Traversing Time with Multi-Resolution Gaussian Process State-Space Models

TL;DR

This paper introduces a multi-resolution Gaussian process state-space model that efficiently captures complex temporal dependencies across different timescales, enabling scalable inference for long sequences with diverse dynamics.

Contribution

The authors propose a novel multi-resolution architecture for Gaussian process state-space models, improving inference efficiency for long sequences with varying transition speeds.

Findings

Outperforms single-scale models on semi-synthetic data

Achieves better modeling of complex dynamics in engine data

Enables efficient inference over long, multi-timescale sequences

Abstract

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.