0479581 20240103214711.820171016235959.9 85044017216 000449616400017 10.1007/978-3-319-55556-0_15 948 27 s. P cav_un_epca*0479580978-3-319-55555-3889-916ChamSpringer2017Le GiaQ. T.MayeliA.MhaskarH.ZhouD.-X. detecting relevant variables multi-penalty regularization behavior of discrepancies cav_un_auth*0247122 Hlaváčková-Schindler Kateřina UTIA-B Adaptivní systémy Department of Adaptive Systems AS AS CZ Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0333744 Naumova V. NO cav_un_auth*0353135 Pereverzyev S. Jr. AT http://library.utia.cas.cz/separaty/2017/AS/hlaváčková-schindler-0479581.pdf 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 relation is described by a nonlinear function depending on a few variables. The method is based on the inspection of the behavior of discrepancies of a multi-penalty regularization with a component-wise penalization for small and large values of regularization parameters. We provide a justification of the proposed method under a certain condition on sampling operators. The effectiveness of the method is demonstrated in an example with simulated data and in the reconstruction of a gene regulatory network. In the latter example, the obtained results provide clear evidence of the competitiveness of the proposed method with respect to the state-of-the-art approaches. BD 10000 10100 10102 2018 3 RVO:67985556 http://hdl.handle.net/11104/0276739 S RIV/67985556:_____/17:00479581!RIV18-AV0-67985556 191975711 Doplnění UT WOS a Scopus 3+4 Article Mathematics Applied 3+4 Article Mathematics Applied 3+4 Article Mathematics Applied 2017 85044017216 SCOPUS PUBMED 000449616400017 WOS cav_un_epca*0479580 Recent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science 978-3-319-55555-3 889 916 Cham Springer 2017 Applied and Numerical Harmonic Analysis Pesenson I. 340 340 Le Gia Q. T. 340 Mayeli A. 340 Mhaskar H. 340 Zhou D.-X.