Stochastic Gradient MCMC with Repulsive Forces
This work addresses the challenge of efficient and robust sampling in Bayesian inference for machine learning practitioners, offering an incremental improvement over existing methods.
The paper tackled the problem of improving Bayesian inference by unifying Stochastic Gradient MCMC and Stein Variational Gradient Descent, resulting in a novel sampling scheme that uses repulsive forces between particles to enhance exploration and avoid collapse, with experiments demonstrating benefits on synthetic and real datasets.
We propose a unifying view of two different Bayesian inference algorithms, Stochastic Gradient Markov Chain Monte Carlo (SG-MCMC) and Stein Variational Gradient Descent (SVGD), leading to improved and efficient novel sampling schemes. We show that SVGD combined with a noise term can be framed as a multiple chain SG-MCMC method. Instead of treating each parallel chain independently from others, our proposed algorithm implements a repulsive force between particles, avoiding collapse and facilitating a better exploration of the parameter space. We also show how the addition of this noise term is necessary to obtain a valid SG-MCMC sampler, a significant difference with SVGD. Experiments with both synthetic distributions and real datasets illustrate the benefits of the proposed scheme.