Ensemble Transport Adaptive Importance Sampling
Ensemble Transport Adaptive Importance Sampling
复制标题
集成传输自适应重要性采样
DOI：
10.1137/17m1114867
复制
发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Cotter C
中科院分区：
文献类型：
--
作者：
Cotter C
马尔可夫链蒙特卡罗方法是一个强大的和常用的数值方法从复杂的概率分布采样的家庭。随着这些方法的应用在规模和复杂性上的增加，对有效方法的需求增加。在本文中，我们提出了一个粒子系综算法。在每次迭代中，使用粒子的集合来形成重要性采样建议分布。从该分布中取出分层样本，并在后验下加权，然后使用最先进的集合传输恢复方法来创建准备用于下一次迭代的均匀加权样本。我们证明，这种方法，称为合奏运输自适应重要性采样（ETAIS），优于马尔可夫链蒙特卡罗（MCMC）方法与低维问题的等效建议分布，事实上，它显示出优于线性的改进收敛速度相对于合奏成员的数量。我们还介绍了一种新的重采样策略，多项式变换（MT），它，而不是准确的合奏运输重采样器，是大大降低成本的大合奏大小，然后它可以与ETAIS用于复杂的问题。我们还专注于如何快速调整混合方案的算法参数以优化性能。特别是，我们证明了这种方法的上级采样的多模态问题，如混合模型的推断所产生的，并与昂贵的可能性，需要解决的微分方程，其中的数量级的速度加快的问题。可能的合奏评估可以计算在一个分布式的方式，这表明这种方法是一个很好的候选人并行贝叶斯计算。
Markov chain Monte Carlo methods are a powerful and commonly used family of numerical methods for sampling from complex probability distributions. As applications of these methods increase in size and complexity, the need for efficient methods increases. In this paper, we present a particle ensemble algorithm. At each iteration, an importance sampling proposal distribution is formed using an ensemble of particles. A stratified sample is taken from this distribution and weighted under the posterior, and then a state-of-the-art ensemble transport resampling method is used to create an evenly weighted sample ready for the next iteration. We demonstrate that this method, called ensemble transport adaptive importance sampling (ETAIS), outperforms Markov chain Monte Carlo (MCMC) methods with equivalent proposal distributions for low-dimensional problems, and in fact it shows better-than-linear improvements in convergence rates with respect to the number of ensemble members. We also introduce a new resampling strategy, multinomial transformation (MT), which, while not as accurate as the ensemble transport resampler, is substantially less costly for large ensemble sizes, and it can then be used in conjunction with ETAIS for complex problems. We also focus on how algorithmic parameters regarding the mixture proposal can be quickly tuned to optimize performance. In particular, we demonstrate this methodology's superior sampling for multimodal problems, such as those arising from inference for mixture models, and for problems with expensive likelihoods requiring the solution of a differential equation, for which speed-ups of orders of magnitude are demonstrated. Likelihood evaluations of the ensemble could be computed in a distributed manner, suggesting that this methodology is a good candidate for parallel Bayesian computations.
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