  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.
