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Chained Gaussian Processes
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en
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10
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Journal of Machine Learning Research: Workshop and Conference Proceedings: AISTATS 2016 Proceedings, Volume 51, pp. 1431-1440, Journal of Machine Learning Research: Workshop and Conference Proceedings ; Volume 51
Abstract
Gaussian process models are flexible, Bayesian non-parametric approaches to regression. Properties of multivariate Gaussians mean that they can be combined linearly in the manner of additive models and via a link function (like in generalized linear models) to handle non-Gaussian data. However, the link function formalism is restrictive, link functions are always invertible and must convert a parameter of interest to an linear combination of the underlying processes. There are many likelihoods and models where a non-linear combination is more appropriate. We term these more general models “Chained Gaussian Processes”: the transformation of the GPs to the likelihood parameters will not generally be invertible, and that implies that linearisation would only be possible with multiple (localized) links, i.e a chain. We develop an approximate inference procedure for Chained GPs that is scalable and applicable to any factorized likelihood. We demonstrate the approximation on a range of likelihood functions.
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Saul, A, Hensman, J, Vehtari, A & Lawrence, N D 2016, Chained Gaussian Processes. in Journal of Machine Learning Research: Workshop and Conference Proceedings : AISTATS 2016 Proceedings. vol. 51, Journal of Machine Learning Research: Workshop and Conference Proceedings, vol. 51, JMLR, pp. 1431-1440, International Conference on Artificial Intelligence and Statistics, Cadiz, Spain, 09/05/2016. < http://jmlr.org/proceedings/papers/v51/saul16.pdf >