mlsanityData to 14 Oct 2026

Transforming Gaussian Processes With Normalizing Flows

arXiv 2011.01596 ↗First posted 3 Nov 2020cs.LGcited by 28

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Abstract (arXiv)

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.

Key facts. Cited by 28 papers in the map (data through 14 Oct 2026). First posted on arXiv 3 Nov 2020.

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Citing papers per year: 2021: 2; 2022: 7; 2023: 12; 2024: 2; 2025: 2; 2026: 3.

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  1. 2021Priors in Bayesian Deep Learning: A Reviewcited by 101
  2. 2023Autoregressive Conditional Neural Processescited by 33
  3. 2022Statistical Deep Learning for Spatial and Spatio-Temporal Datacited by 15
  4. 2022Posterior Refinement Improves Sample Efficiency in Bayesian Neural Networkscited by 14
  5. 2023Robust and Conjugate Gaussian Process Regressioncited by 14
  6. 2025Stochastic Process Learning via Operator Flow Matchingcited by 14
  7. 2021Non-Gaussian Gaussian Processes for Few-Shot Regressioncited by 12
  8. 2024Universal Functional Regression with Neural Operator Flowscited by 9
  9. 2022Efficient Transformed Gaussian Processes for Non-Stationary Dependent Multi-class Classificationcited by 7
  10. 2023Deep Stochastic Processes via Functional Markov Transition Operatorscited by 7
  11. 2023Bayesian Gaussian Process ODEs via Double Normalizing Flowscited by 7
  12. 2023Towards Flexibility and Interpretability of Gaussian Process State-Space Modelcited by 5
16 more
  1. 2022AdaAnn: Adaptive Annealing Scheduler for Probability Density Approximationcited by 3
  2. 2022Sample-Efficient Optimisation with Probabilistic Transformer Surrogatescited by 3
  3. 2023Towards Efficient Modeling and Inference in Multi-Dimensional Gaussian Process State-Space Modelscited by 3
  4. 2025Efficient Transformed Gaussian Process State-Space Models for Non-Stationary High-Dimensional Dynamical Systemscited by 2
  5. 2022TreeFlow: Going beyond Tree-based Gaussian Probabilistic Regressioncited by 1
  6. 2023Deep Transformed Gaussian Processescited by 1
  7. 2023Variational Elliptical Processescited by 1
  8. 2026GGMPs: Generalized Gaussian Mixture Processescited by 1
  9. 2026Flow-Transformed Implicit Processes for Function-Space Variational Inferencecited by 1
  10. 2022Generative structured normalizing flow Gaussian processes applied to spectroscopic datacited by 0
  11. 2023Applications of Gaussian Processes at Extreme Lengthscales: From Molecules to Black Holescited by 0
  12. 2023Monte Carlo inference for semiparametric Bayesian regressioncited by 0
  13. 2023Kernelised Normalising Flowscited by 0
  14. 2023Estimation of Counterfactual Interventions under Uncertaintiescited by 0
  15. 2024Efficient modeling of sub-kilometer surface wind with Gaussian processes and neural networkscited by 0
  16. 2026Complex normalizing flows can almost be information K"ahler-Ricci flowscited by 0