Intersecting singularities for multi-structured estimation

Emile Richard, Francis BACH, Jean-Philippe Vert
; Proceedings of the 30th International Conference on Machine Learning, PMLR 28(3):1157-1165, 2013.

Abstract

We address the problem of designing a convex nonsmooth regularizer encouraging multiple structural effects simultaneously. Focusing on the inference of sparse and low-rank matrices we suggest a new complexity index and a convex penalty approximating it. The new penalty term can be written as the trace norm of a linear function of the matrix. By analyzing theoretical properties of this family of regularizers we come up with oracle inequalities and compressed sensing results ensuring the quality of our regularized estimator. We also provide algorithms and supporting numerical experiments.

Cite this Paper


BibTeX
@InProceedings{pmlr-v28-richard13, title = {Intersecting singularities for multi-structured estimation}, author = {Emile Richard and Francis BACH and Jean-Philippe Vert}, booktitle = {Proceedings of the 30th International Conference on Machine Learning}, pages = {1157--1165}, year = {2013}, editor = {Sanjoy Dasgupta and David McAllester}, volume = {28}, number = {3}, series = {Proceedings of Machine Learning Research}, address = {Atlanta, Georgia, USA}, month = {17--19 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v28/richard13.pdf}, url = {http://proceedings.mlr.press/v28/richard13.html}, abstract = {We address the problem of designing a convex nonsmooth regularizer encouraging multiple structural effects simultaneously. Focusing on the inference of sparse and low-rank matrices we suggest a new complexity index and a convex penalty approximating it. The new penalty term can be written as the trace norm of a linear function of the matrix. By analyzing theoretical properties of this family of regularizers we come up with oracle inequalities and compressed sensing results ensuring the quality of our regularized estimator. We also provide algorithms and supporting numerical experiments.} }
Endnote
%0 Conference Paper %T Intersecting singularities for multi-structured estimation %A Emile Richard %A Francis BACH %A Jean-Philippe Vert %B Proceedings of the 30th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2013 %E Sanjoy Dasgupta %E David McAllester %F pmlr-v28-richard13 %I PMLR %J Proceedings of Machine Learning Research %P 1157--1165 %U http://proceedings.mlr.press %V 28 %N 3 %W PMLR %X We address the problem of designing a convex nonsmooth regularizer encouraging multiple structural effects simultaneously. Focusing on the inference of sparse and low-rank matrices we suggest a new complexity index and a convex penalty approximating it. The new penalty term can be written as the trace norm of a linear function of the matrix. By analyzing theoretical properties of this family of regularizers we come up with oracle inequalities and compressed sensing results ensuring the quality of our regularized estimator. We also provide algorithms and supporting numerical experiments.
RIS
TY - CPAPER TI - Intersecting singularities for multi-structured estimation AU - Emile Richard AU - Francis BACH AU - Jean-Philippe Vert BT - Proceedings of the 30th International Conference on Machine Learning PY - 2013/02/13 DA - 2013/02/13 ED - Sanjoy Dasgupta ED - David McAllester ID - pmlr-v28-richard13 PB - PMLR SP - 1157 DP - PMLR EP - 1165 L1 - http://proceedings.mlr.press/v28/richard13.pdf UR - http://proceedings.mlr.press/v28/richard13.html AB - We address the problem of designing a convex nonsmooth regularizer encouraging multiple structural effects simultaneously. Focusing on the inference of sparse and low-rank matrices we suggest a new complexity index and a convex penalty approximating it. The new penalty term can be written as the trace norm of a linear function of the matrix. By analyzing theoretical properties of this family of regularizers we come up with oracle inequalities and compressed sensing results ensuring the quality of our regularized estimator. We also provide algorithms and supporting numerical experiments. ER -
APA
Richard, E., BACH, F. & Vert, J.. (2013). Intersecting singularities for multi-structured estimation. Proceedings of the 30th International Conference on Machine Learning, in PMLR 28(3):1157-1165

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