# Particle-based Online Bayesian Sampling

## TL;DR

This paper introduces an online particle-based variational inference algorithm that effectively tracks dynamic posterior distributions in streaming data scenarios, with theoretical guarantees and superior empirical performance.

## Contribution

It proposes a novel online Bayesian sampling method using particles and a variance reduction technique, with theoretical analysis and improved results over existing methods.

## Key findings

- Achieves better tracking of dynamic posteriors in experiments.
- Provides theoretical analysis using Wasserstein gradient flow.
- Outperforms naive Bayesian sampling in online settings.

## Abstract

Online optimization has gained increasing interest due to its capability of tracking real-world streaming data. Although online optimization methods have been widely studied in the setting of frequentist statistics, few works have considered online optimization with the Bayesian sampling problem. In this paper, we study an Online Particle-based Variational Inference (OPVI) algorithm that uses a set of particles to represent the approximating distribution. To reduce the gradient error caused by the use of stochastic approximation, we include a sublinear increasing batch-size method to reduce the variance. To track the performance of the OPVI algorithm with respect to a sequence of dynamically changing target posterior, we provide a detailed theoretical analysis from the perspective of Wasserstein gradient flow with a dynamic regret. Synthetic and Bayesian Neural Network experiments show that the proposed algorithm achieves better results than naively applying existing Bayesian sampling methods in the online setting.