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Sparse projections onto the simplex

Anastasios Kyrillidis, Stephen Becker, Volkan Cevher, Christoph Koch
;
JMLR W&CP 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.

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