Neural Network Gradient Hamiltonian Monte Carlo

TL;DR

This paper introduces a neural network-based approach to approximate gradients in Hamiltonian Monte Carlo, significantly reducing computational costs while maintaining convergence to the true distribution, validated through experiments.

Contribution

It presents a novel neural network method for gradient approximation in Hamiltonian Monte Carlo that preserves convergence guarantees.

Findings

Reduces gradient computation time in HMC.

Maintains convergence despite gradient approximation.

Validated on synthetic and real datasets.

Abstract

Hamiltonian Monte Carlo is a widely used algorithm for sampling from posterior distributions of complex Bayesian models. It can efficiently explore high-dimensional parameter spaces guided by simulated Hamiltonian flows. However, the algorithm requires repeated gradient calculations, and these computations become increasingly burdensome as data sets scale. We present a method to substantially reduce the computation burden by using a neural network to approximate the gradient. First, we prove that the proposed method still maintains convergence to the true distribution though the approximated gradient no longer comes from a Hamiltonian system. Second, we conduct experiments on synthetic examples and real data sets to validate the proposed method.