Learning of Tree-Structured Gaussian Graphical Models on Distributed Data under Communication Constraints
This addresses the challenge of distributed learning under communication constraints for applications like sensor networks or federated learning, but it is incremental as it builds on existing tree-structured models.
The paper tackles the problem of learning tree-structured Gaussian graphical models from distributed data where each machine only has a subset of features, by proposing communication-efficient strategies that allow the central node to recover the structure with high accuracy, as shown in simulations achieving desired accuracy with small communication budgets.
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.