Title: Gradient-based Adaptive Markov Chain Monte Carlo Show Chinese title

Title: 基于梯度的自适应马尔可夫链蒙特卡罗

Abstract: We introduce a gradient-based learning method to automatically adapt Markov chain Monte Carlo (MCMC) proposal distributions to intractable targets. We define a maximum entropy regularised objective function, referred to as generalised speed measure, which can be robustly optimised over the parameters of the proposal distribution by applying stochastic gradient optimisation. An advantage of our method compared to traditional adaptive MCMC methods is that the adaptation occurs even when candidate state values are rejected. This is a highly desirable property of any adaptation strategy because the adaptation starts in early iterations even if the initial proposal distribution is far from optimum. We apply the framework for learning multivariate random walk Metropolis and Metropolis-adjusted Langevin proposals with full covariance matrices, and provide empirical evidence that our method can outperform other MCMC algorithms, including Hamiltonian Monte Carlo schemes. Show Chinese abstract

Abstract: 我们引入一种基于梯度的学习方法，以自动适应不可处理的目标的马尔可夫链蒙特卡洛（MCMC）提议分布。 我们定义了一个最大熵正则化的目标函数，称为广义速度度量，可以通过应用随机梯度优化，在提议分布的参数上稳健地进行优化。 与传统的自适应MCMC方法相比，我们方法的一个优势是，即使候选状态值被拒绝，适应也会发生。 这是任何适应策略的一个高度期望的特性，因为即使初始提议分布远离最优，适应也可以在早期迭代中开始。 我们应用该框架来学习具有全协方差矩阵的多变量随机游走Metropolis和Metropolis调整的Langevin提议，并提供实证证据表明，我们的方法可以优于其他MCMC算法，包括哈密顿蒙特卡洛方案。