# Structure Learning of Sparse GGMs over Multiple Access Networks

## TL;DR

This paper investigates structure learning of sparse Gaussian Graphical Models over distributed data in a wireless network, proposing two communication strategies and analyzing their theoretical and empirical performance.

## Contribution

It introduces two novel methods, Signs and Uncoded, for reliable GGM structure learning over noisy wireless channels with limited power and bandwidth.

## Key findings

- Both methods can recover the structure with high probability given sufficient samples.
- Signs method outperforms Uncoded method in various scenarios.
- Theoretical analysis confirms the effectiveness of the proposed strategies.

## Abstract

A central machine is interested in estimating the underlying structure of a sparse Gaussian Graphical Model (GGM) from datasets distributed across multiple local machines. The local machines can communicate with the central machine through a wireless multiple access channel. In this paper, we are interested in designing effective strategies where reliable learning is feasible under power and bandwidth limitations. Two approaches are proposed: Signs and Uncoded methods. In Signs method, the local machines quantize their data into binary vectors and an optimal channel coding scheme is used to reliably send the vectors to the central machine where the structure is learned from the received data. In Uncoded method, data symbols are scaled and transmitted through the channel. The central machine uses the received noisy symbols to recover the structure. Theoretical results show that both methods can recover the structure with high probability for large enough sample size. Experimental results indicate the superiority of Signs method over Uncoded method under several circumstances.