Gaussian Process Uniform Error Bounds with Unknown Hyperparameters for Safety-Critical Applications

• URL: http://arxiv.org/abs/2109.02606v1
• Date: Mon, 6 Sep 2021 17:10:01 GMT
• Title: Gaussian Process Uniform Error Bounds with Unknown Hyperparameters for Safety-Critical Applications
• Authors: Alexandre Capone, Armin Lederer, Sandra Hirche
• Abstract summary: We introduce robust Gaussian process uniform error bounds in settings with unknown hyper parameters. Our approach computes a confidence region in the space of hyper parameters, which enables us to obtain a probabilistic upper bound for the model error. Experiments show that the bound performs significantly better than vanilla and fully Bayesian processes.
• Score: 71.23286211775084
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Gaussian processes have become a promising tool for various safety-critical settings, since the posterior variance can be used to directly estimate the model error and quantify risk. However, state-of-the-art techniques for safety-critical settings hinge on the assumption that the kernel hyperparameters are known, which does not apply in general. To mitigate this, we introduce robust Gaussian process uniform error bounds in settings with unknown hyperparameters. Our approach computes a confidence region in the space of hyperparameters, which enables us to obtain a probabilistic upper bound for the model error of a Gaussian process with arbitrary hyperparameters. We do not require to know any bounds for the hyperparameters a priori, which is an assumption commonly found in related work. Instead, we are able to derive bounds from data in an intuitive fashion. We additionally employ the proposed technique to derive performance guarantees for a class of learning-based control problems. Experiments show that the bound performs significantly better than vanilla and fully Bayesian Gaussian processes.

Related papers

• Information-Theoretic Safe Bayesian Optimization [59.758009422067005]
  We consider a sequential decision making task, where the goal is to optimize an unknown function without evaluating parameters that violate an unknown (safety) constraint. Most current methods rely on a discretization of the domain and cannot be directly extended to the continuous case. We propose an information-theoretic safe exploration criterion that directly exploits the GP posterior to identify the most informative safe parameters to evaluate.
  arXiv  Detail & Related papers  (2024-02-23T14:31:10Z)
• Stochastic Marginal Likelihood Gradients using Neural Tangent Kernels [78.6096486885658]
  We introduce lower bounds to the linearized Laplace approximation of the marginal likelihood. These bounds are amenable togradient-based optimization and allow to trade off estimation accuracy against computational complexity.
  arXiv  Detail & Related papers  (2023-06-06T19:02:57Z)
• Error Bounds for Kernel-Based Linear System Identification with Unknown Hyperparameters [0.38073142980733]
  kernel-based method has been successfully applied in linear system identification using stable kernel designs. From a Gaussian process, it automatically provides probabilistic error bounds for the identified models.
  arXiv  Detail & Related papers  (2023-03-17T08:52:16Z)
• Sharp Calibrated Gaussian Processes [58.94710279601622]
  State-of-the-art approaches for designing calibrated models rely on inflating the Gaussian process posterior variance. We present a calibration approach that generates predictive quantiles using a computation inspired by the vanilla Gaussian process posterior variance. Our approach is shown to yield a calibrated model under reasonable assumptions.
  arXiv  Detail & Related papers  (2023-02-23T12:17:36Z)
• Information-Theoretic Safe Exploration with Gaussian Processes [89.31922008981735]
  We consider a sequential decision making task where we are not allowed to evaluate parameters that violate an unknown (safety) constraint. Most current methods rely on a discretization of the domain and cannot be directly extended to the continuous case. We propose an information-theoretic safe exploration criterion that directly exploits the GP posterior to identify the most informative safe parameters to evaluate.
  arXiv  Detail & Related papers  (2022-12-09T15:23:58Z)
• Sparse Gaussian Process Hyperparameters: Optimize or Integrate? [5.949779668853556]
  We propose an algorithm for sparse Gaussian process regression which leverages MCMC to sample from the hyperparameter posterior. We compare this scheme against natural baselines in literature along with variational GPs (SVGPs) along with an extensive computational analysis.
  arXiv  Detail & Related papers  (2022-11-04T14:06:59Z)
• Scalable Gaussian Process Hyperparameter Optimization via Coverage Regularization [0.0]
  We present a novel algorithm which estimates the smoothness and length-scale parameters in the Matern kernel in order to improve robustness of the resulting prediction uncertainties. We achieve improved UQ over leave-one-out likelihood while maintaining a high degree of scalability as demonstrated in numerical experiments.
  arXiv  Detail & Related papers  (2022-09-22T19:23:37Z)
• 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)
• Uniform Error and Posterior Variance Bounds for Gaussian Process Regression with Application to Safe Control [11.42419064387567]
  We present a novel uniform error bound using Lipschitz and an analysis of the posterior variance function for a large class of kernels. We show how these results can be used to guarantee safe control of an unknown dynamical system.
  arXiv  Detail & Related papers  (2021-01-13T20:06:30Z)

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.