Overcoming Mean-Field Approximations in Recurrent Gaussian Process Models
Alessandro Davide Ialongo, Mark Van Der Wilk, James Hensman, Carl Edward Rasmussen
Abstract
We identify a new variational inference scheme for dynamical systems whose transition function is modelled by a Gaussian process. Inference in this setting has either employed computationally intensive MCMC methods, or relied on factorisations of the variational posterior. As we demonstrate in our experiments, the factorisation between latent system states and transition function can lead to a miscalibrated posterior and to learning unnecessarily large noise terms. We eliminate this factorisation by explicitly modelling the dependence between state trajectories and the low-rank representation of our Gaussian process posterior. Samples of the latent states can then be tractably generated by conditioning on this representation. The method we obtain gives better predictive performance and more calibrated estimates of the transition function, yet maintains the same time and space complexities as mean-field methods.
BibTeX
@InProceedings{pmlr-v97-ialongo19a,
title = {Overcoming Mean-Field Approximations in Recurrent {G}aussian Process Models},
author = {Ialongo, Alessandro Davide and Van Der Wilk, Mark and Hensman, James and Rasmussen, Carl Edward},
booktitle = {Proceedings of the 36th International Conference on Machine Learning},
pages = {2931--2940},
year = {2019},
editor = {Chaudhuri, Kamalika and Salakhutdinov, Ruslan},
volume = {97},
series = {Proceedings of Machine Learning Research},
month = {09--15 Jun},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v97/ialongo19a/ialongo19a.pdf},
url = {https://proceedings.mlr.press/v97/ialongo19a.html},
abstract = {We identify a new variational inference scheme for dynamical systems whose transition function is modelled by a Gaussian process. Inference in this setting has either employed computationally intensive MCMC methods, or relied on factorisations of the variational posterior. As we demonstrate in our experiments, the factorisation between latent system states and transition function can lead to a miscalibrated posterior and to learning unnecessarily large noise terms. We eliminate this factorisation by explicitly modelling the dependence between state trajectories and the low-rank representation of our Gaussian process posterior. Samples of the latent states can then be tractably generated by conditioning on this representation. The method we obtain gives better predictive performance and more calibrated estimates of the transition function, yet maintains the same time and space complexities as mean-field methods.}
}