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采用可扩展子采样的 Metropolis–Hastings 算法AI 解读

The Metropolis–Hastings (MH) algorithm is one of the most widely used Markov Chain Monte Carlo schemes for generating samples from Bayesian posterior distributions. The algorithm is asymptotically exact, flexible and easy to implement. However, in the context of Bayesian inference for large datasets, evaluating the likelihood on the full data for thousands of iterations until convergence can be prohibitively expensive. This paper introduces a new subsample MH algorithm that…

随机游走 Metropolis 算法的可扩展耦合AI 解读

Abstract There has been a recent surge of interest in coupling methods for Markov chain Monte Carlo algorithms: they facilitate convergence quantification and unbiased estimation, while exploiting embarrassingly parallel computing capabilities. Motivated by these, we consider the design and analysis of couplings of the random walk Metropolis algorithm which scale well with the dimension of the target measure. Methodologically, we introduce a low-rank modification of the…

Papp、Fearnhead 与 Sherlock 对机器学习概率统计讨论会的评论AI 解读

We provide comments only on the read paper “From Denoising Diffusions to Denoising Markov Models” by Benton, Shi, De Bortoli, Deligiannidis and Doucet. We congratulate the authors on an important contribution to the exciting area of generative models: providing a simple framework for applying the idea of diffusion generative models to data defined on general spaces and for general noising processes. Diffusion models have shown remarkable empirical performance for several…

延迟接受随机游走 Metropolis 算法的效率AI 解读

Delayed-acceptance Metropolis–Hastings and delayed-acceptance pseudo-marginal Metropolis–Hastings algorithms can be applied when it is computationally expensive to calculate the true posterior or an unbiased stochastic approximation thereof, but a computationally cheap deterministic approximation is available. An initial accept–reject stage uses the cheap approximation for computing the Metropolis–Hastings ratio; proposals which are accepted at this stage are subjected to a…

利用无偏估计量平均值的伪边际 Metropolis–Hastings 抽样AI 解读

Summary We consider a pseudo-marginal Metropolis–Hastings kernel ${\mathbb{P}}_m$ that is constructed using an average of $m$ exchangeable random variables, and an analogous kernel ${\mathbb{P}}_s$ that averages $s<m$ of these same random variables. Using an embedding technique to facilitate comparisons, we provide a lower bound for the asymptotic variance of any ergodic average associated with ${\mathbb{P}}_m$ in terms of the asymptotic variance of the corresponding ergodic…

粒子 Metropolis 校正 Langevin 算法AI 解读

In this paper we propose a new sampling scheme based on Langevin dynamics that is applicable in pseudo-marginal and particle Markov chain Monte Carlo algorithms. We investigate the algorithm's theoretical properties under standard asymptotics, which correspond to an increasing dimension |$n$| of the parameters. Our results show that the behaviour of the algorithm depends crucially on how accurately one can estimate the gradient of the log target density. If the error in the…

伪边际随机游走Metropolis算法的效率AI 解读

We examine the behaviour of the pseudo-marginal random walk Metropolis algorithm, where evaluations of the target density for the accept/reject probability are estimated rather than computed precisely. Under relatively general conditions on the target distribution, we obtain limiting formulae for the acceptance rate and for the expected squared jump distance, as the dimension of the target approaches infinity, under the assumption that the noise in the estimate of the…

马尔可夫调制泊松过程的精确Gibbs采样器AI 解读

Summary A Markov-modulated Poisson process is a Poisson process whose intensity varies according to a Markov process. We present a novel technique for simulating from the exact distribution of a continuous time Markov chain over an interval given the start and end states and the infinitesimal generator, and we use this to create a Gibbs sampler which samples from the exact distribution of the hidden Markov chain in a Markov-modulated Poisson process. We apply the Gibbs…