MCMC Variational Inference via Uncorrected Hamiltonian Annealing
This addresses the challenge of tuning parameters in variational inference for researchers in machine learning, though it appears incremental as it builds on existing Annealed Importance Sampling methods.
The paper tackles the problem of obtaining approximate samples and tight lower bounds on the normalization constant of unnormalized target distributions, proposing Uncorrected Hamiltonian Annealing to replace non-differentiable kernels in Annealed Importance Sampling, which results in differentiable lower bounds and empirically better performance than competing approaches.
Given an unnormalized target distribution we want to obtain approximate samples from it and a tight lower bound on its (log) normalization constant log Z. Annealed Importance Sampling (AIS) with Hamiltonian MCMC is a powerful method that can be used to do this. Its main drawback is that it uses non-differentiable transition kernels, which makes tuning its many parameters hard. We propose a framework to use an AIS-like procedure with Uncorrected Hamiltonian MCMC, called Uncorrected Hamiltonian Annealing. Our method leads to tight and differentiable lower bounds on log Z. We show empirically that our method yields better performances than other competing approaches, and that the ability to tune its parameters using reparameterization gradients may lead to large performance improvements.