  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.
