论文标题
分布式高斯过程回归的最佳恢复和不确定性定量
Optimal recovery and uncertainty quantification for distributed Gaussian process regression
论文作者
论文摘要
高斯过程（GP）广泛用于概率建模和非参数回归的推断。但是，它们的计算复杂性随着样本量的形式缩放，使它们对于大数据集而言不可行。为了加快计算，文献中提出了各种分布式方法。但是，这些方法限制了理论的基础。在我们的工作中，在非参数回归模型的背景下，我们为恢复和不确定性量化而言，在一系列普通GP先验的分布式方法中得出了常见的理论保证和局限性。作为具体示例，我们考虑了与多项式和指数衰减特征值的协方差内核。我们在数值研究中使用合成数据集证明了所研究方法的实际性能。
Gaussian Processes (GP) are widely used for probabilistic modeling and inference for nonparametric regression. However, their computational complexity scales cubicly with the sample size rendering them unfeasible for large data sets. To speed up the computations various distributed methods were proposed in the literature. These methods have, however, limited theoretical underpinning. In our work we derive frequentist theoretical guarantees and limitations for a range of distributed methods for general GP priors in context of the nonparametric regression model, both for recovery and uncertainty quantification. As specific examples we consider covariance kernels both with polynomially and exponentially decaying eigenvalues. We demonstrate the practical performance of the investigated approaches in a numerical study using synthetic data sets.
