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.