使用批量矩阵计算的 GPU 加速 Vecchia 高斯过程地理空间数据近似
GPU-Accelerated Vecchia Approximations of Gaussian Processes for Geospatial Data using Batched Matrix Computations
AI总结：
本文提出基于 GPU 批量矩阵计算与 KBLAS 的并行 Vecchia 高斯过程近似，最高加速 1380 倍，并在单 GPU 上支持百万位置且保持精度。
摘要：
高斯过程（GPs）通常用于地理空间分析，但在处理海量数据时面临很高的计算复杂度。例如，估计地理空间数据的统计模型参数所需的对数似然函数是一个计算密集型过程，涉及计算大小为 n×n 的协方差矩阵的逆，其中 n 表示地理位置的数量。因此，在已有文献中，研究已转向近似方法，以便在保持高精度的同时有效处理更大的 n。这些方法包含一系列技术，包括低秩近似和稀疏近似。Vecchia approximation 是加速对数似然函数求值最有前景的方法之一。本研究提出 Vecchia approximation 的一种并行实现，在当代 GPU 上利用批量矩阵计算。所提出的实现依赖于批量线性代数例程，以高效执行 Vecchia 算法中的各个条件分布。我们依赖 KBLAS 线性代数库执行批量线性代数运算，与 ExaGeoStat 软件中似然估计操作的最先进并行实现相比，在 32GB GV100、80GB A100 和 80GB H100 GPU 上将求解时间分别最高缩短 700 倍、833 倍和 1380 倍。我们还在单块 NVIDIA GPU 上成功处理更大的问题规模，在 80GB A100 和 H100 GPU 上可容纳多达 100 万个位置，同时保持必要的应用精度。我们进一步评估了所实现算法的精度表现，确定了 Vecchia approximation 算法在两个真实地理空间数据集上保持精度的最佳设置：密西西比河流域地区的土壤湿度数据和中东地区的风速数据。
英文摘要：
Gaussian processes (GPs) are commonly used for geospatial analysis, but they suffer from high computational complexity when dealing with massive data. For instance, the log-likelihood function required in estimating the statistical model parameters for geospatial data is a computationally intensive procedure that involves computing the inverse of a covariance matrix with size n X n, where n represents the number of geographical locations. As a result, in the literature, studies have shifted towards approximation methods to handle larger values of n effectively while maintaining high accuracy. These methods encompass a range of techniques, including low-rank and sparse approximations. Vecchia approximation is one of the most promising methods to speed up evaluating the log-likelihood function. This study presents a parallel implementation of the Vecchia approximation, utilizing batched matrix computations on contemporary GPUs. The proposed implementation relies on batched linear algebra routines to efficiently execute individual conditional distributions in the Vecchia algorithm. We rely on the KBLAS linear algebra library to perform batched linear algebra operations, reducing the time to solution compared to the state-of-the-art parallel implementation of the likelihood estimation operation in the ExaGeoStat software by up to 700X, 833X, 1380X on 32GB GV100, 80GB A100, and 80GB H100 GPUs, respectively. We also successfully manage larger problem sizes on a single NVIDIA GPU, accommodating up to 1M locations with 80GB A100 and H100 GPUs while maintaining the necessary application accuracy. We further assess the accuracy performance of the implemented algorithm, identifying the optimal settings for the Vecchia approximation algorithm to preserve accuracy on two real geospatial datasets: soil moisture data in the Mississippi Basin area and wind speed data in the Middle East.
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