NeuTra-lizing Bad Geometry in Hamiltonian Monte Carlo Using Neural Transport

Abstract

Hamiltonian Monte Carlo is a powerful algorithm for sampling from difficult-to-normalize posterior distributions. However, when the geometry of the posterior is unfavorable, it may take many expensive evaluations of the target distribution and its gradient to converge and mix. We propose neural transport (NeuTra) HMC, a technique for learning to correct this sort of unfavorable geometry using inverse autoregressive flows (IAF), a powerful neural variational inference technique. The IAF is trained to minimize the KL divergence from an isotropic Gaussian to the warped posterior, and then HMC sampling is performed in the warped space. We evaluate NeuTra HMC on a variety of synthetic and real problems, and find that it significantly outperforms vanilla HMC both in time to reach the stationary distribution and asymptotic effective-sample-size rates.

References in corpus (3)

• Markov Chain Monte Carlo and Variational Inference: Bridging the Gap
• Rapid Mixing of Hamiltonian Monte Carlo on Strongly Log-Concave Distributions
• Learning Model Reparametrizations: Implicit Variational Inference by Fitting MCMC distributions

Cited by in corpus (34)

• Normalizing Flows for Probabilistic Modeling and Inference
• Event Generation with Normalizing Flows
• Nested Sampling with Normalising Flows for Gravitational-Wave Inference
• i-flow: High-dimensional Integration and Sampling with Normalizing Flows
• Bilby-MCMC: An MCMC sampler for gravitational-wave inference
• Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Models
• Solution of Physics-based Bayesian Inverse Problems with Deep Generative Priors
• JAX-COSMO: An End-to-End Differentiable and GPU Accelerated Cosmology Library
• Your GAN is Secretly an Energy-based Model and You Should use Discriminator Driven Latent Sampling
• Advances in machine-learning-based sampling motivated by lattice quantum chromodynamics
• Learning Symmetries of Classical Integrable Systems
• Scaling Hamiltonian Monte Carlo Inference for Bayesian Neural Networks with Symmetric Splitting
• tfp.mcmc: Modern Markov Chain Monte Carlo Tools Built for Modern Hardware
• Stochastic Normalizing Flows
• Neural Bridge Sampling for Evaluating Safety-Critical Autonomous Systems
• Markovian Score Climbing: Variational Inference with KL(p||q)
• Deep Learning Hamiltonian Monte Carlo
• VAEBM: A Symbiosis between Variational Autoencoders and Energy-based Models
• Path Integral Sampler: a stochastic control approach for sampling
• Telescoping Density-Ratio Estimation
• Learning Equivariant Energy Based Models with Equivariant Stein Variational Gradient Descent
• MetFlow: A New Efficient Method for Bridging the Gap between Markov Chain Monte Carlo and Variational Inference
• Automatic Reparameterisation of Probabilistic Programs
• A Neural Network MCMC sampler that maximizes Proposal Entropy
• Density Ratio Estimation via Infinitesimal Classification
• Projected Latent Markov Chain Monte Carlo: Conditional Sampling of Normalizing Flows
• Efficient Multimodal Sampling via Tempered Distribution Flow
• Sampling in Combinatorial Spaces with SurVAE Flow Augmented MCMC
• Involutive MCMC: a Unifying Framework
• Reparameterized Sampling for Generative Adversarial Networks
• Entropy-based adaptive Hamiltonian Monte Carlo
• Contributions to Large Scale Bayesian Inference and Adversarial Machine Learning
• Hamiltonian Dynamics with Non-Newtonian Momentum for Rapid Sampling
• Hamiltonian Monte Carlo Swindles