马尔科夫链蒙特卡洛方法(Markov Chain Monte Carlo),简称MCMC,产生于19世纪50年代早期,是在贝叶斯理论框架下,通过计算机进行模拟的蒙特卡洛方法(Monte Carlo)。该方法将马尔科夫(Markov)过程引入到Monte Carlo模拟中,实现抽样分布随模拟的进行而改变的动态模拟,弥补了传统的蒙特卡罗积分只能静态模拟的缺陷。MCMC是一种简单有效的计算方法,在很多领域到广泛的应用,如统计物、贝叶斯(Bayes)问题、计算机问题等。

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书名

部分观测动态系统的贝叶斯学习:Bayesian Learning for partially observed dynamical systems

书简介

本书主要整理了最近关于动态系统中贝叶斯学习的著名讲座,这里包含了关于该方面的最新知识讲解,方便机器学习从事者及时快捷了解相关最新技术与研究。

目录

  • 马尔可夫链:核,不变测度。包括观察驱动模型的示例
  • 贝叶斯推论,马尔可夫链极大似然估计的渐近性质
  • 马尔可夫链蒙特卡罗算法
  • MCMC算法的一些性质
  • 伪边缘MCMC及其应用
  • 哈密顿蒙特卡罗算法
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最新论文

Hamiltonian Monte Carlo (HMC) is a popular Markov Chain Monte Carlo (MCMC) algorithm to sample from an unnormalized probability distribution. A leapfrog integrator is commonly used to implement HMC in practice, but its performance can be sensitive to the choice of mass matrix used therein. We develop a gradient-based algorithm that allows for the adaptation of the mass matrix by encouraging the leapfrog integrator to have high acceptance rates while also exploring all dimensions jointly. In contrast to previous work that adapt the hyperparameters of HMC using some form of expected squared jumping distance, the adaptation strategy suggested here aims to increase sampling efficiency by maximizing an approximation of the proposal entropy. We illustrate that using multiple gradients in the HMC proposal can be beneficial compared to a single gradient-step in Metropolis-adjusted Langevin proposals. Empirical evidence suggests that the adaptation method can outperform different versions of HMC schemes by adjusting the mass matrix to the geometry of the target distribution and by providing some control on the integration time.

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