Sparse projections onto the simplex
Journal Article
Overview
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.
