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Transforming Gaussian processes with normalizing flows

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Maronas, Juan, Hamelijnck, Oliver, Knoblauch, Jeremias and Damoulas, Theodoros (2021) Transforming Gaussian processes with normalizing flows. In: 24th International Conference on Artificial Intelligence and Statistics (AISTATS 2021), Virtual, 13-15 Apr 2021. Published in: Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, 130 pp. 1081-1089. ISSN 2640-3498.

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Official URL: https://proceedings.mlr.press/v130/maronas21a.html

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Abstract

Gaussian Processes (GP) can be used as flexible, non-parametric function priors. Inspired by the growing body of work on Normalizing Flows, we enlarge this class of priors through a parametric invertible transformation that can be made input-dependent. Doing so also allows us to encode interpretable prior knowledge (e.g., boundedness constraints). We derive a variational approximation to the resulting Bayesian inference problem, which is as fast as stochastic variational GP regression (Hensman et al., 2013; Dezfouli and Bonilla, 2015). This makes the model a computationally efficient alternative to other hierarchical extensions of GP priors (Lázaro-Gredilla,2012; Damianou and Lawrence,2013). The resulting algorithm’s computational and inferential performance is excellent, and we demonstrate this on a range of data sets. For example, even with only 5 inducing points and an input-dependent flow, our method is consistently competitive with a standard sparse GP fitted using 100 inducing points.

Item Type: Conference Item (Paper)
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Engineering and Medicine > Science > Computer Science
Faculty of Science, Engineering and Medicine > Science > Statistics
Library of Congress Subject Headings (LCSH): Gaussian processes, Machine learning, Statistics, Bayesian statistical decision theory -- Data processing
Series Name: Proceedings of Machine Learning Research
Journal or Publication Title: Proceedings of The 24th International Conference on Artificial Intelligence and Statistics
Publisher: PMLR
ISSN: 2640-3498
Official Date: 2021
Dates:
DateEvent
4 January 2022Modified
2021Available
23 January 2021Accepted
Volume: 130
Page Range: pp. 1081-1089
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Copyright Holders: Copyright 2021 by the author(s)
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
EP/T004134/1[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
EP/L016710/1[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
EP/N510129/1Alan Turing Institutehttp://dx.doi.org/10.13039/100012338
EP/V02678X/1Alan Turing Institutehttp://dx.doi.org/10.13039/100012338
IDIFEDER/2018/025European Commissionhttp://dx.doi.org/10.13039/501100000780
Conference Paper Type: Paper
Title of Event: 24th International Conference on Artificial Intelligence and Statistics (AISTATS 2021)
Type of Event: Conference
Location of Event: Virtual
Date(s) of Event: 13-15 Apr 2021
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