Dai, Hongsheng and Fan, Xiequan and Lu, Jianya (2026) Self-normalized Cramer-type Moderate Deviation of Stochastic Gradient Langevin Dynamics. Journal of Applied Probability, 63 (3). pp. 1034-1061. DOI https://doi.org/10.1017/jpr.2025.10065
Dai, Hongsheng and Fan, Xiequan and Lu, Jianya (2026) Self-normalized Cramer-type Moderate Deviation of Stochastic Gradient Langevin Dynamics. Journal of Applied Probability, 63 (3). pp. 1034-1061. DOI https://doi.org/10.1017/jpr.2025.10065
Dai, Hongsheng and Fan, Xiequan and Lu, Jianya (2026) Self-normalized Cramer-type Moderate Deviation of Stochastic Gradient Langevin Dynamics. Journal of Applied Probability, 63 (3). pp. 1034-1061. DOI https://doi.org/10.1017/jpr.2025.10065
Abstract
In this paper, we study the self-normalized Cramér-type moderate deviation of the empirical measure of the stochastic gradient Langevin dynamics (SGLD). Consequently, we also derive the Berry–Esseen bound for the SGLD. Our approach is by constructing a stochastic differential equation to approximate the SGLD and then applying Stein’s method to decompose the empirical measure into a martingale difference series sum and a negligible remainder term.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | Self-normalized Cramér-type moderate deviation; stochastic gradient Langevin dynamics; Stein’s method; Diffusion approximation; Berry–Esseen bound |
| Divisions: | Faculty of Science and Health Faculty of Science and Health > Mathematics, Statistics and Actuarial Science, School of |
| SWORD Depositor: | Unnamed user with email elements@essex.ac.uk |
| Depositing User: | Unnamed user with email elements@essex.ac.uk |
| Date Deposited: | 13 Apr 2026 14:27 |
| Last Modified: | 18 Aug 2026 12:56 |
| URI: | http://repository.essex.ac.uk/id/eprint/42187 |
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