Channel-Driven Monte Carlo Sampling for Bayesian Distributed Learning in Wireless Data Centers

Dongzhu Liu, Osvaldo Simeone

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


Conventional frequentist learning, as assumed by existing federated learning protocols, is limited in its ability to quantify uncertainty, incorporate prior knowledge, guide active learning, and enable continual learning. Bayesian learning provides a principled approach to address all these limitations, at the cost of an increase in computational complexity. This paper studies distributed Bayesian learning in a wireless data center setting encompassing a central server and multiple distributed workers. Prior work on wireless distributed learning has focused exclusively on frequentist learning, and has introduced the idea of leveraging uncoded transmission to enable 'over-the-air' computing. Unlike frequentist learning, Bayesian learning aims at evaluating approximations or samples from a global posterior distribution in the model parameter space. This work investigates for the first time the design of distributed one-shot, or 'embarrassingly parallel', Bayesian learning protocols in wireless data centers via consensus Monte Carlo (CMC). Uncoded transmission is introduced not only as a way to implement 'over-the-air' computing, but also as a mechanism to deploy channel-driven MC sampling: Rather than treating channel noise as a nuisance to be mitigated, channel-driven sampling utilizes channel noise as an integral part of the MC sampling process. A simple wireless CMC scheme is first proposed that is asymptotically optimal under Gaussian local posteriors. Then, for arbitrary local posteriors, a variational optimization strategy is introduced. Simulation results demonstrate that, if properly accounted for, channel noise can indeed contribute to MC sampling and does not necessarily decrease the accuracy level.

Original languageEnglish (US)
Pages (from-to)562-577
Number of pages16
JournalIEEE Journal on Selected Areas in Communications
Issue number2
StatePublished - Feb 1 2022

All Science Journal Classification (ASJC) codes

  • Computer Networks and Communications
  • Electrical and Electronic Engineering


  • Distributed Bayesian learning
  • consensus Monte Carlo
  • federated learning
  • over-the-air computation
  • uncoded transmission
  • wireless data centers


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