Traversing Time with Multi-Resolution Gaussian Process State-Space Models
This addresses a bottleneck in time-series modeling for applications with complex multi-scale dynamics, such as engine modeling, but is incremental as it builds on existing Gaussian Process state-space frameworks.
The paper tackled the problem of modeling long sequences with both fast and slow transitions in Gaussian Process state-space models, which is difficult due to conflicting requirements for tight discretizations and long gradient backpropagation. The result was a novel multi-resolution architecture that allows adaptive time scaling, providing efficient inference and favorable performance compared to single-scale state-of-the-art alternatives on semi-synthetic data and an engine modeling task.
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.