This paper is intended to appear as a chapter for the Handbook of Markov
Chain Monte Carlo. The goal of this chapter is to unify various problems at the
intersection of Markov chain Monte Carlo (MCMC) and machine
learning$\unicode{x2014}$which includes black-box variational inference,
adaptive MCMC, normalizing flow construction and transport-assisted MCMC,
surrogate-likelihood MCMC, coreset construction for MCMC with big data, Markov
chain gradient descent, Markovian score climbing, and
more$\unicode{x2014}$within one common framework. By doing so, the theory and
methods developed for each may be translated and generalized.

该论文旨在统一马尔科夫链蒙特卡洛（MCMC）与机器学习的各种问题，包括黑箱变分推断、自适应 MCMC、理论流构建和辅助传输 MCMC、代理似然 MCMC，并通过一个共同的框架进行泛化与翻译。

MCMC 驱动学习

MCMC-driven learning

We define an optimal preconditioning for the Langevin diffusion by
analytically maximizing the expected squared jumped distance. This yields as
the optimal preconditioning an inverse Fisher information covariance matrix,
where the covariance matrix is computed as the outer product of log target
gradients averaged under the target. We apply this result to the Metropolis
adjusted Langevin algorithm (MALA) and derive a computationally efficient
adaptive MCMC scheme that learns the preconditioning from the history of
gradients produced as the algorithm runs. We show in several experiments that
the proposed algorithm is very robust in high dimensions and significantly
outperforms other methods, including a closely related adaptive MALA scheme
that learns the preconditioning with standard adaptive MCMC as well as the
position-dependent Riemannian manifold MALA sampler.

本文提出了一种基于最优先决条件的 Langevin 扩散优化方法，使用 Fisher 信息协方差矩阵作为最优先决条件，通过一种自适应 MCMC 方法从目标函数的梯度历史中学习先决条件，实现了在高维数据中的高效数据采样与处理。