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Spectrum Gaussian Processes Based On Tunable Basis Functions

arXiv 2107.06473 ↗First posted 14 Jul 2021stat.ML cs.LGcited by 0

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Abstract (arXiv)

Spectral approximation and variational inducing learning for the Gaussian process are two popular methods to reduce computational complexity. However, in previous research, those methods always tend to adopt the orthonormal basis functions, such as eigenvectors in the Hilbert space, in the spectrum method, or decoupled orthogonal components in the variational framework. In this paper, inspired by quantum physics, we introduce a novel basis function, which is tunable, local and bounded, to approximate the kernel function in the Gaussian process. There are two adjustable parameters in these functions, which control their orthogonality to each other and limit their boundedness. And we conduct extensive experiments on open-source datasets to testify its performance. Compared to several state-of-the-art methods, it turns out that the proposed method can obtain satisfactory or even better results, especially with poorly chosen kernel functions.

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References · 18

  1. 2016Variational Inference: A Review for Statisticianscited by 1,472
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  3. 2013Gaussian Process Kernels for Pattern Discovery and Extrapolationcited by 132
  4. 2020Efficiently Sampling Functions from Gaussian Process Posteriorscited by 127
  5. 2014Hilbert Space Methods for Reduced-Rank Gaussian Process Regressioncited by 88
  6. 2016Variational Fourier features for Gaussian processescited by 85
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  8. 2020Sparse Gaussian Processes with Spherical Harmonic Featurescited by 43
  9. 2020Optimal Transport Kernels for Sequential and Parallel Neural Architecture Searchcited by 29
  10. 2018Orthogonally Decoupled Variational Gaussian Processescited by 19
  11. 2016Gaussian process emulators for computer experiments with inequality constraintscited by 17
  12. 2019Function-Space Distributions over Kernelscited by 17
6 more
  1. 2017Finite-dimensional Gaussian approximation with linear inequality constraintscited by 12
  2. 2015Improving the Gaussian Process Sparse Spectrum Approximation by Representing Uncertainty in Frequency Inputscited by 11
  3. 2019Know Your Boundaries: Constraining Gaussian Processes by Variational Harmonic Featurescited by 10
  4. 2020Variational Orthogonal Featurescited by 9
  5. 2020Sparse Gaussian Processes via Parametric Families of Compactly-supported Kernelscited by 2
  6. 2020Sparse Gaussian Process Based On Hat Basis Functionscited by 1

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