Sparse projections onto the simplex

Anastasios Kyrillidis, Stephen Becker, Volkan Cevher, Christoph Koch
; Proceedings of the 30th International Conference on Machine Learning, PMLR 28(2):235-243, 2013.

Abstract

Most learning methods with rank or sparsity constraints use convex relaxations, which lead to optimization with the nuclear norm or the \ell_1-norm. However, several important learning applications cannot benefit from this approach as they feature these convex norms as constraints in addition to the non-convex rank and sparsity constraints. In this setting, we derive efficient sparse projections onto the simplex and its extension, and illustrate how to use them to solve high-dimensional learning problems in quantum tomography, sparse density estimation and portfolio selection with non-convex constraints.

Cite this Paper


BibTeX
@InProceedings{pmlr-v28-kyrillidis13, title = {Sparse projections onto the simplex}, author = {Anastasios Kyrillidis and Stephen Becker and Volkan Cevher and Christoph Koch}, booktitle = {Proceedings of the 30th International Conference on Machine Learning}, pages = {235--243}, year = {2013}, editor = {Sanjoy Dasgupta and David McAllester}, volume = {28}, number = {2}, series = {Proceedings of Machine Learning Research}, address = {Atlanta, Georgia, USA}, month = {17--19 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v28/kyrillidis13.pdf}, url = {http://proceedings.mlr.press/v28/kyrillidis13.html}, abstract = {Most learning methods with rank or sparsity constraints use convex relaxations, which lead to optimization with the nuclear norm or the \ell_1-norm. However, several important learning applications cannot benefit from this approach as they feature these convex norms as constraints in addition to the non-convex rank and sparsity constraints. In this setting, we derive efficient sparse projections onto the simplex and its extension, and illustrate how to use them to solve high-dimensional learning problems in quantum tomography, sparse density estimation and portfolio selection with non-convex constraints.} }
Endnote
%0 Conference Paper %T Sparse projections onto the simplex %A Anastasios Kyrillidis %A Stephen Becker %A Volkan Cevher %A Christoph Koch %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-kyrillidis13 %I PMLR %J Proceedings of Machine Learning Research %P 235--243 %U http://proceedings.mlr.press %V 28 %N 2 %W PMLR %X Most learning methods with rank or sparsity constraints use convex relaxations, which lead to optimization with the nuclear norm or the \ell_1-norm. However, several important learning applications cannot benefit from this approach as they feature these convex norms as constraints in addition to the non-convex rank and sparsity constraints. In this setting, we derive efficient sparse projections onto the simplex and its extension, and illustrate how to use them to solve high-dimensional learning problems in quantum tomography, sparse density estimation and portfolio selection with non-convex constraints.
RIS
TY - CPAPER TI - Sparse projections onto the simplex AU - Anastasios Kyrillidis AU - Stephen Becker AU - Volkan Cevher AU - Christoph Koch 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-kyrillidis13 PB - PMLR SP - 235 DP - PMLR EP - 243 L1 - http://proceedings.mlr.press/v28/kyrillidis13.pdf UR - http://proceedings.mlr.press/v28/kyrillidis13.html AB - Most learning methods with rank or sparsity constraints use convex relaxations, which lead to optimization with the nuclear norm or the \ell_1-norm. However, several important learning applications cannot benefit from this approach as they feature these convex norms as constraints in addition to the non-convex rank and sparsity constraints. In this setting, we derive efficient sparse projections onto the simplex and its extension, and illustrate how to use them to solve high-dimensional learning problems in quantum tomography, sparse density estimation and portfolio selection with non-convex constraints. ER -
APA
Kyrillidis, A., Becker, S., Cevher, V. & Koch, C.. (2013). Sparse projections onto the simplex. Proceedings of the 30th International Conference on Machine Learning, in PMLR 28(2):235-243

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