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 discrepancies of a multi-penalty regularization with a component-wise penalization for small and large values of regularization parameters. We provide the justification 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 example, the obtained results provide a clear evidence of the competitiveness of the proposed method.