  Developing efficient solutions for inference problems in intelligent sensor
networks is crucial for the next generation of location, tracking, and mapping
services. This paper develops a scalable distributed probabilistic inference
algorithm that applies to continuous variables, intractable posteriors and
large-scale real-time data in sensor networks. In a centralized setting,
variational inference is a fundamental technique for performing approximate
Bayesian estimation, in which an intractable posterior density is approximated
with a parametric density. Our key contribution lies in the derivation of a
separable lower bound on the centralized estimation objective, which enables
distributed variational inference with one-hop communication in a sensor
network. Our distributed evidence lower bound (DELBO) consists of a weighted
sum of observation likelihood and divergence to prior densities, and its gap to
the measurement evidence is due to consensus and modeling errors. To solve
binary classification and regression problems while handling streaming data, we
design an online distributed algorithm that maximizes DELBO, and specialize it
to Gaussian variational densities with non-linear likelihoods. The resulting
distributed Gaussian variational inference (DGVI) efficiently inverts a
$1$-rank correction to the covariance matrix. Finally, we derive a diagonalized
version for online distributed inference in high-dimensional models, and apply
it to multi-robot probabilistic mapping using indoor LiDAR data.
