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

arXiv: https://arxiv.org/abs/2112.03230 · HTML: https://mlsanity.com/paper/2112.03230/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 38 references that are in the map.
- First posted on arXiv 6 Dec 2021.

## Builds on (most cited first, 13 of 13)

- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Variational Dropout and the Local Reparameterization Trick](https://mlsanity.com/paper/1506.02557/) (2015)
- [On human motion prediction using recurrent neural networks](https://mlsanity.com/paper/1705.02445/) (2017)
- [Learning to Diagnose with LSTM Recurrent Neural Networks](https://mlsanity.com/paper/1511.03677/) (2015)
- [Probabilistic Recurrent State-Space Models](https://mlsanity.com/paper/1801.10395/) (2018)
- [Identification of Gaussian Process State Space Models](https://mlsanity.com/paper/1705.10888/) (2017)
- [Learning Stochastic Differential Equations With Gaussian Processes Without Gradient Matching](https://mlsanity.com/paper/1807.05748/) (2018)
- [Overcoming Mean-Field Approximations in Recurrent Gaussian Process Models](https://mlsanity.com/paper/1906.05828/) (2019)
- [Deep learning with differential Gaussian process flows](https://mlsanity.com/paper/1810.04066/) (2018)
- [Beyond the Mean-Field: Structured Deep Gaussian Processes Improve the Predictive Uncertainties](https://mlsanity.com/paper/2005.11110/) (2020)
- [Stochastic Gradient MCMC for Nonlinear State Space Models](https://mlsanity.com/paper/1901.10568/) (2019)

## Abstract (arXiv)

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.