Conventional methods to analyze genomic data do not make use of the interplay between multiple factors, such as between microRNAs (miRNAs) and the mRNA transcripts they regulate, and thereby often fail to identify the cellular processes that are unique to specific tissues. We developed PUMA (PANDA Using MicroRNA Associations), a computational tool that uses message passing to integrate a prior network of miRNA target predictions with protein-protein interaction and target gene co-expression information to model genome-wide gene regulation by miRNAs. We applied PUMA to 38 tissues from the Genotype-Tissue Expression (GTEx) project, integrating RNA-Seq data with two different miRNA target predictions priors, built on predictions from TargetScan and miRanda, respectively. We found that while target predictions obtained from these two different resources are considerably different, PUMA captures similar tissue-specific miRNA-target gene regulatory interactions in the different network models. Furthermore, tissue-specific functions of miRNAs, which we identified by analyzing their regulatory profiles and which we made available through a Shiny app (https://kuijjer.shinyapps.io/puma_gtex/), are highly similar between networks modeled on the two target prediction resources. This indicates that PUMA consistently captures important tissue-specific regulatory processes of miRNAs. In addition, using PUMA we identified miRNAs regulating important tissue-specific processes that, when mutated, may result in disease development in the same tissue. PUMA is available in C++, MATLAB, and Python code on GitHub (https://github.com/kuijjerlab/PUMA and https://github.com/kuijjerlab/PyPuma).