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Hierarchical Penalization

Abstract : Hierarchical penalization is a generic framework for incorporating prior information in the fitting of statistical models, when the explicative variables are organized in a hierarchical structure. The penalizer is a convex functional that performs soft selection at the group level, and shrinks variables within each group. This favors solutions with few leading terms in the final combination. The framework, originally derived for taking prior knowledge into account, is shown to be useful in linear regression, when several parameters are used to model the influence of one feature, or in kernel regression, for learning multiple kernels.
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Contributor : Marie Szafranski <>
Submitted on : Thursday, March 27, 2008 - 11:35:32 AM
Last modification on : Saturday, June 27, 2020 - 12:20:03 AM
Long-term archiving on: : Friday, September 28, 2012 - 11:50:08 AM


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  • HAL Id : hal-00267338, version 1


Marie Szafranski, Yves Grandvalet, Pierre Morizet-Mahoudeaux. Hierarchical Penalization. Neural Information Processing Systems (NIPS), 2007, Canada. pp.1457--1464. ⟨hal-00267338⟩



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