Generalizing Hamiltonian Monte Carlo with Neural Networks
This work addresses the bottleneck of mixing speed in MCMC methods for probabilistic inference, offering a general-purpose solution with empirical improvements, though it appears incremental as it builds upon existing HMC techniques.
The authors tackled the problem of slow mixing in Markov chain Monte Carlo methods by introducing a neural network-based approach that generalizes Hamiltonian Monte Carlo, achieving up to a 106x improvement in effective sample size on challenging distributions and demonstrating gains in latent-variable generative modeling.
We present a general-purpose method to train Markov chain Monte Carlo kernels, parameterized by deep neural networks, that converge and mix quickly to their target distribution. Our method generalizes Hamiltonian Monte Carlo and is trained to maximize expected squared jumped distance, a proxy for mixing speed. We demonstrate large empirical gains on a collection of simple but challenging distributions, for instance achieving a 106x improvement in effective sample size in one case, and mixing when standard HMC makes no measurable progress in a second. Finally, we show quantitative and qualitative gains on a real-world task: latent-variable generative modeling. We release an open source TensorFlow implementation of the algorithm.