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Abstract: This paper investigates the estimation problem in a regression-type model. Tobe able to deal with potential high dimensions, we provide a procedure calledLOL, for Learning Out of Leaders with no optimization step. LOL is anauto-driven algorithm with two thresholding steps. A first adaptivethresholding helps to select leaders among the initial regressors in order toobtain a first reduction of dimensionality. Then a second thresholding isperformed on the linear regression upon the leaders. The consistency of theprocedure is investigated. Exponential bounds are obtained, leading to minimaxand adaptive results for a wide class of sparse parameters, with quasi norestriction on the number p of possible regressors. An extensive computationalexperiment is conducted to emphasize the practical good performances of LOL.

Author: Mathilde Mougeot PMA, Dominique Picard PMA, Karine Tribouley PMA, MODAL'X

Source: https://arxiv.org/

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