Optimal friction matrix for underdamped Langevin sampling
Optimal friction matrix for underdamped Langevin sampling
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DOI：
10.1051/m2an/2023083
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发表时间：
2021-11
期刊：
影响因子：
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通讯作者：
Martin Chak;N. Kantas;T. Lelièvre;G. Pavliotis
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文献类型：
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作者：
Martin Chak;N. Kantas;T. Lelièvre;G. Pavliotis
我们提出了一个程序，用于优化摩擦矩阵的欠阻尼朗之万动力学时，用于连续时间马尔可夫链蒙特卡罗。从遍历平均的中心极限定理出发，给出了摩擦矩阵的渐近方差梯度的一个新表达式。此外，我们提出了一种近似方法，使用相关的第一变分/正切过程的模拟。我们的算法被应用到各种数值的例子，如玩具问题与易处理的渐近方差，扩散桥抽样和贝叶斯推理问题的高维逻辑回归。
We propose a procedure for optimising the friction matrix of underdamped Langevin dynamics when used for continuous time Markov Chain Monte Carlo. Starting from a central limit theorem for the ergodic average, we present a new expression of the gradient of the asymptotic variance with respect to friction matrix. In addition, we present an approximation method that uses simulations of the associated first variation/tangent process. Our algorithm is applied to a variety of numerical examples such as toy problems with tractable asymptotic variance, diffusion bridge sampling and Bayesian inference problem for high dimensional logistic regression.