Hierarchical Penalization
Marie Szafranski, Yves Grandvalet and Pierre Morizet-Mahoudeaux
In: CAp 2007, 04-06 July 2007, Grenoble, France.

Abstract

Hierarchical penalization is a generic framework enabling to process hierarchically structured variables by usual statistical models. The structure information is conveyed to the model thanks to the shape of constraints that are applied to the parameters attached to each variable. The model parameters \beta are estimated by minimizing a penalized fitting criterion L(\beta) + \lambda P(\beta), where L(·) is the data-fitting term, P(·) is the penalizer, and \lambda is the regularization parameter responsible for the trade-off between the two terms. Here, we devise a penalizer P(·) that promotes sparse solutions that take into account the structure of variables, that is, solutions where a small number groups of variables intervene, and where each group is represented by a few leading components

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