Transport Map Accelerated Adaptive Importance Sampling, and Application to Inverse Problems Arising from Multiscale Stochastic Reaction Networks
Transport Map Accelerated Adaptive Importance Sampling, and Application to Inverse Problems Arising from Multiscale Stochastic Reaction Networks
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传输图加速自适应重要性采样及其在多尺度随机反应网络反演问题中的应用
DOI：
10.1137/19m1239416
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Cotter S
中科院分区：
文献类型：
--
作者：
Cotter S
在许多应用中，贝叶斯逆问题会产生概率分布，由于Hessian在参数空间中变化很大，因此概率分布包含复杂性。这种复杂性通常表现为低维流形上的似然函数是不变的，或变化很小。这可能是由于试图推断不可观察的参数，或者由于用于描述数据的模型中的草率。在这种情况下，用于表征后验分布的标准采样方法，其不包含关于该结构的信息，将是非常低效的。在本文中，我们寻求开发一种方法来解决这个问题时，使用自适应重要性抽样方法，采用最佳运输地图，以简化后验分布集中在低维流形。这种方法适用于整个范围的问题，其中蒙特卡洛马尔可夫链方法混合缓慢。我们证明的方法，考虑部分观察到的随机反应网络所产生的反问题。特别是，我们考虑系统表现出多尺度行为，但只有系统中的慢变量是可观察的。我们证明，某些多尺度近似比其他多尺度近似能产生更一致的后验近似。最佳传输图的使用稳定了系综变换自适应重要性采样方法，并允许以较小的系综尺寸进行有效采样。这种方法使我们能够利用自适应重要性采样方法的效率大幅提高，以前棘手的贝叶斯逆问题与复杂的后验结构。
In many applications, Bayesian inverse problems can give rise to probability distributions which contain complexities due to the Hessian varying greatly across parameter space. This complexity often manifests itself as lower-dimensional manifolds on which the likelihood function is invariant, or varies very little. This can be due to trying to infer unobservable parameters, or due to sloppiness in the model which is being used to describe the data. In such a situation, standard sampling methods for characterizing the posterior distribution, which do not incorporate information about this structure, will be highly inefficient. In this paper, we seek to develop an approach to tackle this problem when using adaptive importance sampling methods by employing optimal transport maps to simplify posterior distributions which are concentrated on lower-dimensional manifolds. This approach is applicable to a whole range of problems for which Monte Carlo Markov chain methods mix slowly. We demonstrate the approach by considering inverse problems arising from partially observed stochastic reaction networks. In particular, we consider systems which exhibit multiscale behavior, but for which only the slow variables in the system are observable. We demonstrate that certain multiscale approximations lead to more consistent approximations of the posterior than others. The use of optimal transport maps stabilizes the ensemble transform adaptive importance sampling method and allows for efficient sampling with smaller ensemble sizes. This approach allows us to take advantage of the large increases of efficiency when using adaptive importance sampling methods for previously intractable Bayesian inverse problems with complex posterior structure.
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集成传输自适应重要性采样
DOI：
10.1137/17m1114867
发表时间：
2019
期刊：
SIAM/ASA Journal on Uncertainty Quantification
影响因子：
--
作者：
Cotter C
通讯作者：
Cotter C
影响因子：
2.1
作者：
Dsilva, Carmeline J.;Talmon, Ronen;Kevrekidis, Ioannis G.
通讯作者：
Kevrekidis, Ioannis G.
影响因子：
0.8
作者：
Bogachev, VI;Kolesnikov, AV;Medvedev, KV
通讯作者：
Medvedev, KV
影响因子：
--
作者：
Apgar JF;Witmer DK;White FM;Tidor B
通讯作者：
Tidor B