In the estimation of gene networks from microarray gene expression data, we propose a statistical method for quantification of the hidden confounders in gene networks, which were possibly removed from the set of genes on the gene networks or are novel biological elements that are not measured by microarrays. Due to high computational cost of the structural learning of Bayesian networks and the limited source of the microarray data, it is usual to perform gene selection prior to the estimation of gene networks. Therefore, there exist missing genes that decrease accuracy and interpretability of the estimated gene networks. The proposed method can identify hidden confounders based on the conflicts of the estimated local Bayesian network structures and estimate their ideal profiles based on the proposed Bayesian networks with hidden variables with an EM algorithm. From the estimated ideal profiles, we can identify genes which are missing in the network or suggest the existence of the novel biological elements if the ideal profiles are not significantly correlated with any expression profiles of genes. To the best of our knowledge, this research is the first study to theoretically characterize missing genes in gene networks and practically utilize this information to refine network estimation.