Yuansi Chen, Francesco Pedrotti, Peter A. Whalley · 2026 · arXiv
DOI: 10.48550/arXiv.2610.31431 · open-access PDF
Unadjusted Langevin Algorithm (ULA) は、高次元バイエシュの推測に広く用いられています。Wasserstein-2 距離における古典的な分析は、次元とともに成長するアシンプトティックな偏見と混合時間を予測しますが、このメトリクスは、多くの統計的タスクに必要なものよりも強力です。代わりに、我々は、平均と任意の低次元の限界を制御するサブスペースの強力な Wasserstein 距離における偏見を分析し、したがって実践的に推定される観測物に適しています。 i.i.d データで形成されたリッジ分離可能な可能性については、我々はベルシャを示す高い確率の境界を証明します。
Machine translation (Meta M2M100); the English original follows.
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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