@inbook {24104,
	title = {Multi-penalty regularization for detecting relevant variables},
	booktitle = {Recent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science},
	volume = {2},
	year = {2017},
	pages = {889-916},
	publisher = {Springer International Publishing},
	organization = {Springer International Publishing},
	edition = {Novel Methods in Harmonic Analysis,},
	abstract = {In this paper we propose a new method for detecting relevant variablesfrom a priori given high-dimensional data under the assumption that input-output dependence is described by a nonlinear function depending on a fewvariables. The method is based on the inspection of the behavior of discrepan-cies of a multi-penalty regularization with a component-wise penalization forsmall 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 syntheticdata and in the reconstruction of gene regulatory networks. In the latter ex-ample, the obtained results provide a clear evidence of the competitiveness ofthe proposed method.},
	keywords = {causality networks, gene regulatory networks., multi-penalty regularization, variables detection},
	url = {http://www.springer.com/de/book/9783319555553},
	author = {Hlavackova-Schindler, Katerina and Naumova, Valeriya and Sergei V {Pereverzyev}},
	editor = {Pesenson, Isaac}
}
