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Sparse Recovery in Linear Spans and Convex Hulls of Infinite Dictionaries

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We will discuss problems of recovery of “sparse” approximations of a target function in linear spans or convex hulls of given infinite (not necessarily countable) dictionaries based on noisy observations of this function at random points. The method is based on penalized empirical risk minimization with $L_1$-penalty in the case of linear spans and with entropy penalty in the case of convex hulls. A number of problems in Statistics and in Machine Learning can be studied in this framework and many results of the theory of sparse recovery for finite dictionaries, including sparsity oracle inequalities, can be extended to the case of infinite dictionaries.

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This talk is part of the Statistics series.

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