Pathfinder: A Parallel Quasi-Newton Algorithm for Reaching Regions of High Probability Mass
This talk introduces Pathfinder, a parallel quasi-Newton algorithm that efficiently reaches regions of high probability mass. Pathfinder locates normal approximations to the target density along a quasi-Newton optimization path and returns draws from the approximation with the lowest estimated Kullback-Leibler divergence to the target distribution. The Monte Carlo KL divergence estimates are embarrassingly parallelizable in the core Pathfinder algorithm, which, along with multiple runs in the resampling version, further increases its speed advantage with multiple cores. Simulation studies have demonstrated that Pathfinder's approximate draws are superior to those generated by automatic differentiation variational inference (ADVI) and comparable to short chains of dynamic Hamiltonian Monte Carlo (HMC), as measured by 1-Wasserstein distance. Despite its efficiency, studies have revealed that the performance of Pathfinder is sensitive to the pathological geometry of the posterior. The talk will also present case studies to shed light on the reasons behind Pathfinder's sensitive behavior, along with a brief summary of ongoing research conducted to address this issue.