  In this paper, learning of tree-structured Gaussian graphical models from
distributed data is addressed. In our model, samples are stored in a set of
distributed machines where each machine has access to only a subset of
features. A central machine is then responsible for learning the structure
based on received messages from the other nodes. We present a set of
communication efficient strategies, which are theoretically proved to convey
sufficient information for reliable learning of the structure. In particular,
our analyses show that even if each machine sends only the signs of its local
data samples to the central node, the tree structure can still be recovered
with high accuracy. Our simulation results on both synthetic and real-world
datasets show that our strategies achieve a desired accuracy in inferring the
underlying structure, while spending a small budget on communication.
