Sparse Variational Contaminated Noise Gaussian Process Regression with Applications in Geomagnetic Perturbations Forecasting

• URL: http://arxiv.org/abs/2402.17570v3
• Date: Tue, 2 Jul 2024 17:25:19 GMT
• Title: Sparse Variational Contaminated Noise Gaussian Process Regression with Applications in Geomagnetic Perturbations Forecasting
• Authors: Daniel Iong, Matthew McAnear, Yuezhou Qu, Shasha Zou, Gabor Toth, Yang Chen,
• Abstract summary: We propose a scalable inference algorithm for fitting sparse Gaussian process regression models with contaminated normal noise on large datasets. We show that our approach yields shorter prediction intervals for similar coverage and accuracy when compared to an artificial dense neural network baseline.
• Score: 4.675221539472143
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Gaussian Processes (GP) have become popular machine-learning methods for kernel-based learning on datasets with complicated covariance structures. In this paper, we present a novel extension to the GP framework using a contaminated normal likelihood function to better account for heteroscedastic variance and outlier noise. We propose a scalable inference algorithm based on the Sparse Variational Gaussian Process (SVGP) method for fitting sparse Gaussian process regression models with contaminated normal noise on large datasets. We examine an application to geomagnetic ground perturbations, where the state-of-the-art prediction model is based on neural networks. We show that our approach yields shorter prediction intervals for similar coverage and accuracy when compared to an artificial dense neural network baseline.

Related papers

• Conditionally-Conjugate Gaussian Process Factor Analysis for Spike Count Data via Data Augmentation [8.114880112033644]
  Recently, GPFA has been extended to model spike count data. We propose a conditionally-conjugate Gaussian process factor analysis (ccGPFA) resulting in both analytically and computationally tractable inference.
  arXiv  Detail & Related papers  (2024-05-19T21:53:36Z)
• Stochastic Gradient Descent for Gaussian Processes Done Right [86.83678041846971]
  We show that when emphdone right -- by which we mean using specific insights from optimisation and kernel communities -- gradient descent is highly effective. We introduce a emphstochastic dual descent algorithm, explain its design in an intuitive manner and illustrate the design choices. Our method places Gaussian process regression on par with state-of-the-art graph neural networks for molecular binding affinity prediction.
  arXiv  Detail & Related papers  (2023-10-31T16:15:13Z)
• Neural Operator Variational Inference based on Regularized Stein Discrepancy for Deep Gaussian Processes [23.87733307119697]
  We introduce Neural Operator Variational Inference (NOVI) for Deep Gaussian Processes. NOVI uses a neural generator to obtain a sampler and minimizes the Regularized Stein Discrepancy in L2 space between the generated distribution and true posterior. We demonstrate that the bias introduced by our method can be controlled by multiplying the divergence with a constant, which leads to robust error control and ensures the stability and precision of the algorithm.
  arXiv  Detail & Related papers  (2023-09-22T06:56:35Z)
• Compound Batch Normalization for Long-tailed Image Classification [77.42829178064807]
  We propose a compound batch normalization method based on a Gaussian mixture. It can model the feature space more comprehensively and reduce the dominance of head classes. The proposed method outperforms existing methods on long-tailed image classification.
  arXiv  Detail & Related papers  (2022-12-02T07:31:39Z)
• Local Random Feature Approximations of the Gaussian Kernel [14.230653042112834]
  We focus on the popular Gaussian kernel and on techniques to linearize kernel-based models by means of random feature approximations. We show that such approaches yield poor results when modelling high-frequency data, and we propose a novel localization scheme that improves kernel approximations and downstream performance significantly.
  arXiv  Detail & Related papers  (2022-04-12T09:52:36Z)
• Non-Gaussian Gaussian Processes for Few-Shot Regression [71.33730039795921]
  We propose an invertible ODE-based mapping that operates on each component of the random variable vectors and shares the parameters across all of them. NGGPs outperform the competing state-of-the-art approaches on a diversified set of benchmarks and applications.
  arXiv  Detail & Related papers  (2021-10-26T10:45:25Z)
• Scalable Variational Gaussian Processes via Harmonic Kernel Decomposition [54.07797071198249]
  We introduce a new scalable variational Gaussian process approximation which provides a high fidelity approximation while retaining general applicability. We demonstrate that, on a range of regression and classification problems, our approach can exploit input space symmetries such as translations and reflections. Notably, our approach achieves state-of-the-art results on CIFAR-10 among pure GP models.
  arXiv  Detail & Related papers  (2021-06-10T18:17:57Z)
• Local approximate Gaussian process regression for data-driven constitutive laws: Development and comparison with neural networks [0.0]
  We show how to use local approximate process regression to predict stress outputs at particular strain space locations. A modified Newton-Raphson approach is proposed to accommodate for the local nature of the laGPR approximation when solving the global structural problem in a FE setting.
  arXiv  Detail & Related papers  (2021-05-07T14:49:28Z)
• Improving predictions of Bayesian neural nets via local linearization [79.21517734364093]
  We argue that the Gauss-Newton approximation should be understood as a local linearization of the underlying Bayesian neural network (BNN) Because we use this linearized model for posterior inference, we should also predict using this modified model instead of the original one. We refer to this modified predictive as "GLM predictive" and show that it effectively resolves common underfitting problems of the Laplace approximation.
  arXiv  Detail & Related papers  (2020-08-19T12:35:55Z)
• SLEIPNIR: Deterministic and Provably Accurate Feature Expansion for Gaussian Process Regression with Derivatives [86.01677297601624]
  We propose a novel approach for scaling GP regression with derivatives based on quadrature Fourier features. We prove deterministic, non-asymptotic and exponentially fast decaying error bounds which apply for both the approximated kernel as well as the approximated posterior.
  arXiv  Detail & Related papers  (2020-03-05T14:33:20Z)
• Robust Gaussian Process Regression with a Bias Model [0.6850683267295248]
  Most existing approaches replace an outlier-prone Gaussian likelihood with a non-Gaussian likelihood induced from a heavy tail distribution. The proposed approach models an outlier as a noisy and biased observation of an unknown regression function. Conditioned on the bias estimates, the robust GP regression can be reduced to a standard GP regression problem.
  arXiv  Detail & Related papers  (2020-01-14T06:21:51Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.