提出新型仿射不变采样器，高维问题下更高效。
New affine invariant ensemble samplers and their dimensional scaling
- 无需导数的侧向移动采样器，提升采样方向有效性。
- 基于导数的哈密顿采样器在高维各向异性分布中表现更优。
- 适合高维复杂分布采样，尤其适用于科学计算与贝叶斯推断。
我们提出了新型仿射不变的集合马尔可夫链蒙特卡洛（MCMC）采样器，构建简单且在高维问题上优于现有方法。首先提出一种无导数的侧向移动采样器，改进了 exttt{emcee} 包中常用采样器的提案方向生成能力。随后，基于互补集合的反对称预处理，发展了一类基于导数的仿射不变集合哈密顿蒙特卡洛（HMC）采样器，在采样高度各向异性分布时显著优于标准非仿射不变的 HMC。我们对高维高斯目标进行了渐近尺度分析，进一步揭示了这些仿射不变集合采样器的特性。特别地，引入导数信息后，仿射不变集合 HMC 在维度增长下的表现远优于无导数的集合采样器。
原文摘要 · Abstract (English)
We introduce new affine invariant ensemble Markov chain Monte Carlo (MCMC) samplers that are easy to construct and improve upon existing methods, especially for high-dimensional problems. We first propose a simple derivative-free side move sampler that improves upon popular samplers in the \texttt{emcee} package by generating more effective proposal directions. We then develop a class of derivative-based affine invariant ensemble Hamiltonian Monte Carlo (HMC) samplers based on antisymmetric preconditioning using complementary ensembles, which outperform standard, non-affine-invariant HMC when sampling highly anisotropic distributions. We provide asymptotic scaling analysis for high-dimensional Gaussian targets to further elucidate the properties of these affine invariant ensemble samplers. In particular, with derivative information, the affine invariant ensemble HMC can scale much better with dimension compared to derivative-free ensemble samplers.
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