MCMC Variational Inference via Uncorrected Hamiltonian Annealing
arXiv:2107.04150
Abstract
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.
arXiv commentPublished at NeurIPS (2021)
References in corpus (18)
- Auto-Encoding Variational Bayes
- Equilibrium free energy differences from nonequilibrium measurements: a master equation approach
- Variational Inference with Normalizing Flows
- Stochastic Gradient Hamiltonian Monte Carlo
- Markov Chain Monte Carlo and Variational Inference: Bridging the Gap
- Reinterpreting Importance-Weighted Autoencoders
- Importance Weighting and Variational Inference
- On the Quantitative Analysis of Decoder-Based Generative Models
- Sandwiching the marginal likelihood using bidirectional Monte Carlo
- Approximate Inference with Amortised MCMC
- A Contrastive Divergence for Combining Variational Inference and MCMC
- Hamiltonian Annealed Importance Sampling for partition function estimation
- Improving Explorability in Variational Inference with Annealed Variational Objectives
- Measuring the reliability of MCMC inference with bidirectional Monte Carlo
- Variational Inference with Hamiltonian Monte Carlo
- Monte Carlo Variational Auto-Encoders
- Learning Deep Generative Models with Annealed Importance Sampling
- Divide and Couple: Using Monte Carlo Variational Objectives for Posterior Approximation