Displaying similar documents to “High-dimensional gaussian model selection on a gaussian design”

Adaptive Dantzig density estimation

K. Bertin, E. Le Pennec, V. Rivoirard (2011)

Annales de l'I.H.P. Probabilités et statistiques

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The aim of this paper is to build an estimate of an unknown density as a linear combination of functions of a dictionary. Inspired by Candès and Tao’s approach, we propose a minimization of the 1-norm of the coefficients in the linear combination under an adaptive Dantzig constraint coming from sharp concentration inequalities. This allows to consider a wide class of dictionaries. Under local or global structure assumptions, oracle inequalities are derived. These theoretical results...

Sparsity in penalized empirical risk minimization

Vladimir Koltchinskii (2009)

Annales de l'I.H.P. Probabilités et statistiques

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Let (, ) be a random couple in × with unknown distribution . Let ( , ), …, ( , ) be i.i.d. copies of (, ), being their empirical distribution. Let , …, :↦[−1, 1] be a dictionary consisting of functions. For ∈ℝ, denote :=∑ . Let :×ℝ↦ℝ be a given loss function, which is convex with...