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Learning out of leaders
Author(s) -
Mougeot Mathilde,
Picard Dominique,
Tribouley Karine
Publication year - 2012
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/j.1467-9868.2011.01024.x
Subject(s) - thresholding , minimax , consistency (knowledge bases) , curse of dimensionality , computer science , regression , dimensionality reduction , artificial intelligence , class (philosophy) , regression analysis , exponential function , linear regression , machine learning , mathematical optimization , mathematics , statistics , mathematical analysis , image (mathematics)
Summary. The 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 autodriven algorithm with two thresholding steps. A first adaptive thresholding helps to select leaders among the initial regressors to obtain a first reduction of dimensionality. Then a second thresholding is performed on the linear regression on 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.