The aim of this article is to present a novel parallelization method for temporal Gaussian process (GP) regression problems. The method allows for solving GP regression problems in logarithmic O(log N) time, where N is the number of time steps. Our approach uses the state-space representation of GPs which in its original form allows for linear O(N) time GP regression by leveraging the Kalman filtering and smoothing methods. By using a recently proposed parallelization method for Bayesian filters and smoothers, we are able to reduce the linear computational complexity of the temporal GP regression problems into logarithmic span complexity. This ensures logarithmic time complexity when run on parallel hardware such as a graphics processing unit (GPU). We experimentally demonstrate the computational benefits on simulated and real datasets via our open-source implementation leveraging the GPflow framework.
翻译:本篇文章的目的是为时间高斯进程回归问题提出一种新的平行方法。 这种方法可以解决对数 O( log N) 时间的对数回归问题, 其中对数 O( log N) 时间是时间步骤的数量。 我们的方法使用GP的状态- 空间表示方式, 最初的形式是利用卡尔曼过滤和平滑方法, 从而允许线性 O( N) 时间GP回归。 通过对巴伊西亚过滤器和平滑器使用最近提出的平行方法, 我们能够降低时间GP回归问题在对数跨度复杂度中的线性计算复杂性。 这确保了以平行硬件运行时的对数时间复杂性, 如图形处理器( GPU ) 。 我们通过利用 GP 流框架的开源实施, 实验性地展示模拟和真实数据集的计算效益 。