mlsanityData to 14 Oct 2026

On the Correspondence between Gaussian Processes and Geometric Harmonics

arXiv 2110.02296 ↗First posted 5 Oct 2021stat.ML cs.LG math.OCcited by 3

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Abstract (arXiv)

We discuss the correspondence between Gaussian process regression and Geometric Harmonics, two similar kernel-based methods that are typically used in different contexts. Research communities surrounding the two concepts often pursue different goals. Results from both camps can be successfully combined, providing alternative interpretations of uncertainty in terms of error estimation, or leading towards accelerated Bayesian Optimization due to dimensionality reduction.

Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Builds on 16 of its 55 references that are in the map. First posted on arXiv 5 Oct 2021.

Builds on

16 of 55 references.

References · 16

  1. 2018A Tutorial on Bayesian Optimizationcited by 744
  2. 2017Deep Neural Networks as Gaussian Processescited by 622
  3. 2020Understanding and mitigating gradient pathologies in physics-informed neural networkscited by 135
  4. 2019Deep Gaussian Processes for Multi-fidelity Modelingcited by 50
  5. 2017Molecular enhanced sampling with autoencoders: On-the-fly collective variable discovery and accelerated free energy landscape explorationcited by 24
  6. 2018Neural-net-induced Gaussian process regression for function approximation and PDE solutioncited by 22
  7. 2021Streaming k-PCA: Efficient guarantees for Oja's algorithm, beyond rank-one updatescited by 21
  8. 2021Learning to Forecast Dynamical Systems from Streaming Datacited by 17
  9. 2020Probabilistic learning on manifolds constrained by nonlinear partial differential equations for small datasetscited by 13
  10. 2017Landmark Diffusion Maps (L-dMaps): Accelerated manifold learning out-of-sample extensioncited by 10
  11. 2018Gaussian Process Landmarking on Manifoldscited by 9
  12. 2019Selecting the independent coordinates of manifolds with large aspect ratioscited by 8
4 more
  1. 2021Probabilistic Learning on Manifolds (PLoM) with Partitioncited by 8
  2. 2019Conditional Karhunen-Lo`eve expansion for uncertainty quantification and active learning in partial differential equation modelscited by 6
  3. 2020Manifold Learning for Accelerating Coarse-Grained Optimizationcited by 2
  4. 2016Gaussian Process Regression for Out-of-Sample Extensioncited by 1

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Cited by year

Citing papers per year: 2022: 1; 2023: 1; 2024: 1.

3 papers.

  1. 2022GANs and Closures: Micro-Macro Consistency in Multiscale Modelingcited by 4
  2. 2024On Learning what to Learn: heterogeneous observations of dynamics and establishing (possibly causal) relations among themcited by 2
  3. 2023On-Manifold Projected Gradient Descentcited by 0