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Model Averaging in Large Scale Learning

Abstract : This thesis explores properties of estimations procedures related to aggregation in the problem of high-dimensional regression in a sparse setting. The exponentially weighted aggregate (EWA) is well studied in the literature. It benefits from strong results in fixed and random designs with a PAC-Bayesian approach. However, little is known about the properties of the EWA with Laplace prior. Chapter 2 analyses the statistical behaviour of the prediction loss of the EWA with Laplace prior in the fixed design setting. Sharp oracle inequalities which generalize the properties of the Lasso to a larger family of estimators are established. These results also bridge the gap from the Lasso to the Bayesian Lasso. Chapter 3 introduces an adjusted Langevin Monte Carlo sampling method that approximates the EWA with Laplace prior in an explicit finite number of iterations for any targeted accuracy. Chapter 4 explores the statisctical behaviour of adjusted versions of the Lasso for the transductive and semi-supervised learning task in the random design setting.
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Submitted on : Thursday, March 15, 2018 - 5:19:07 PM
Last modification on : Friday, August 5, 2022 - 2:49:41 PM
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  • HAL Id : tel-01735320, version 1


Edwin Grappin. Model Averaging in Large Scale Learning. Statistics [math.ST]. Université Paris-Saclay, 2018. English. ⟨NNT : 2018SACLG001⟩. ⟨tel-01735320⟩



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