# Recurrent Gaussian Processes

arXiv: https://arxiv.org/abs/1511.06644 · HTML: https://mlsanity.com/paper/1511.06644/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Nov 2015.

## Built on by (most cited first, 9 of 9)

- [RNN with Particle Flow for Probabilistic Spatio-temporal Forecasting](https://mlsanity.com/paper/2106.06064/) (2021)
- [Gaussian Processes for Missing Value Imputation](https://mlsanity.com/paper/2204.04648/) (2022)
- [Learning Interacting Dynamical Systems with Latent Gaussian Process ODEs](https://mlsanity.com/paper/2205.11894/) (2022)
- [Learning Nonparametric Volterra Kernels with Gaussian Processes](https://mlsanity.com/paper/2106.05582/) (2021)
- [B'ezier Curve Gaussian Processes](https://mlsanity.com/paper/2205.01754/) (2022)
- [Residual Deep Gaussian Processes on Manifolds](https://mlsanity.com/paper/2411.00161/) (2024)
- [Evolving-Graph Gaussian Processes](https://mlsanity.com/paper/2106.15127/) (2021)
- [Dream to Explore: Adaptive Simulations for Autonomous Systems](https://mlsanity.com/paper/2110.14157/) (2021)
- [Learning Individual Interactions from Population Dynamics with Discrete-Event Simulation Model](https://mlsanity.com/paper/2205.02332/) (2022)

## Abstract (arXiv)

We define Recurrent Gaussian Processes (RGP) models, a general family of Bayesian nonparametric models with recurrent GP priors which are able to learn dynamical patterns from sequential data. Similar to Recurrent Neural Networks (RNNs), RGPs can have different formulations for their internal states, distinct inference methods and be extended with deep structures. In such context, we propose a novel deep RGP model whose autoregressive states are latent, thereby performing representation and dynamical learning simultaneously. To fully exploit the Bayesian nature of the RGP model we develop the Recurrent Variational Bayes (REVARB) framework, which enables efficient inference and strong regularization through coherent propagation of uncertainty across the RGP layers and states. We also introduce a RGP extension where variational parameters are greatly reduced by being reparametrized through RNN-based sequential recognition models. We apply our model to the tasks of nonlinear system identification and human motion modeling. The promising obtained results indicate that our RGP model maintains its highly flexibility while being able to avoid overfitting and being applicable even when larger datasets are not available.