Abstract / truncated to 115 words (read the full abstract)

This doctorate thesis focuses on sparse regression, a statistical modeling tool for selecting valuable predictors in underdetermined linear models. By imposing different constraints on the structure of the variable vector in the regression problem, one obtains estimates which have sparse supports, i.e., where only a few of the elements in the response variable have non-zero values. The thesis collects six papers which, to a varying extent, deals with the applications, implementations, modifications, translations, and other analysis of such problems. Sparse regression is often used to approximate additive models with intricate, non-linear, non-smooth or otherwise problematic functions, by creating an underdetermined model consisting of candidate values for these functions, and linear response variables which selects among ... toggle 15 keywords

sparse regression – group-sparsity – statistical modeling – regularization – hyperparameter-selection – spectral analysis – audio signal processing – classification – localization – multi-pitch estimation – chroma estimation – convex optimization – ADMM – cyclic coordinate descent – proximal gradient.

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