标题： 快速变分贝叶斯方法用于大规模空间数据 显示英文标题

标题： Fast Variational Bayes for Large Spatial Data

摘要： 最近的变分贝叶斯方法用于地理空间回归，作为计算成本高昂的马尔可夫链蒙特卡洛（MCMC）采样的替代方法，已经利用最近邻高斯过程（NNGP）来实现可扩展性。 然而，这些变分方法在准确性和速度方面仍不如基于MCMC的spNNGP，后者是NNGP的最先进软件。 我们引入了spVarBayes，这是一个使用NNGP进行大规模地理空间数据分析的快速变分贝叶斯方法套件。 我们的贡献主要是计算方面的。 我们用变分法、闭式梯度更新和线性响应校正的组合代替自动微分，以提高方差估计。 我们还在模型中容纳协变量（固定效应），并提供对方差参数的推断。 模拟实验表明，我们实现了与spNNGP相当的准确性，但计算成本降低了，并且在准确性和速度方面显著优于现有的变分推断方法。 对一个大型森林冠层高度数据集的分析展示了所提出方法的实际应用，并表明推断结果与从MCMC方法获得的结果一致。 所提出的方法已实现在公开可用的Github R包spVarBayes中。 显示英文摘要

摘要： Recent variational Bayes methods for geospatial regression, proposed as an alternative to computationally expensive Markov chain Monte Carlo (MCMC) sampling, have leveraged Nearest Neighbor Gaussian processes (NNGP) to achieve scalability. Yet, these variational methods remain inferior in accuracy and speed compared to spNNGP, the state-of-the-art MCMC-based software for NNGP. We introduce spVarBayes, a suite of fast variational Bayesian approaches for large-scale geospatial data analysis using NNGP. Our contributions are primarily computational. We replace auto-differentiation with a combination of calculus of variations, closed-form gradient updates, and linear response corrections for improved variance estimation. We also accommodate covariates (fixed effects) in the model and offer inference on the variance parameters. Simulation experiments demonstrate that we achieve comparable accuracy to spNNGP but with reduced computational costs, and considerably outperform existing variational inference methods in terms of both accuracy and speed. Analysis of a large forest canopy height dataset illustrates the practical implementation of proposed methods and shows that the inference results are consistent with those obtained from the MCMC approach. The proposed methods are implemented in publicly available Github R-package spVarBayes.