提出一种高效采样方法，可快速从高维病态分布中生成样本。
Subspace Langevin Monte Carlo
- 在每步更新中将Langevin梯度投影到动态预条件矩阵的子空间上
- 理论证明误差可控，实验显示在病态分布上采样更快更准
- 适合需要高效采样的高维概率建模任务，如贝叶斯推断
从高维分布中采样在数据科学和机器学习中有广泛应用，但计算挑战巨大。我们提出子空间Langevin蒙特卡洛（SLMC），一种新颖且高效的采样方法，通过在每次迭代中将Langevin更新投影到时变预条件矩阵的子采样特征块上，推广了随机坐标Langevin蒙特卡洛和预条件Langevin蒙特卡洛。SLMC相比传统Langevin蒙特卡洛和预条件方法具有更好的自适应性和计算效率。通过耦合论证，我们建立了SLMC的误差保证，并在若干病态分布采样实验中展示了其实际有效性。
原文摘要 · Abstract (English)
Sampling from high-dimensional distributions has wide applications in data science and machine learning but poses significant computational challenges. We introduce Subspace Langevin Monte Carlo (SLMC), a novel and efficient sampling method that generalizes random-coordinate Langevin Monte Carlo and preconditioned Langevin Monte Carlo by projecting the Langevin update onto subsampled eigenblocks of a time-varying preconditioner at each iteration. The advantage of SLMC is its superior adaptability and computational efficiency compared to traditional Langevin Monte Carlo and preconditioned Langevin Monte Carlo. Using coupling arguments, we establish error guarantees for SLMC and demonstrate its practical effectiveness through a few experiments on sampling from ill-conditioned distributions.
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