Distributed Variational Inference for Online Supervised Learning

This article introduces a scalable distributed probabilistic inference algorithm for intelligent sensor networks, tackling challenges of continuous variables, intractable posteriors, and large-scale real-time data. In a centralized setting, variational inference is a fundamental tool to extend the utility of Bayesian estimation by approximating a parameterized form of an intractable posterior density. Our key contribution is deriving the distributed evidence lower bound (DELBO) from the centralized estimation objective, whose separable structure enables distributed inference with one-hop sensor communication. The DELBO consists of observation likelihood and divergences to prior estimates, and the gap in the measurement evidence is ascribed to consensus and modeling errors. For supervised learning, we design a DELBO-maximizing online distributed algorithm and specialize it to Gaussian variational densities with nonlinear likelihoods. We extend the resulting distributed Gaussian variational inference updates via diagonalized and 1-rank covariance inversions for high-dimensional estimates and apply it to multirobot probabilistic mapping using indoor LiDAR data.