Pathfinder: Parallel quasi-Newton variational inference
By Lu Zhang, Bob Carpenter, Andrew Gelman, Aki Vehtari. 2021
61 citations recorded by the source corpus.
We propose Pathfinder, a variational method for approximately sampling from differentiable probability 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 target distribution. 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.
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
- Aki Vehtari
- Andrew Gelman
- Jonah Gabry
- Yuling Yao
- Paul-Christian Burkner
- Daniel P. Simpson
- Yong Luo
- Jasper A. Vrugt
Citations in the corpus
- Foundation Posteriors for Approximate Probabilistic Inference (2022, neutral): “We would like to make inference queries given all entries but naive unrolling is unscalable.”
- PyMC: a modern, and comprehensive probabilistic programming framework in Python (2023, unknown): “The Pathfinder variational inference algorithm (Zhang et al., 2022).”
- Pareto Smoothed Importance Sampling (2015, methodology): “PSIS has been used to improve and diagnose variational approximations to posteriors (Yao et al., 2018b; Magnusson et al., 2019, 2020; Dhaka et al., 2020, 2021; Zhang et al., 2021).”