Particle-based Online Bayesian Sampling
This work addresses the challenge of online optimization in Bayesian settings for applications requiring real-time data processing, representing an incremental improvement over prior methods.
The paper tackles the problem of online Bayesian sampling for streaming data by proposing an Online Particle-based Variational Inference (OPVI) algorithm, which achieves better results than existing methods in synthetic and Bayesian Neural Network experiments.
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.