HMCF - Hamiltonian Monte Carlo Sampling for Fields - A Python framework for HMC sampling with NIFTy

TL;DR

HMCF is a Python software extension for the NIFTy framework that implements advanced Hamiltonian Monte Carlo sampling techniques, enabling efficient high-dimensional Bayesian inference in spatially correlated problems like image reconstruction.

Contribution

It introduces an HMC sampler with automatic parameter tuning and advanced features to NIFTy, enhancing high-dimensional inference capabilities.

Findings

Efficient full-posterior sampling in high-dimensional spaces.

Automatic adjustment of HMC parameters improves sampling performance.

Supports hierarchical Bayesian models with hyperparameter sampling.

Abstract

HMCF "Hamiltonian Monte Carlo for Fields" is a software add-on for the NIFTy "Numerical Information Field Theory" framework implementing Hamiltonian Monte Carlo (HMC) sampling in Python. HMCF as well as NIFTy are designed to address inference problems in high-dimensional spatially correlated setups such as image reconstruction. HMCF adds an HMC sampler to NIFTy that automatically adjusts the many free parameters steering the HMC sampling machinery. A wide variety of features ensure efficient full-posterior sampling for high-dimensional inference problems. These features include integration step size adjustment, evaluation of the mass matrix, convergence diagnostics, higher order symplectic integration and simultaneous sampling of parameters and hyperparameters in Bayesian hierarchical models.