Variational inference for latent variables and uncertain inputs in Gaussian processes
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Publication Date
2016-04-01Journal Title
Journal of Machine Learning Research
ISSN
1532-4435
Volume
17
Type
Article
This Version
VoR
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Damianou, A., Titsias, M., & Lawrence, N. (2016). Variational inference for latent variables and uncertain inputs in Gaussian processes. Journal of Machine Learning Research, 17 https://doi.org/10.17863/CAM.48192
Abstract
The Gaussian process latent variable model (GP-LVM) provides a flexible approach for non-linear dimensionality reduction that has been widely applied. However, the current approach for training GP-LVMs is based on maximum likelihood, where the latent projection variables are maximised over rather than integrated out. In this paper we present a Bayesian method for training GP-LVMs by introducing a non-standard variational inference framework that allows to approximately integrate out the latent variables and subsequently train a GP-LVM by maximising an analytic lower bound on the exact marginal likelihood. We apply this method for learning a GP-LVM from i.i.d. observations and for learning non-linear dynamical systems where the observations are temporally correlated. We show that a benefit of the variational Bayesian procedure is its robustness to overfitting and its ability to automatically select the dimensionality of the non-linear latent space. The resulting framework is generic, flexible and easy to extend for other purposes, such as Gaussian process regression with uncertain or partially missing inputs. We demonstrate our method on synthetic data and standard machine learning benchmarks, as well as challenging real world datasets, including high resolution video data.
Sponsorship
This research was partially funded by the European research project EU FP7-ICT (Project
Ref 612139 \WYSIWYD"), the Greek State Scholarships Foundation (IKY) and the University
of She eld Moody endowment fund. We also thank Colin Litster and \Fit Fur Life"
for allowing us to use their video les as datasets.
Identifiers
This record's DOI: https://doi.org/10.17863/CAM.48192
This record's URL: https://www.repository.cam.ac.uk/handle/1810/301116
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