Title: Enhancing Uncertainty Quantification in Latent Variable Models via Subsampling Markov Chain Monte Carlo

Abstract:

Stochastic gradient Langevin dynamics, when integrated with Gibbs sampling steps (referred to as SGLD--Gibbs), offers a highly scalable method for approximating Bayesian inference within latent variable models. Despite this scalability, there is a lack of principled strategies for adjusting the algorithm's hyperparameters to guarantee that the resulting uncertainty estimates are statistically robust. To bridge this gap in tuning methodology, this study establishes a statistical scaling limit theory for SGLD--Gibbs. We derive a joint asymptotic limit concerning both global parameters and latent variables, achieved through specific space-time rescaling. Our analysis demonstrates that global parameters converge toward a diffusion-type limit, whereas individual latent variables converge to a jump process, a behavior that mirrors the application of intermittent Gibbs updates. This combined jump-diffusion framework elucidates the role of latent-variable randomness in shaping the stationary distribution of global parameters. Building on these findings, we provide explicit recommendations for hyperparameter tuning in SGLD--Gibbs to facilitate meaningful uncertainty quantification. Empirical results indicate that applying our tuning guidelines yields superior parameter estimation, uncertainty quantification, and predictive accuracy compared to stochastic variational inference.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC