论文标题
稀疏的内核高斯工艺通过迭代图表的改进（ICR）进行
Sparse Kernel Gaussian Processes through Iterative Charted Refinement (ICR)
论文作者
论文摘要
高斯过程（GPS）是高度表达的概率模型。一个主要的限制是他们的计算复杂性。天真的，精确的GP推理需要$ \ Mathcal {o}（n^3）$计算$ n $表示建模点的数量。当前克服此限制的方法分别依赖于数据或内核的稀疏，结构化或随机表示形式，并且通常涉及嵌套的优化以评估GP。我们提出了一种新的，生成的方法，名为迭代图表的改进（ICR），以在几乎任意间隔点上建模$ \ Mathcal {o}（n）$时间的GPS，用于腐烂的内核，而无需嵌套优化。 ICR通过将建模位置在不同的分辨率和用户提供的坐标图中结合在一起，代表长期和短距离相关性。在我们对两个数量级以上间距有所不同的点的实验中，ICR的准确性与最新的GP方法相媲美。 ICR在CPU和GPU上以一个数量级的计算速度来胜过现有方法，并且已经成功地应用于建模GP，该GP具有122亿美元的参数。
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.
