标题： 图形处理单元和高维优化 显示英文标题

标题： Graphics Processing Units and High-Dimensional Optimization

摘要： 本文讨论了图形处理单元（GPUs）在高维优化问题中的潜力。 一张带有数百个算术核心的GPU卡可以插入个人计算机，并显著加速许多统计算法。 为了充分利用这些设备，优化算法应减少到多个并行任务，每个任务访问有限的数据量。 这些标准有利于EM和MM算法，它们将参数和数据分开。 在较小的程度上，块松弛和坐标下降和上升也符合要求。 我们展示了GPU在非负矩阵分解、PET图像重建和多维缩放中的实用性。 轻松实现100倍的加速。 在未来十年内，GPU将根本改变计算统计学的格局。 是时候让更多的统计学家加入这一行列了。 显示英文摘要

摘要： This paper discusses the potential of graphics processing units (GPUs) in high-dimensional optimization problems. A single GPU card with hundreds of arithmetic cores can be inserted in a personal computer and dramatically accelerates many statistical algorithms. To exploit these devices fully, optimization algorithms should reduce to multiple parallel tasks, each accessing a limited amount of data. These criteria favor EM and MM algorithms that separate parameters and data. To a lesser extent block relaxation and coordinate descent and ascent also qualify. We demonstrate the utility of GPUs in nonnegative matrix factorization, PET image reconstruction, and multidimensional scaling. Speedups of 100 fold can easily be attained. Over the next decade, GPUs will fundamentally alter the landscape of computational statistics. It is time for more statisticians to get on-board.