Dimension-free regimes for unadjusted Langevin in ridge-separable models: A subspace robust Wasserstein analysis
The Unadjusted Langevin Algorithm (ULA) is widely used for high-dimensional Bayesian inference. Classical analyses in Wasserstein-2 distance predict an asymptotic bias and a mixing time that grow with dimension, but this metric is stronger than necessary for many statistical tasks. We instead analyze the bias in subspace robust Wasserstein distance, which controls the mean and arbitrary low-dimensional marginals and is therefore well suited to observables typically estimated in practice. For ridge-separable potentials formed with i.i.d. data, we prove high-probability bounds showing a bell-shaped mixing profile as the number of data points $N$ varies relative to the dimension $d$. In the ...
| Authors | Yuansi Chen, Francesco Pedrotti, Peter A. Whalley |
|---|---|
| Primary category | stat.ML |
| Published | 22 October 2026 |
| Last updated at source | 22 October 2026 |
Silytics shows public metadata from arXiv and links to the original. Information may be incomplete or out of date. Last refreshed 23 October 2026. Licenses and terms of the original apply to the work itself. Not financial, legal or professional advice.