@inbook{13607,
  keywords = {causality networks, gene regulatory networks., multi-penalty regularization, variables detection},
  author = {Katerina Hlavackova-Schindler and Valeriya Naumova and Sergei Pereverzyev V},
  title = {Multi-penalty regularization for detecting relevant variables},
  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.},
  year = {2017},
  journal = {Recent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science},
  volume = {2},
  edition = {Novel Methods in Harmonic Analysis,},
  pages = {889-916},
  publisher = {Springer International Publishing},
  url = {http://www.springer.com/de/book/9783319555553},
  editor = {Isaac Pesenson},
}