The Mean Field Variational Bayes (MFVB) method is one of the most computationally efficient techniques for Bayesian inference. However, its use has been restricted to models with conjugate priors or those that require analytical calculations. This paper proposes a novel particle-based MFVB approach that greatly expands the applicability of the MFVB method. We establish the theoretical basis of the new method by leveraging the connection between Wasserstein gradient flows and Langevin diffusion dynamics, and demonstrate the effectiveness of this approach using Bayesian logistic regression, stochastic volatility, and deep neural networks.

翻译：平均场变分贝叶斯（MFVB）方法是最为计算高效的贝叶斯推断技术之一，但其应用长期局限于具有共轭先验或需解析计算的模型。本文提出了一种新型粒子化MFVB方法，显著拓展了MFVB方法的适用范围。我们通过利用Wasserstein梯度流与Langevin扩散动力学之间的关联建立了该新方法的理论基础，并采用贝叶斯逻辑回归、随机波动率模型及深度神经网络验证了该方法的有效性。