🤖 AI Summary
Distributed Bayesian estimation in sensor networks—specifically, collaborative density estimation over continuous-variable function spaces using only local subset observations—lacks provably convergent algorithms.
Method: We propose the first distributed algorithmic framework with rigorous convergence guarantees, integrating distributed consensus optimization and variational inference. Our approach incorporates nonlinear likelihood modeling, Gaussian approximations, and marginal density projection, yielding a memory-aware marginal distribution estimator adaptable to heterogeneous observation structures.
Contribution/Results: We establish the first theoretical proof of almost-sure convergence of each node’s density estimate to the global posterior marginal density in the function space. Experiments on LiDAR mapping demonstrate substantial reductions in communication and storage overhead. The framework provides a provably correct, scalable paradigm for distributed Bayesian estimation in subset-observation settings—including cooperative localization and federated learning—where data decentralization and structural heterogeneity are inherent.
📝 Abstract
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.
