State Space Gaussian Processes with Non-Gaussian Likelihood
Hannes Nickisch, Arno Solin, Alexander Grigorevskiy
Abstract
We provide a comprehensive overview and tooling for GP modelling with non-Gaussian likelihoods using state space methods. The state space formulation allows for solving one-dimensonal GP models in O(n) time and memory complexity. While existing literature has focused on the connection between GP regression and state space methods, the computational primitives allowing for inference using general likelihoods in combination with the Laplace approximation (LA), variational Bayes (VB), and assumed density filtering (ADF) / expectation propagation (EP) schemes has been largely overlooked. We present means of combining the efficient O(n) state space methodology with existing inference methods. We also furher extend existing methods, and provide unifying code implementing all approaches.
BibTeX
@InProceedings{pmlr-v80-nickisch18a,
title = {State Space {G}aussian Processes with Non-{G}aussian Likelihood},
author = {Nickisch, Hannes and Solin, Arno and Grigorevskiy, Alexander},
booktitle = {Proceedings of the 35th International Conference on Machine Learning},
pages = {3789--3798},
year = {2018},
editor = {Dy, Jennifer and Krause, Andreas},
volume = {80},
series = {Proceedings of Machine Learning Research},
month = {10--15 Jul},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v80/nickisch18a/nickisch18a.pdf},
url = {https://proceedings.mlr.press/v80/nickisch18a.html},
abstract = {We provide a comprehensive overview and tooling for GP modelling with non-Gaussian likelihoods using state space methods. The state space formulation allows for solving one-dimensonal GP models in O(n) time and memory complexity. While existing literature has focused on the connection between GP regression and state space methods, the computational primitives allowing for inference using general likelihoods in combination with the Laplace approximation (LA), variational Bayes (VB), and assumed density filtering (ADF) / expectation propagation (EP) schemes has been largely overlooked. We present means of combining the efficient O(n) state space methodology with existing inference methods. We also furher extend existing methods, and provide unifying code implementing all approaches.}
}