Particle Mean Field Variational Bayes
This work expands the applicability of MFVB to a broader range of models, addressing a computational bottleneck for researchers and practitioners in Bayesian inference.
The paper tackles the limitation of Mean Field Variational Bayes (MFVB) to models with conjugate priors by proposing a particle-based MFVB approach, demonstrating its effectiveness in Bayesian logistic regression, stochastic volatility, and deep neural networks.
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.