Deep Involutive Generative Models for Neural MCMC

Abstract

We introduce deep involutive generative models, a new architecture for deep generative modeling, and use them to define Involutive Neural MCMC, a new approach to fast neural MCMC. An involutive generative model represents a probability kernel $G(\varphi \mapsto {\varphi }^{\prime })$ as an involutive (i.e., self-inverting) deterministic function $f(\varphi ,\pi )$ on an enlarged state space containing auxiliary variables $\pi$. We show how to make these models volume preserving, and how to use deep volume-preserving involutive generative models to make valid Metropolis-Hastings updates based on an auxiliary variable scheme with an easy-to-calculate acceptance ratio. We prove that deep involutive generative models and their volume-preserving special case are universal approximators for probability kernels. This result implies that with enough network capacity and training time, they can be used to learn arbitrarily complex MCMC updates. We define a loss function and optimization algorithm for training parameters given simulated data. We also provide initial experiments showing that Involutive Neural MCMC can efficiently explore multi-modal distributions that are intractable for Hybrid Monte Carlo, and can converge faster than A-NICE-MC, a recently introduced neural MCMC technique.

arXiv comment13 pages, 6 figures. Revised discussion of the Jacobian determinant factor in the acceptance ratio

References in corpus (6)

• Auto-Encoding Variational Bayes
• Stochastic Backpropagation and Approximate Inference in Deep Generative Models
• NICE: Non-linear Independent Components Estimation
• Fast and reliable MCMC for cosmological parameter estimation
• Analyzing Inverse Problems with Invertible Neural Networks
• Meta-Learning MCMC Proposals

Cited by in corpus (5)

• Path Integral Sampler: a stochastic control approach for sampling
• Automating Involutive MCMC using Probabilistic and Differentiable Programming
• A Neural Network MCMC sampler that maximizes Proposal Entropy
• Nonreversible MCMC from conditional invertible transforms: a complete recipe with convergence guarantees
• Neural Group Actions