Implementable confidence sets in high dimensional regression

Alexandra Carpentier
Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics, PMLR 38:120-128, 2015.

Abstract

We consider the setting of linear regression in high dimension. We focus on the problem of constructing adaptive and honest confidence sets for the sparse parameter θ, i.e. we want to construct a confidence set for theta that contains theta with high probability, and that is as small as possible. The l_2 diameter of a such confidence set should depend on the sparsity S of θ- the larger S, the wider the confidence set. However, in practice, S is unknown. This paper focuses on constructing a confidence set for θwhich contains θwith high probability, whose diameter is adaptive to the unknown sparsity S, and which is implementable in practice.

Cite this Paper

BibTeX
@InProceedings{pmlr-v38-carpentier15, title = {{Implementable confidence sets in high dimensional regression}}, author = {Carpentier, Alexandra}, booktitle = {Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics}, pages = {120--128}, year = {2015}, editor = {Lebanon, Guy and Vishwanathan, S. V. N.}, volume = {38}, series = {Proceedings of Machine Learning Research}, address = {San Diego, California, USA}, month = {09--12 May}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v38/carpentier15.pdf}, url = {https://proceedings.mlr.press/v38/carpentier15.html}, abstract = {We consider the setting of linear regression in high dimension. We focus on the problem of constructing adaptive and honest confidence sets for the sparse parameter θ, i.e. we want to construct a confidence set for theta that contains theta with high probability, and that is as small as possible. The l_2 diameter of a such confidence set should depend on the sparsity S of θ- the larger S, the wider the confidence set. However, in practice, S is unknown. This paper focuses on constructing a confidence set for θwhich contains θwith high probability, whose diameter is adaptive to the unknown sparsity S, and which is implementable in practice.} }
Endnote
%0 Conference Paper %T Implementable confidence sets in high dimensional regression %A Alexandra Carpentier %B Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2015 %E Guy Lebanon %E S. V. N. Vishwanathan %F pmlr-v38-carpentier15 %I PMLR %P 120--128 %U https://proceedings.mlr.press/v38/carpentier15.html %V 38 %X We consider the setting of linear regression in high dimension. We focus on the problem of constructing adaptive and honest confidence sets for the sparse parameter θ, i.e. we want to construct a confidence set for theta that contains theta with high probability, and that is as small as possible. The l_2 diameter of a such confidence set should depend on the sparsity S of θ- the larger S, the wider the confidence set. However, in practice, S is unknown. This paper focuses on constructing a confidence set for θwhich contains θwith high probability, whose diameter is adaptive to the unknown sparsity S, and which is implementable in practice.
RIS
TY - CPAPER TI - Implementable confidence sets in high dimensional regression AU - Alexandra Carpentier BT - Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics DA - 2015/02/21 ED - Guy Lebanon ED - S. V. N. Vishwanathan ID - pmlr-v38-carpentier15 PB - PMLR DP - Proceedings of Machine Learning Research VL - 38 SP - 120 EP - 128 L1 - http://proceedings.mlr.press/v38/carpentier15.pdf UR - https://proceedings.mlr.press/v38/carpentier15.html AB - We consider the setting of linear regression in high dimension. We focus on the problem of constructing adaptive and honest confidence sets for the sparse parameter θ, i.e. we want to construct a confidence set for theta that contains theta with high probability, and that is as small as possible. The l_2 diameter of a such confidence set should depend on the sparsity S of θ- the larger S, the wider the confidence set. However, in practice, S is unknown. This paper focuses on constructing a confidence set for θwhich contains θwith high probability, whose diameter is adaptive to the unknown sparsity S, and which is implementable in practice. ER -
APA
Carpentier, A.. (2015). Implementable confidence sets in high dimensional regression. Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 38:120-128 Available from https://proceedings.mlr.press/v38/carpentier15.html.

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