Gaussian Processes (GPs) are highly expressive, probabilistic models. A major limitation is their computational complexity. Naively, exact GP inference requires $\mathcal{O}(N^3)$ computations with $N$ denoting the number of modeled points. Current approaches to overcome this limitation either rely on sparse, structured or stochastic representations of data or kernel respectively and usually involve nested optimizations to evaluate a GP. We present a new, generative method named Iterative Charted Refinement (ICR) to model GPs on nearly arbitrarily spaced points in $\mathcal{O}(N)$ time for decaying kernels without nested optimizations. ICR represents long- as well as short-range correlations by combining views of the modeled locations at varying resolutions with a user-provided coordinate chart. In our experiment with points whose spacings vary over two orders of magnitude, ICR's accuracy is comparable to state-of-the-art GP methods. ICR outperforms existing methods in terms of computational speed by one order of magnitude on the CPU and GPU and has already been successfully applied to model a GP with $122$ billion parameters.

翻译：Gausian processes (GPs) 是高度直观、概率模型。 一个主要的限制是其计算复杂性。 精确的GP推论要求用$\mathcal{O}(NQ3) 来计算以美元表示的模型点数。 目前克服这一限制的方法有的依靠数据或内核的稀疏、结构化或随机化的表达方式,通常包括嵌套优化来评价GP。 我们提出了一个新的、 基因化的方法,名为“ 迭代图表调整” (ICR), 用来模拟以$\mathcal{O}(N) 为近乎任意空间点的GPGS( ) 。 ICR 将不同分辨率的模型位置观点与用户提供的坐标表结合起来,代表了长期和短期的相互关系。 在我们的实验中,其间距在两个级别上不同,ICR的精确度可与最高级的GPM方法相比。 ICR 将现有方法比值超过10亿的GPI, 其计算速度已经成功地应用到12PIPI。