Transforming Gaussian Processes With Normalizing Flows

• URL: http://arxiv.org/abs/2011.01596v2
• Date: Thu, 25 Feb 2021 17:19:34 GMT
• Title: Transforming Gaussian Processes With Normalizing Flows
• Authors: Juan Maro\~nas, Oliver Hamelijnck, Jeremias Knoblauch, Theodoros Damoulas
• Abstract summary: We show that a parametric invertible transformation can be made input-dependent and encode interpretable prior knowledge. We derive a variational approximation to the resulting inference problem, which is as fast as variational GP regression. The resulting algorithm's computational and inferential performance is excellent, and we demonstrate this on a range of data sets.
• Score: 15.886048234706633
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Gaussian Processes (GPs) 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 (Lazaro-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.

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