  Real world systems typically feature a variety of different dependency types
and topologies that complicate model selection for probabilistic graphical
models. We introduce the ensemble-of-forests model, a generalization of the
ensemble-of-trees model. Our model enables structure learning of Markov random
fields (MRF) with multiple connected components and arbitrary potentials. We
present two approximate inference techniques for this model and demonstrate
their performance on synthetic data. Our results suggest that the
ensemble-of-forests approach can accurately recover sparse, possibly
disconnected MRF topologies, even in presence of non-Gaussian dependencies
and/or low sample size. We applied the ensemble-of-forests model to learn the
structure of perturbed signaling networks of immune cells and found that these
frequently exhibit non-Gaussian dependencies with disconnected MRF topologies.
In summary, we expect that the ensemble-of-forests model will enable MRF
structure learning in other high dimensional real world settings that are
governed by non-trivial dependencies.
