Title: Collaborative graphical lasso

Abstract: In recent years, the availability of multi-omics data has increased substantially. Multi-omics data integration methods mainly aim to leverage different molecular data sets to gain a complete molecular description of biological processes. An attractive integration approach is the reconstruction of multi-omics networks. However, the development of effective multi-omics network reconstruction strategies lags behind. This hinders maximizing the potential of multi-omics data sets. With this study, we advance the frontier of multi-omics network reconstruction by introducing "collaborative graphical lasso" as a novel strategy. Our proposed algorithm synergizes "graphical lasso" with the concept of "collaboration", effectively harmonizing multi-omics data sets integration, thereby enhancing the accuracy of network inference. Besides, to tackle model selection in this framework, we designed an ad hoc procedure based on network stability. We assess the performance of collaborative graphical lasso and the corresponding model selection procedure through simulations, and we apply them to publicly available multi-omics data. This demonstrated collaborative graphical lasso is able to reconstruct known biological connections and suggest previously unknown and biologically coherent interactions, enabling the generation of novel hypotheses. We implemented collaborative graphical lasso as an R package, available on CRAN as coglasso.