Semi-described and semi-supervised learning with Gaussian processes

Andreas Damianou, Neil Lawrence
Proceedings of the 31st Conference on Uncertainty in Artificial Intelligence, PMLR R13:672-681, 2015.

Abstract

Propagating input uncertainty through non-linear Gaussian process (GP) mappings is intractable. This hinders the task of training GPs using uncertain and partially observed inputs. In this paper, we christen this task "semi-described learning". We then introduce a GP framework that solves both, the semi-described and the semi-supervised learning problem (where missing values occur in the outputs). Auto-regressive state space simulation is also recognised as a special case of semi-described learning. To achieve our goal, we develop variational methods for handling semi-described inputs in GPs, and couple them with algorithms that allow for imputing the missing values while treating the uncertainty in a principled, Bayesian manner. Extensive experiments on simulated and real-world data study the problems of iterative forecasting and regression/classification with missing values. The results suggest that the principled propagation of uncertainty stemming from our framework can significantly improve performance in these tasks.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR13-damianou15a, title = {Semi-described and semi-supervised learning with {G}aussian processes}, author = {Damianou, Andreas and Lawrence, Neil}, booktitle = {Proceedings of the 31st Conference on Uncertainty in Artificial Intelligence}, pages = {672--681}, year = {2015}, editor = {Meila, Marina and Heskes, Tom}, volume = {R13}, series = {Proceedings of Machine Learning Research}, month = {12--16 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r13/main/assets/damianou15a/damianou15a.pdf}, url = {https://proceedings.mlr.press/r13/damianou15a.html}, abstract = {Propagating input uncertainty through non-linear Gaussian process (GP) mappings is intractable. This hinders the task of training GPs using uncertain and partially observed inputs. In this paper, we christen this task "semi-described learning". We then introduce a GP framework that solves both, the semi-described and the semi-supervised learning problem (where missing values occur in the outputs). Auto-regressive state space simulation is also recognised as a special case of semi-described learning. To achieve our goal, we develop variational methods for handling semi-described inputs in GPs, and couple them with algorithms that allow for imputing the missing values while treating the uncertainty in a principled, Bayesian manner. Extensive experiments on simulated and real-world data study the problems of iterative forecasting and regression/classification with missing values. The results suggest that the principled propagation of uncertainty stemming from our framework can significantly improve performance in these tasks.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Semi-described and semi-supervised learning with Gaussian processes %A Andreas Damianou %A Neil Lawrence %B Proceedings of the 31st Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2015 %E Marina Meila %E Tom Heskes %F pmlr-vR13-damianou15a %I PMLR %P 672--681 %U https://proceedings.mlr.press/r13/damianou15a.html %V R13 %X Propagating input uncertainty through non-linear Gaussian process (GP) mappings is intractable. This hinders the task of training GPs using uncertain and partially observed inputs. In this paper, we christen this task "semi-described learning". We then introduce a GP framework that solves both, the semi-described and the semi-supervised learning problem (where missing values occur in the outputs). Auto-regressive state space simulation is also recognised as a special case of semi-described learning. To achieve our goal, we develop variational methods for handling semi-described inputs in GPs, and couple them with algorithms that allow for imputing the missing values while treating the uncertainty in a principled, Bayesian manner. Extensive experiments on simulated and real-world data study the problems of iterative forecasting and regression/classification with missing values. The results suggest that the principled propagation of uncertainty stemming from our framework can significantly improve performance in these tasks. %Z Reissued by PMLR on 04 October 2026.
APA
Damianou, A. & Lawrence, N.. (2015). Semi-described and semi-supervised learning with Gaussian processes. Proceedings of the 31st Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R13:672-681 Available from https://proceedings.mlr.press/r13/damianou15a.html. Reissued by PMLR on 04 October 2026.

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