论文标题
高维高斯抽样：基于随机近端算法的综述和统一方法
High-dimensional Gaussian sampling: a review and a unifying approach based on a stochastic proximal point algorithm
论文作者
论文摘要
从高维高斯分布中进行有效的采样是一个古老但高的问题。香草·乔勒斯基（Vanilla Cholesky）采样器暗示了计算成本和内存要求，在高维度上可能会迅速变得过于刺激。为了解决这些问题，已经提出了从迭代数值线性代数到马尔可夫链蒙特卡洛（MCMC）方法的不同社区提出的多种方法。令人惊讶的是，没有对这些方法进行完整的审查和比较。本文旨在通过指出它们的差异，亲密关系，收益和局限性来审查所有这些方法。除了这种最新的状态外，本文还提出了一个统一的高斯模拟框架，它通过在优化中得出了著名的近端点算法的随机对应物。该框架为大多数现有MCMC方法提供了一种新颖而统一的重新访问，同时扩展了它们。提出并用数值示例为给定采样问题选择适当的高斯模拟方法的准则。
Efficient sampling from a high-dimensional Gaussian distribution is an old but high-stake issue. Vanilla Cholesky samplers imply a computational cost and memory requirements which can rapidly become prohibitive in high dimension. To tackle these issues, multiple methods have been proposed from different communities ranging from iterative numerical linear algebra to Markov chain Monte Carlo (MCMC) approaches. Surprisingly, no complete review and comparison of these methods have been conducted. This paper aims at reviewing all these approaches by pointing out their differences, close relations, benefits and limitations. In addition to this state of the art, this paper proposes a unifying Gaussian simulation framework by deriving a stochastic counterpart of the celebrated proximal point algorithm in optimization. This framework offers a novel and unifying revisit of most of the existing MCMC approaches while extending them. Guidelines to choose the appropriate Gaussian simulation method for a given sampling problem in high dimension are proposed and illustrated with numerical examples.
