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

TL;DR

This paper proposes communication-efficient methods for learning tree-structured Gaussian graphical models from distributed data, demonstrating high accuracy with minimal communication, including sign-based data transmission.

Contribution

It introduces novel strategies for structure learning in distributed settings that are proven to be effective with limited communication, including sign-based data sharing.

Findings

High-accuracy structure recovery with minimal communication

Sign-based data sharing suffices for reliable learning

Strategies perform well on synthetic and real datasets

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.