提出新方法降低高维时空高斯过程的计算成本。
Dynamic Gaussian Processes and the Vanilla-SPDE Exchange
- 利用标准与SPDE形式的等价性构建混合推断框架
- 时间复杂度降至线性，空间复杂度显著优于传统方法
- 适合大规模时空数据建模，尤其观测点分散时
高斯过程推断常受限于立方级计算开销，在时空场景下尤为突出，因需在密集网格上进行后验推断。尽管状态空间SPDE方法可实现时间上的线性复杂度，但精确推断在空间上仍为立方级，且当观测点与预测点不重合时，空间点数量激增导致性能进一步下降。为此，我们提出Vanilla-SPDE Exchange，通过挖掘标准与SPDE形式之间的等价关系，构建一种新型混合推断方案，有效降低计算复杂度。我们通过复杂度分析和数值实验验证了该方法的优越性。
原文摘要 · Abstract (English)
Gaussian process inference is often limited by cubic computational costs, a challenge that becomes more pronounced in spatio-temporal settings where posterior inference is required over dense grids. While state-space SPDE formulations enable linear complexity in time, exact inference remains cubic in space and deteriorates further when observation locations are disjoint from the prediction locations, which inflates the number of considered spatial points. To address this, we propose the Vanilla-SPDE Exchange, which exploits an equivalence between the standard and SPDE formulations of GP inference to construct a hybrid scheme with improved computational cost. We demonstrate these gains through complexity analysis and numerical experiments.
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