AuthorsK. Hlavackova-Schindler, V. Naumova and S. V. Pereverzyev
EditorsI. Pesenson
TitleMulti-penalty regularization for detecting relevant variables
AfilliationScientific Computing
Project(s)Center for Biomedical Computing (SFF)
Publication TypeBook Chapter
Year of Publication2017
Book TitleRecent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science
EditionNovel Methods in Harmonic Analysis,
PublisherSpringer International Publishing
Keywordscausality networks, gene regulatory networks., multi-penalty regularization, variables detection

In this paper we propose a new method for detecting relevant variables
from a priori given high-dimensional data under the assumption that input-
output dependence is described by a nonlinear function depending on a few
variables. The method is based on the inspection of the behavior of discrepan-
cies of a multi-penalty regularization with a component-wise penalization for
small and large values of regularization parameters. We provide the justifica-
tion of the proposed method under a certain condition on sampling operators.
The effectiveness of the method is demonstrated in the example with synthetic
data and in the reconstruction of gene regulatory networks. In the latter ex-
ample, the obtained results provide a clear evidence of the competitiveness of
the proposed method.


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