  We propose Pathfinder, a variational method for approximately sampling from
differentiable log densities. Starting from a random initialization, Pathfinder
locates normal approximations to the target density along a quasi-Newton
optimization path, with local covariance estimated using the inverse Hessian
estimates produced by the optimizer. Pathfinder returns draws from the
approximation with the lowest estimated Kullback-Leibler (KL) divergence to the
true posterior. We evaluate Pathfinder on a wide range of posterior
distributions, demonstrating that its approximate draws are better than those
from automatic differentiation variational inference (ADVI) and comparable to
those produced by short chains of dynamic Hamiltonian Monte Carlo (HMC), as
measured by 1-Wasserstein distance. Compared to ADVI and short dynamic HMC
runs, Pathfinder requires one to two orders of magnitude fewer log density and
gradient evaluations, with greater reductions for more challenging posteriors.
Importance resampling over multiple runs of Pathfinder improves the diversity
of approximate draws, reducing 1-Wasserstein distance further and providing a
measure of robustness to optimization failures on plateaus, saddle points, or
in minor modes. The Monte Carlo KL divergence estimates are embarrassingly
parallelizable in the core Pathfinder algorithm, as are multiple runs in the
resampling version, further increasing Pathfinder's speed advantage with
multiple cores.
