Dimension-free regimes for unadjusted Langevin in ridge-separable models: A subspace robust Wasserstein analysis

Yuansi Chen, Francesco Pedrotti, Peter A. Whalley · 2026 · arXiv

DOI: 10.48550/arXiv.2610.31431 · open-access PDF

Abstract

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-sha

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