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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
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) | ||||||||||||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||||||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Computer Science Faculty of Science, Engineering and Medicine > Science > Statistics |
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| 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 | ||||||||||||||||||
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| 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) | ||||||||||||||||||
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| 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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