Learning Out of Leaders

Dominique Picard (PMA); Karine Tribouley (PMA; Mathilde Mougeot (PMA); Modal'x)

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Learning Out of Leaders

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arxiv 1001.1919 v2 pith:QGW3NR4V submitted 2010-01-12 math.ST stat.TH

Learning Out of Leaders

Mathilde Mougeot (PMA) , Dominique Picard (PMA) , Karine Tribouley (PMA , MODAL'X) This is my paper

classification math.ST stat.TH

keywords leadersthresholdingadaptivefirstlearningprocedureregressorsable

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This paper investigates the estimation problem in a regression-type model. To be able to deal with potential high dimensions, we provide a procedure called LOL, for Learning Out of Leaders with no optimization step. LOL is an auto-driven algorithm with two thresholding steps. A first adaptive thresholding helps to select leaders among the initial regressors in order to obtain a first reduction of dimensionality. Then a second thresholding is performed on the linear regression upon the leaders. The consistency of the procedure is investigated. Exponential bounds are obtained, leading to minimax and adaptive results for a wide class of sparse parameters, with (quasi) no restriction on the number p of possible regressors. An extensive computational experiment is conducted to emphasize the practical good performances of LOL.

Learning Out of Leaders

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