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Theoretical Analysis of Heteroscedastic Gaussian Processes with Posterior Distributions

arXiv 2409.12622 ↗First posted 19 Sep 2024math.OC cs.LGcited by 0

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Abstract (arXiv)

This study introduces a novel theoretical framework for analyzing heteroscedastic Gaussian processes (HGPs) that identify unknown systems in a data-driven manner. Although HGPs effectively address the heteroscedasticity of noise in complex training datasets, calculating the exact posterior distributions of the HGPs is challenging, as these distributions are no longer multivariate normal. This study derives the exact means, variances, and cumulative distributions of the posterior distributions. Furthermore, the derived theoretical findings are applied to a chance-constrained tracking controller. After an HGP identifies an unknown disturbance in a plant system, the controller can handle chance constraints regarding the system despite the presence of the disturbance.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 14 of its 41 references that are in the map. First posted on arXiv 19 Sep 2024.

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References · 14

  1. 2017Safe Model-based Reinforcement Learning with Stability Guaranteescited by 347
  2. 2015Gaussian Processes for Data-Efficient Learning in Robotics and Controlcited by 97
  3. 2015Safe Controller Optimization for Quadrotors with Gaussian Processescited by 77
  4. 2016Safe Learning of Regions of Attraction for Uncertain, Nonlinear Systems with Gaussian Processescited by 38
  5. 2015Non-Stationary Gaussian Process Regression with Hamiltonian Monte Carlocited by 29
  6. 2021Risk-averse Heteroscedastic Bayesian Optimizationcited by 17
  7. 2022On Controller Tuning with Time-Varying Bayesian Optimizationcited by 13
  8. 2020Heteroscedastic Bayesian Optimisation for Stochastic Model Predictive Controlcited by 6
  9. 2019Stochastic Optimization for Trajectory Planning with Heteroscedastic Gaussian Processescited by 3
  10. 2016Matching models across abstraction levels with Gaussian Processescited by 1
  11. 2023Stochastic Cell Transmission Models of Traffic Networkscited by 1
  12. 2023Gaussian Processes with State-Dependent Noise for Stochastic Controlcited by 1
2 more
  1. 2024Polynomial Chaos Expanded Gaussian Processcited by 1
  2. 2024An Uncertainty-aware, Mesh-free Numerical Method for Kolmogorov PDEscited by 1

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