Gene regulatory networks are commonly used for modeling biological processes and revealing underlying molecular mechanisms. The reconstruction of gene regulatory networks from observational data is a challenging task, especially, considering the large number of involved players (e.g. genes) and much fewer biological replicates available for analysis. We propose a new statistical method of estimating the number of erroneous edges that strongly enhances the commonly used inference approaches. This method is based on special relationship between correlation and causality, and allows to identify and to remove approximately half of erroneous edges. Using positive correlation inequalities we established a mathematical foundation for our method. Joint work with A. Yambartsev, M. Perlin, N. Shulzhenko, K.L. Mine, X. Dong, and A. Morgun.