Benefits of Pathfinder in high-dimensional Bayesian inference

Determine the benefits of the Pathfinder algorithm—parallel quasi-Newton variational inference used to generate initial values for Hamiltonian Monte Carlo—for posterior inference in high-dimensional models, specifically to ascertain whether Pathfinder improves convergence, reduces warm-up time, and enhances sampling efficiency compared to standard initializations when the parameter dimension is large.

Background

Pathfinder is a hybrid approach that fits a Gaussian approximation along a quasi-Newton optimization path (via L-BFGS), selects the step with minimal Kullback–Leibler divergence to the target posterior, and draws samples to serve as initial values for Hamiltonian Monte Carlo. The intent is to shorten the burn-in phase by starting in high-density regions of the posterior.

While Pathfinder has been evaluated on posteriors in the posteriordb database, it has not been explicitly assessed in high-dimensional scenarios. The authors highlight that potential advantages in such settings—where parameter dimensionality is large and standard MCMC warm-up may be costly—remain to be determined.