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Sparsity in penalized empirical risk minimization

Vladimir Koltchinskii — 2009

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

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 respect to the...

L 1 -penalization in functional linear regression with subgaussian design

Vladimir KoltchinskiiStanislav Minsker — 2014

Journal de l’École polytechnique — Mathématiques

We study functional regression with random subgaussian design and real-valued response. The focus is on the problems in which the regression function can be well approximated by a functional linear model with the slope function being “sparse” in the sense that it can be represented as a sum of a small number of well separated “spikes”. This can be viewed as an extension of now classical sparse estimation problems to the case of infinite dictionaries. We study an estimator of the regression function...

Statistical-learning control of multiple-delay systems with application to ATM networks

Congestion control in the ABR class of ATM network presents interesting challenges due to the presence of multiple uncertain delays. Recently, probabilistic methods and statistical learning theory have been shown to provide approximate solutions to challenging control problems. In this paper, using some recent results by the authors, an efficient statistical algorithm is used to design a robust, fixed-structure, controller for a high-speed communication network with multiple uncertain propagation...

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