Gaussian Process state-space models capture complex temporal dependencies in a principled manner by placing a Gaussian Process prior on the transition function. These models have a natural interpretation as discretized stochastic differential equations, but inference for long sequences with fast and slow transitions is difficult. Fast transitions need tight discretizations whereas slow transitions require backpropagating the gradients over long subtrajectories. We propose a novel Gaussian process state-space architecture composed of multiple components, each trained on a different resolution, to model effects on different timescales. The combined model allows traversing time on adaptive scales, providing efficient inference for arbitrarily long sequences with complex dynamics. We benchmark our novel method on semi-synthetic data and on an engine modeling task. In both experiments, our approach compares favorably against its state-of-the-art alternatives that operate on a single time-scale only.

翻译：高斯进程状态- 空间模型以原则方式捕捉复杂的时间依赖性, 将高斯进程置于过渡功能之前。 这些模型具有作为分解随机差异方程式的自然解释, 但对快速和缓慢过渡的长序列的推论很困难。 快速过渡需要紧密分离, 而缓慢过渡则需要在长子轨道上对梯度进行回映。 我们提出了一个由多个组成部分组成的新型高斯进程状态- 空间结构, 每个组成部分都受过不同分辨率的培训, 以在不同时间尺度上产生模型效果。 合并模型允许在适应尺度上穿梭时间, 为具有复杂动态的任意长序列提供有效的推论。 我们将我们的新方法以半合成数据和引擎模型任务为基准。 在这两个实验中, 我们的方法比得更优于仅以单一时间尺度运行的、 最先进的替代品 。