Understanding BIF Sensitivity to SGLD Hyperparameters and Sampling Budget

Characterize and quantify how the performance of local Bayesian influence function estimation depends on the stochastic gradient Langevin dynamics hyperparameters—step size ε, localization strength γ, inverse temperature β—and on the total number of posterior draws, and derive guidelines or guarantees that explain and control this sensitivity.

Background

The local BIF relies on SGLD-based sampling of the localized posterior to estimate covariances. While the method avoids Hessian inversion and is architecture-agnostic, its practical accuracy and efficiency depend on tuning several SGLD hyperparameters and the number of samples collected.

The authors report that BIF performance is sensitive to these choices and explicitly note that this dependence is not fully understood, motivating a formal analysis of hyperparameter-sensitivity and sampling-budget effects to support reliable deployment.