mlsanityData to 7 Oct 2026

Manifold Gaussian Processes for Regression

arXiv 1402.5876 ↗First posted 24 Feb 2014stat.ML cs.LGcited by 79

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Abstract (arXiv)

Off-the-shelf Gaussian Process (GP) covariance functions encode smoothness assumptions on the structure of the function to be modeled. To model complex and non-differentiable functions, these smoothness assumptions are often too restrictive. One way to alleviate this limitation is to find a different representation of the data by introducing a feature space. This feature space is often learned in an unsupervised way, which might lead to data representations that are not useful for the overall regression task. In this paper, we propose Manifold Gaussian Processes, a novel supervised method that jointly learns a transformation of the data into a feature space and a GP regression from the feature space to observed space. The Manifold GP is a full GP and allows to learn data representations, which are useful for the overall regression task. As a proof-of-concept, we evaluate our approach on complex non-smooth functions where standard GPs perform poorly, such as step functions and robotics tasks with contacts.

Key facts. Cited by 79 papers in the map (data through 7 Oct 2026). First posted on arXiv 24 Feb 2014.

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Citing papers per year: 2021: 20; 2022: 17; 2023: 13; 2024: 10; 2025: 11; 2026: 8.

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  2. 2021Priors in Bayesian Deep Learning: A Reviewcited by 101
  3. 2021On Feature Collapse and Deep Kernel Learning for Single Forward Pass Uncertaintycited by 87
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  5. 2021Personalized Federated Learning with Gaussian Processescited by 76
  6. 2023PFNs4BO: In-Context Learning for Bayesian Optimizationcited by 70
  7. 2022A Simple Approach to Improve Single-Model Deep Uncertainty via Distance-Awarenesscited by 49
  8. 2022Invariance Learning in Deep Neural Networks with Differentiable Laplace Approximationscited by 42
  9. 2023Deep networks for system identification: a Surveycited by 35
  10. 2021GP-Tree: A Gaussian Process Classifier for Few-Shot Incremental Learningcited by 26
  11. 2021Last Layer Marginal Likelihood for Invariance Learningcited by 21
  12. 2022Meta-learning Adaptive Deep Kernel Gaussian Processes for Molecular Property Predictioncited by 21
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  2. 2022A survey of unsupervised learning methods for high-dimensional uncertainty quantification in black-box-type problemscited by 20
  3. 2021Dense Gaussian Processes for Few-Shot Segmentationcited by 17
  4. 2022Statistical Deep Learning for Spatial and Spatio-Temporal Datacited by 15
  5. 2024Predictive Churn with the Set of Good Modelscited by 15
  6. 2022Constraining Gaussian Processes to Systems of Linear Ordinary Differential Equationscited by 14
  7. 2021Kernel Identification Through Transformerscited by 13
  8. 2024Bayesian Uncertainty for Gradient Aggregation in Multi-Task Learningcited by 11
  9. 2021JUMBO: Scalable Multi-task Bayesian Optimization using Offline Datacited by 8
  10. 2022Scalable Gaussian-process regression and variable selection using Vecchia approximationscited by 8
  11. 2022Efficient Transformed Gaussian Processes for Non-Stationary Dependent Multi-class Classificationcited by 7
  12. 2024DKL-KAN: Scalable Deep Kernel Learning using Kolmogorov-Arnold Networkscited by 7
  13. 2022Maximum Likelihood Uncertainty Estimation: Robustness to Outlierscited by 6
  14. 2022Deep Kernel Learning of Dynamical Models from High-Dimensional Noisy Datacited by 6
  15. 2023Guided Deep Kernel Learningcited by 6
  16. 2024Bayesian Exploration of Pre-trained Models for Low-shot Image Classificationcited by 6
  17. 2022Federated Bayesian Neural Regression: A Scalable Global Federated Gaussian Processcited by 5
  18. 2023Emulating the dynamics of complex systems using autoregressive models on manifolds (mNARX)cited by 5
  19. 2021End-to-End Learning of Deep Kernel Acquisition Functions for Bayesian Optimizationcited by 4
  20. 2022Towards a Unified Framework for Uncertainty-aware Nonlinear Variable Selection with Theoretical Guaranteescited by 4
  21. 2023Promises of Deep Kernel Learning for Control Synthesiscited by 4
  22. 2021Calibrated simplex-mapping classificationcited by 3
  23. 2021Data-driven Aerodynamic Analysis of Structures using Gaussian Processescited by 3
  24. 2021GP-ConvCNP: Better Generalization for Convolutional Conditional Neural Processes on Time Series Datacited by 3
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  26. 2023Thin and Deep Gaussian Processescited by 3
  27. 2025Surrogate-based optimization of system architectures subject to hidden constraintscited by 3
  28. 2025Geometry-aware Active Learning of Spatiotemporal Dynamic Systemscited by 3
  29. 2025Transformer with Koopman-Enhanced Graph Convolutional Network for Spatiotemporal Dynamics Forecastingcited by 3
  30. 2022Modelling Non-Smooth Signals with Complex Spectral Structurecited by 2
  31. 2022Probabilistic partition of unity networks for high-dimensional regression problemscited by 2
  32. 2022Gaussian Process regression over discrete probability measures: on the non-stationarity relation between Euclidean and Wasserstein Squared Exponential Kernelscited by 2
  33. 2023Deep Pipeline Embeddings for AutoMLcited by 2
  34. 2023Evaluation of machine learning architectures on the quantification of epistemic and aleatoric uncertainties in complex dynamical systemscited by 2
  35. 2023Projecting basis functions with tensor networks for Gaussian process regressioncited by 2
  36. 2024High-Dimensional Bayesian Optimization via Random Projection of Manifold Subspacescited by 2
  37. 2026ResWM: Residual-Action World Model for Visual RLcited by 2
  38. 2021Attentive Gaussian processes for probabilistic time-series generationcited by 1

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