块状Vecchia近似用于可扩展且高效的高斯过程计算
Block Vecchia Approximation for Scalable and Efficient Gaussian Process Computations
AI总结：
本文提出块状Vecchia近似方法，通过K-means分块和GPU并发计算多变量条件分布，提高高斯过程在大规模数据上的计算效率，并在百万点风速数据上验证了其可扩展性和有效性。
摘要：
高斯过程（GPs）对于建模和预测不规则间隔的大规模地理空间数据至关重要。然而，在大规模应用中，其计算常常面临重大挑战。一种流行的近似GP的方法是Vecchia近似，它通过一系列条件概率来近似完整似然。经典的Vecchia近似使用单变量条件分布，这导致冗余评估和内存负担。为了解决这一挑战，我们的研究引入了块状Vecchia，它评估一组观测的每个多变量条件分布，块使用K-means算法形成。所提出的用于块状Vecchia的GPU框架使用变化的批量线性代数操作来并发计算多变量条件分布，显著减少了频繁的似然评估。深入探讨影响块状Vecchia精度的因素，我们研究了邻居选择标准，发现当块数量变大时，随机排序显著提高了近似质量。为了验证算法的可扩展性和效率，我们进行了一系列数值研究和模拟，展示了与精确GP相比的实际效用和有效性。此外，我们使用块状Vecchia方法处理大规模真实数据集，即具有百万个点的高分辨率3D剖面风速数据。
英文摘要：
Gaussian Processes (GPs) are vital for modeling and predicting irregularly-spaced, large geospatial datasets. However, their computations often pose significant challenges in large-scale applications. One popular method to approximate GPs is the Vecchia approximation, which approximates the full likelihood via a series of conditional probabilities. The classical Vecchia approximation uses univariate conditional distributions, which leads to redundant evaluations and memory burdens. To address this challenge, our study introduces block Vecchia, which evaluates each multivariate conditional distribution of a block of observations, with blocks formed using the K-means algorithm. The proposed GPU framework for the block Vecchia uses varying batched linear algebra operations to compute multivariate conditional distributions concurrently, notably diminishing the frequent likelihood evaluations. Diving into the factor affecting the accuracy of the block Vecchia, the neighbor selection criterion is investigated, where we found that the random ordering markedly enhances the approximated quality as the block count becomes large. To verify the scalability and efficiency of the algorithm, we conduct a series of numerical studies and simulations, demonstrating their practical utility and effectiveness compared to the exact GP. Moreover, we tackle large-scale real datasets using the block Vecchia method, i.e., high-resolution 3D profile wind speed with a million points.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
