# Wireless Federated Langevin Monte Carlo: Repurposing Channel Noise for Bayesian Sampling and Privacy

arXiv: https://arxiv.org/abs/2108.07644 · HTML: https://mlsanity.com/paper/2108.07644/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Aug 2021.

## Built on by (most cited first, 10 of 10)

- [FedPop: A Bayesian Approach for Personalised Federated Learning](https://mlsanity.com/paper/2206.03611/) (2022)
- [Edge Intelligence Over the Air: Two Faces of Interference in Federated Learning](https://mlsanity.com/paper/2306.10299/) (2023)
- [ELF: Federated Langevin Algorithms with Primal, Dual and Bidirectional Compression](https://mlsanity.com/paper/2303.04622/) (2023)
- [Leveraging Channel Noise for Sampling and Privacy via Quantized Federated Langevin Monte Carlo](https://mlsanity.com/paper/2202.13932/) (2022)
- [Pre-Training and Personalized Fine-Tuning via Over-the-Air Federated Meta-Learning: Convergence-Generalization Trade-Offs](https://mlsanity.com/paper/2406.11569/) (2024)
- [Convergence Analysis of Over-the-Air FL with Compression and Power Control via Clipping](https://mlsanity.com/paper/2305.11135/) (2023)
- [Robust Distributed Bayesian Learning with Stragglers via Consensus Monte Carlo](https://mlsanity.com/paper/2112.09794/) (2021)
- [Batch Selection and Communication for Active Learning with Edge Labeling](https://mlsanity.com/paper/2311.08053/) (2023)
- [Compressed Bayesian Federated Learning for Reliable Passive Radio Sensing in Industrial IoT](https://mlsanity.com/paper/2405.05855/) (2024)
- [Bayesian Federated Learning for Continual Training](https://mlsanity.com/paper/2504.15328/) (2025)

## Abstract (arXiv)

Most works on federated learning (FL) focus on the most common frequentist formulation of learning whereby the goal is minimizing the global empirical loss. Frequentist learning, however, is known to be problematic in the regime of limited data as it fails to quantify epistemic uncertainty in prediction. Bayesian learning provides a principled solution to this problem by shifting the optimization domain to the space of distribution in the model parameters. colorblackThis paper proposes a novel mechanism for the efficient implementation of Bayesian learning in wireless systems. Specifically, we focus on a standard gradient-based Markov Chain Monte Carlo (MCMC) method, namely Langevin Monte Carlo (LMC), and we introduce a novel protocol, termed Wireless Federated LMC (WFLMC), that is able to repurpose channel noise for the double role of seed randomness for MCMC sampling and of privacy preservation. To this end, based on the analysis of the Wasserstein distance between sample distribution and global posterior distribution under privacy and power constraints, we introduce a power allocation strategy as the solution of a convex program. The analysis identifies distinct operating regimes in which the performance of the system is power-limited, privacy-limited, or limited by the requirement of MCMC sampling. Both analytical and simulation results demonstrate that, if the channel noise is properly accounted for under suitable conditions, it can be fully repurposed for both MCMC sampling and privacy preservation, obtaining the same performance as in an ideal communication setting that is not subject to privacy constraints.