论文标题
耦合排斥采样器
The Coupled Rejection Sampler
论文作者
论文摘要
我们提出了一种从任意分布的耦合中取样的耦合拒绝抽样方法。该方法依赖于接受或拒绝来自边际边缘的耦合样本。与现有的接受拒绝耦合方法相反，所提出方法的执行时间的差异受到限制，并且在两个目标边缘彼此接近的情况下，在总变化规范的意义上保持有限。在将多元高斯与不同的手段和协方差耦合的重要特殊情况下，我们为算法的耦合概率得出了正界的阳性下限，然后我们展示了如何以封闭形式优化耦合方法。最后，我们展示了如何修改耦合的拒绝抽样方法，以从提案集合中提出建议，以渐近地恢复最大耦合。然后，我们将该方法应用于耦合稀有事件采样器的问题，得出一种并行耦合的重采样算法以在粒子过滤中使用，并显示如何使用耦合的拒绝采样器来加快基于耦合的无偏MCMC方法。
We propose a coupled rejection-sampling method for sampling from couplings of arbitrary distributions. The method relies on accepting or rejecting coupled samples coming from dominating marginals. Contrary to existing acceptance-rejection coupling methods, the variance of the execution time of the proposed method is limited and stays finite as the two target marginals approach each other in the sense of the total variation norm. In the important special case of coupling multivariate Gaussians with different means and covariances, we derive positive lower bounds for the resulting coupling probability of our algorithm, and we then show how the coupling method can be optimized in closed form. Finally, we show how we can modify the coupled rejection-sampling method to propose from coupled ensemble of proposals, so as to asymptotically recover a maximal coupling. We then apply the method to the problem of coupling rare events samplers, derive a parallel coupled resampling algorithm to use in particle filtering, and show how the coupled rejection-sampler can be used to speed up unbiased MCMC methods based on couplings.
