  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.
