MAXIMUM CONDITIONAL ENTROPY HAMILTONIAN MONTE CARLO SAMPLER

The performance of a Hamiltonian Monte Carlo (HMC) sampler depends critically on some algorithm parameters, such as the total integration time and the numerical integration stepsize. The parameter tuning is particularly challenging when the mass matrix of the HMC sampler is adapted. We propose in this work a Kolmogorov--Sinai entropy (KSE)--based design criterion to optimize these algorithm parameters, which can avoid some potential issues in the often-used jumping-distance--based measures. For near-Gaussian distributions, we are able to derive the optimal algorithm parameters with respect to the KSE criterion analytically. As a by-product, the KSE criterion also provides a theoretical justification for the need to adapt the mass matrix in the HMC sampler. Based on the results, we propose an adaptive HMC algorithm, and we then demonstrate the performance of the proposed algorithm with numerical examples.

Automated summary

The paper introduces a design criterion based on KSE for optimizing algorithm parameters of HMC sampler, especially when the mass matrix is adapted. Analytically derivations of optimal algorithm parameters for near-Gaussian distributions are provided, as well as theoretical justification for adapting mass matrix in HMC sampler. An adaptive HMC algorithm is proposed and its performance demonstrated with numerical examples.