Learning of Tree-Structured Gaussian Graphical Models on Distributed Data under Communication Constraints

Abstract--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. In many situations, it is impossible to transfer the distributed data completely to a central machine due to communication constraints. Designing communication-efficient learning algorithms is desired to transfer enough information from repositories to the central machine and to reliably infer the learning model. Many learning algorithms can be modified to run distributively at several machines to perform a learning task.