Variational Inference with Hamiltonian Monte Carlo
This work addresses a bottleneck in variational inference for machine learning practitioners, offering incremental enhancements to existing methods.
The paper tackles the problem of improving variational inference by incorporating Hamiltonian Monte Carlo steps to better approximate the posterior, resulting in theoretical asymptotic convergence and performance improvements in experiments.
Variational inference lies at the core of many state-of-the-art algorithms. To improve the approximation of the posterior beyond parametric families, it was proposed to include MCMC steps into the variational lower bound. In this work we explore this idea using steps of the Hamiltonian Monte Carlo (HMC) algorithm, an efficient MCMC method. In particular, we incorporate the acceptance step of the HMC algorithm, guaranteeing asymptotic convergence to the true posterior. Additionally, we introduce some extensions to the HMC algorithm geared towards faster convergence. The theoretical advantages of these modifications are reflected by performance improvements in our experimental results.