Papers › The Polynomial Stein Discrepancy for Assessing Moment Convergence
The Polynomial Stein Discrepancy for Assessing Moment Convergence
Narayan Srinivasan, Matthew Sutton, Christopher Drovandi, Leah F South
We propose a novel method for measuring the discrepancy between a set of samples and a desired posterior distribution for Bayesian inference. Classical methods for assessing sample quality like the effective sample size are not appropriate for scalable Bayesian sampling algorithms, such as stochastic gradient Langevin dynamics, that are asymptotically biased. Instead, the gold standard is to use the kernel Stein Discrepancy (KSD), which is itself not scalable given its quadratic cost in the number of samples. The KSD and its faster extensions also typically suffer from the curse-of-dimensionality and can require extensive tuning. To address these limitations, we develop the polynomial Stein discrepancy (PSD) and an associated goodness-of-fit test. While the new test is not fully convergence-determining, we prove that it detects differences in the first r moments in the Bernstein-von Mises limit. We empirically show that the test has higher power than its competitors in several examples, and at a lower computational cost. Finally, we demonstrate that the PSD can assist practitioners to select hyper-parameters of Bayesian sampling algorithms more efficiently than competitors.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Tasks
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Methods
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections