Distributed Bayesian Inference in Massive Spatial Data
Distributed Bayesian Inference in Massive Spatial Data
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DOI：
10.1214/22-sts868
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发表时间：
2023-01
影响因子：
5.7
通讯作者：
Rajarshi Guhaniyogi;Cheng Li;T. Savitsky;Sanvesh Srivastava
中科院分区：
文献类型：
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作者：
Rajarshi Guhaniyogi;Cheng Li;T. Savitsky;Sanvesh Srivastava
。在涉及海量数据的空间应用中，高斯过程（GP）回归的计算成本很高。有多种方法可以解决此限制，包括少量基于分布式计算（或分而治之策略）的贝叶斯方法。着眼于后者的文献，我们实现了三个主要目标。首先，我们为分布式空间 GP 回归开发了一个可扩展的贝叶斯框架，其中嵌入了许多流行的方法。所提出的框架包含三个步骤，将整个数据划分为许多子集，在所有子集上并行应用现成的贝叶斯空间过程模型，并将所有子集上估计的后验分布组合成以整个数据为条件的伪后验分布。组合伪后验分布在预测和推理问题中取代了全数据后验分布。为了证明我们框架的通用性，我们在分布式设置之前使用平稳全秩和非平稳低秩 GP 扩展了（非分布式）空间过程模型的后验计算。其次，我们将流行的分布式方法的实证性能与一些广泛使用的非分布式替代方案进行比较，并强调它们的相对优点和缺点。第三，我们为我们的数值观察提供了理论支持，并表明从分而治之方法的子类获得的组合后验分布的贝叶斯 L 2 -风险在使用各种类型的协方差函数估计真实空间表面时实现了接近最优的收敛率。此外，我们还提供了子集数量的上限，以实现这些接近最优的速率。
. Gaussian process (GP) regression is computationally expensive in spatial applications involving massive data. Various methods address this limitation, including a small number of Bayesian methods based on distributed computations (or the divide-and-conquer strategy). Focusing on the latter literature, we achieve three main goals. First, we develop an extensible Bayesian framework for distributed spatial GP regression that embeds many popular methods. The proposed framework has three steps that partition the entire data into many subsets, apply a readily available Bayesian spatial process model in parallel on all the subsets, and combine the posterior distributions estimated on all the subsets into a pseudo posterior distribution that conditions on the entire data. The combined pseudo posterior distribution replaces the full data posterior distribution in prediction and inference problems. Demonstrating our framework’s generality, we extend posterior computations for (non-distributed) spatial process models with a stationary full-rank and a nonstationary low-rank GP priors to the distributed setting. Second, we contrast the empirical performance of popular distributed approaches with some widely used non-distributed alternatives and highlight their relative advantages and shortcomings. Third, we provide theoretical support for our numerical observations and show that the Bayes L 2 -risks of the combined posterior distributions obtained from a subclass of the divide-and-conquer methods achieves the near-optimal convergence rate in estimating the true spatial surface with various types of covariance functions. Additionally, we provide upper bounds on the number of subsets to achieve these near-optimal rates.