Distributed Variational Inference for Online Supervised Learning

TL;DR

This paper introduces a scalable distributed variational inference algorithm for real-time sensor networks, enabling efficient Bayesian estimation with one-hop communication and application to high-dimensional mapping tasks.

Contribution

It derives a novel distributed evidence lower bound (DELBO) that facilitates distributed variational inference with minimal communication in sensor networks.

Findings

Developed a distributed Gaussian variational inference (DGVI) method.

Applied the algorithm to multi-robot probabilistic mapping with LiDAR data.

Achieved efficient online inference in high-dimensional models.

Abstract

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.