# Distributed Bayesian Estimation in Sensor Networks: Consensus on Marginal Densities

arXiv: https://arxiv.org/abs/2312.01227 · HTML: https://mlsanity.com/paper/2312.01227/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 63 references that are in the map.
- First posted on arXiv 2 Dec 2023.

## Builds on (most cited first, 16 of 16)

- [Convex Optimization: Algorithms and Complexity](https://mlsanity.com/paper/1405.4980/) (2014)
- [The Bayesian Learning Rule](https://mlsanity.com/paper/2107.04562/) (2021)
- [Distributed optimization over time-varying directed graphs](https://mlsanity.com/paper/1303.2289/) (2013)
- [A Survey of Indoor Localization Systems and Technologies](https://mlsanity.com/paper/1709.01015/) (2017)
- [Fast Convergence Rates for Distributed Non-Bayesian Learning](https://mlsanity.com/paper/1508.05161/) (2015)
- [Fusion of Probability Density Functions](https://mlsanity.com/paper/2202.11633/) (2022)
- [Social Learning and Distributed Hypothesis Testing](https://mlsanity.com/paper/1410.4307/) (2014)
- [Convergence of sequences: a survey](https://mlsanity.com/paper/2111.11374/) (2021)
- [Convergence of the Iterates in Mirror Descent Methods](https://mlsanity.com/paper/1805.01526/) (2018)
- [On the Arithmetic and Geometric Fusion of Beliefs for Distributed Inference](https://mlsanity.com/paper/2204.13741/) (2022)
- [Sigma Point Belief Propagation](https://mlsanity.com/paper/1309.0363/) (2013)
- [Non-Bayesian Social Learning with Uncertain Models](https://mlsanity.com/paper/1909.09228/) (2019)
- [Joint Estimation and Localization in Sensor Networks](https://mlsanity.com/paper/1404.3580/) (2014)
- [Distributed Estimation using Bayesian Consensus Filtering](https://mlsanity.com/paper/1403.3117/) (2014)
- [A New Approach for Distributed Hypothesis Testing with Extensions to Byzantine-Resilience](https://mlsanity.com/paper/1903.05817/) (2019)
- [Distributed Variational Inference for Online Supervised Learning](https://mlsanity.com/paper/2309.02606/) (2023)

## Built on by (most cited first, 1 of 1)

- [Generalising maximum mean discrepancy: kernelised functional Bregman divergences](https://mlsanity.com/paper/2604.24047/) (2026)

## Abstract (arXiv)

In this paper, we aim to design and analyze distributed Bayesian estimation algorithms for sensor networks. The challenges we address are to (i) derive a distributed provably-correct algorithm in the functional space of probability distributions over continuous variables, and (ii) leverage these results to obtain new distributed estimators restricted to subsets of variables observed by individual agents. This relates to applications such as cooperative localization and federated learning, where the data collected at any agent depends on a subset of all variables of interest. We present Bayesian density estimation algorithms using data from non-linear likelihoods at agents in centralized, distributed, and marginal distributed settings. After setting up a distributed estimation objective, we prove almost-sure convergence to the optimal set of pdfs at each agent. Then, we prove the same for a storage-aware algorithm estimating densities only over relevant variables at each agent. Finally, we present a Gaussian version of these algorithms and implement it in a mapping problem using variational inference to handle non-linear likelihood models associated with LiDAR sensing.