An optimal adaptive procedure is also described.
APA
Ndaoud, M.. (2019). Interplay of minimax estimation and minimax support recovery under sparsity. Proceedings of the 30th International Conference on Algorithmic Learning Theory, in PMLR 98:647-668

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