Identifying microRNA signatures for the different types and subtypes of cancer can result in improved detection, characterization and understanding of cancer and move us towards more personalized treatment strategies. However, using microRNA's differential expression (tumour versus normal) to determine these signatures may lead to inaccurate predictions and low interpretability because of the noisy nature of miRNA expression data. We present a method for the selection of biologically active microRNAs using gene expression data and microRNA-to-gene interaction network. Our method is based on a linear regression with an elastic net regularization. Our simulations show that, with our method, the active miRNAs can be detected with high accuracy and our approach is robust to high levels of noise and missing information. Furthermore, our results on real datasets for glioblastoma and prostate cancer are confirmed by microRNA expression measurements. Our method leads to the selection of potentially functionally important microRNAs. The associations of some of our identified miRNAs with cancer mechanisms are already confirmed in other studies (hypoxia related hsa-mir-210 and apoptosis-related hsa-mir-296-5p). We have also identified additional miRNAs that were not previously studied in the context of cancer but are coherently predicted as active by our method and may warrant further investigation. The code is available in Matlab and R and can be downloaded on http://www.cs.toronto.edu/goldenberg/Anna_Goldenberg/Current_Research.html.