SLEIPNIR: Deterministic and Provably Accurate Feature Expansion for Gaussian Process Regression with Derivatives

• URL: http://arxiv.org/abs/2003.02658v1
• Date: Thu, 5 Mar 2020 14:33:20 GMT
• Title: SLEIPNIR: Deterministic and Provably Accurate Feature Expansion for Gaussian Process Regression with Derivatives
• Authors: Emmanouil Angelis, Philippe Wenk, Bernhard Sch\"olkopf, Stefan Bauer and Andreas Krause
• Abstract summary: 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.
• Score: 86.01677297601624
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Gaussian processes are an important regression tool with excellent analytic properties which allow for direct integration of derivative observations. However, vanilla GP methods scale cubically in the amount of observations. In this work, we propose a novel approach for scaling GP regression with derivatives based on quadrature Fourier features. We then prove deterministic, non-asymptotic and exponentially fast decaying error bounds which apply for both the approximated kernel as well as the approximated posterior. To furthermore illustrate the practical applicability of our method, we then apply it to ODIN, a recently developed algorithm for ODE parameter inference. In an extensive experiments section, all results are empirically validated, demonstrating the speed, accuracy, and practical applicability of this approach.

Related papers

• Amortized Variational Inference for Deep Gaussian Processes [0.0]
  Deep Gaussian processes (DGPs) are multilayer generalizations of Gaussian processes (GPs) We introduce amortized variational inference for DGPs, which learns an inference function that maps each observation to variational parameters. Our method performs similarly or better than previous approaches at less computational cost.
  arXiv  Detail & Related papers  (2024-09-18T20:23:27Z)
• 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)
• Promises and Pitfalls of the Linearized Laplace in Bayesian Optimization [73.80101701431103]
  The linearized-Laplace approximation (LLA) has been shown to be effective and efficient in constructing Bayesian neural networks. We study the usefulness of the LLA in Bayesian optimization and highlight its strong performance and flexibility.
  arXiv  Detail & Related papers  (2023-04-17T14:23:43Z)
• Kernel-based off-policy estimation without overlap: Instance optimality beyond semiparametric efficiency [53.90687548731265]
  We study optimal procedures for estimating a linear functional based on observational data. For any convex and symmetric function class $mathcalF$, we derive a non-asymptotic local minimax bound on the mean-squared error.
  arXiv  Detail & Related papers  (2023-01-16T02:57:37Z)
• Rigorous dynamical mean field theory for stochastic gradient descent methods [17.90683687731009]
  We prove closed-form equations for the exact high-dimensionals of a family of first order gradient-based methods. This includes widely used algorithms such as gradient descent (SGD) or Nesterov acceleration.
  arXiv  Detail & Related papers  (2022-10-12T21:10:55Z)
• FaDIn: Fast Discretized Inference for Hawkes Processes with General Parametric Kernels [82.53569355337586]
  This work offers an efficient solution to temporal point processes inference using general parametric kernels with finite support. The method's effectiveness is evaluated by modeling the occurrence of stimuli-induced patterns from brain signals recorded with magnetoencephalography (MEG) Results show that the proposed approach leads to an improved estimation of pattern latency than the state-of-the-art.
  arXiv  Detail & Related papers  (2022-10-10T12:35:02Z)
• 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)

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.